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n CIC-14 REPORT COLLECTION i
I REPRODUCTIONCOPY I
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A nA f i i m s a l i v cA c t i o n / E q u a lo p p o r t u n i tE m p l o y I
T f om or er e pi t s eu n c la L AL AO O 6 9L A - 1 0a L A - 1
T hw ow p e r fu nt a u so t U D eo E nD i v io R e aR e sa T e c hO fo B E nS eaO f fo F u sE n e
D I S C L A I M E R
T h i sr e p o r rw a sp r e p a r e da sa na c c o u n to fw o r ks p o n s o r e db a a g e n co f t hU n i tS s a tG o v c r nN c i \ h e rt h eU n i t e dS r a [ e sG o . e m m c n tn o ra n ya g e n c yt h e r e o fn o r a n y o f t h c i r c m p l o y em a ka ns w w r a r r [ y ,e x p r e s so ri m p l i e d ,o ra s s u m e sa n yl e g a ll i a b i l i t yo r e s p o n s i b i l if ot ha c c u r ac o m p l e to ru s e f u l n e s so fa n yi n f o r m a t i o n .a p p a r a m s .p r o d u c l ,o rp r o c e sd i s c l o s eo r e p r e s et hi tu sw on o ti n f r i n g ep r i v a t e l yo w n e dc i g h I s .R e f e r e n c eh e r e i n1 0a ns p e c i f ic o m m e r c ip r o d up r o c eo s e rb yt r a d en a m e ,t r a d e m a r k ,m a n u f a c t u r e r ,o r o t h e r w i s e ,d o en on e c e s s a r ic o n s t i m ti m pi te n d o r s e m e n t ,r e c o m m e n d a t i o n ,o rf h v o n n g b yt h eU n i t e dS s a w s G o v e m m e no a na g e n{ h e rTv i e w sa n do p i n i o n so fa u t h o r se x p r e s s e dh e r e i nd on o tn e c e s s a r i l ys t a to r e l l et h oo f tU n iS r aG o v e r n m e n to r a n y a g e n c y[ h e r e o f .
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ABOUT THIS REPORT
This official electronic version was created by scanning the best available paper or microfiche copy of the original report at a 300 dpi resolution. Original color illustrations appear as black and white images. For additional information or comments, contact: Library Without Walls Project Los Alamos National Laboratory Research Library Los Alamos, NM 87544 Phone: (505)667-4448 E-mail: [email protected]
C O N
ABSTRACT........................................................................1
I T H EA NE V A L UO N U CC RS E C............................1
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L o w - ET r a n sf P o ld R e a...................1R - M aA n a lo R e a ci t 7 a ‘ S y....... .R - M aA n a lo R e a ci t S S y............ ..
B i b l i o gS u ro M eE nI n cR eD . .I m p r o vo A c t i vC rS e cN ef R C a lC a l c u l ao E n e rN e ua P rR e ao A l.I m p rO p tM of N e uR e ao I f 0 t100 MeV..............................................................1C a l c u lo H i gE n eN e ua P rR eo 5 4C a l c u l ao H i gE nP ra N eR eo5 8 9 6 0 9 6 2 N i. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2C a l c u lo ( pa ( nR e ao 6 3u tE = 50 MeV..........................................................2E ~ t e no T h e o rC a l c uo N uI nR eoT u n gI s o tt 5 M e....................................S y s t eR e c a l co C rS e cf N eR eoYttrium Isotopes.....................................................3C o m p ao C a l c u2 3 9 PC rS ew NExperimentalData....................................................31G l oS p h e rO p tM oP o t ef N e......... .P e r f o ro G l oO p tP o t ei C a lo n + 5Reactions............................................................4R aE a r t h - AP o t e n1 62 32 4..............R e a cT h eC a l c uo n + 1 6R e a..................5G N AO u tC o n v eC of E NF 6 G N....... .M o d eL e vo O d dD e fN u.................... .N u c lS t r uS t uf G a mL a................. .C o m p a ro F oR e p r e so t P rN eS pf ot hS p o n tF i so 2 5.......................... .C o u pE n e r g yD i s t ro R e cN u......... .T e so t G NP r e e q uM oa L E n........ .
I IN U C LC R O S S - SP R O CA T E S........................ .
A NJOY Development..........................................,..........73B R e i c h -R e s oF o r.........................................7c Photon InteractionCross Sections....................................76D ENDF/B-VIThermal Data...............................................77E Cross-SectionProduction.............................................7
I IN E WA C T I V AF I SP R O DA A C T.......................8
A D e l aN e uS p ef rF i sP u.................... .1 Pn Values........................................................82 Number of Precursors.............................................83 PrecursorSpectra................................................84 SummationCalculations...........................................895 Confirmationof Spectra..........................................9
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Japanese Measurements (Pulse)........................................93D E v a l uo 9l o , l l B ( ~ , n ,C Y O S Ss e c t i o n s .. . . . . . . . . . . . . . . . . . . . . . . . . . . .
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t ic o n s ii t 1 9M o lp o t5 a t m r i t 15p o t e no W a la G us tu nd e v e
F i g u3 a 3 c o mv ao S a S c af t g
p a r a m e t e r ii T aV w iv a5
i nf e qd
S i m i l aF i3 c o m pc a l cR v aw ‘ m eN t
t hE n g e l ba F i e dp o t5 i n i nb i e qt
t hM o l d ap o t ea l
o pb B e r s i5
w u si
* AS S a R c a l c u
e n eT S c oc S d
a t s p ho pc a l
i t p aa f 1 n e
3
N E U
T AV
S G LP o t
R e f e rP o t e n, (r a C (
M o l d a1 9 6‘ = 4 61 ,0 0
E S IW = 1 41 .0 1
A > 40 ‘ = 71 .0 0- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N o tB a so f it s C a a Ed af n e ub 1 M A = 4- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
W i l ma n‘
= 4 7 . 0 1 - 0 . 21 . 3 2o
H o d g s1 91 ( 4 . 0 -
E S 15 MeV 0
A > 4 M e
‘ = 9 . 5 2 -1 . 2 6o
( 2 . 0 -
0- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N o tD e r if rt hn o n -5, e n e r g y - ip o to P a B
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
E n g e l b ra n‘
= 4 6e x p [ - 0 . 0 0 61 .0 0
F i e d e l1 952 w,D= 1 4e x p [ - 0 . 0 1 71 .0 1
E = 0 - 1M e% = 0 . 1e x p [ - 0 . 01 .0 0
A 4 0 - 2vs = 7 e x p [ - 0 . 0 0 61 .0 0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N o tD e v e lf ra n o n -p o t es i mt P~ ~B ub ii nv o l ua b s o r pC o n s tt m aM o lp o ta E - 0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
B e c c h ea n‘
= 5 6 . 3 - O . 31 .0 0
G r e e n l1 9 6‘
= 1 3 . O - O . 21 .0 0
E < 5 M e‘= 0 . 2 2 E1 .0 0
A > 40 ‘ s= 61 .0 0- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N o tS t a r tf ra p r op o t eb ao f t e x tO EP df oE = 1 0 -M ea nA =
‘ 2 05 8 -f n e uC a U Ef E = 1 M A =
5 -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
a E n e ri M eq = ( n - Ze x p on o te x( 7= 7 x 1
3
R e f e r
P a t t ee a l
1 9 7
E = 7 -P H
A 2 7 -
T AV ( C
P o t e, (r a C (
‘ = 5 5 . 8 - O .1 0 0
‘ = 9 . 6 - O . 2 2 E1 0 .O
‘ = - 1 . 41 0 .O
‘ = 6 1 0 0- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3N o ; ; ; e : ;‘ O d
d e t ei s op o tf B eaa n a la i s o vp o tf ( pa nd i
t i oa E = 2 5M eA = 4 8 -n N e ud u o f c o
R a p a pe a l‘
= 5 4 . 1 9 - O . 3 3 E
1 9( SA )‘= 4 . 2 8 + 0E S 15
E = 7 -M = 1 4 . O - O .E > 15
1 0 0
1 0 0
A = 4 0 -‘v = 0 E S 15
}
1 0 0= - 4 . 3E > 15
‘ s= 61 0 0
N o tF in e u te l aa n gd i s t rb e7 M f so d o uc l os hn u co ni t r aA = 4 0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
W a la nG u s‘
= 5 2 . 5 6 - O . 3 1 E -E
1 9 8= 5 2 . 5[ l( EI 1 0 0
E = 1 0 -M e+ { 1 6 .[ l + J ? nEI
A > 53 w = 1 0 . 81 5 7 EE ‘ 1 0 0u
‘ v= - 0 .0 .E <
= - ( ) . g 6 3“
[ 1 - O( E /E .
‘ s= 5 . 7 6 7 - O
‘ s= 0 . 7 9 1
1 . o0 . 5
1 0 0
1 0 0
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N o tU s iL a❑o df o r m uf n eC u ( A b 1a n4 M ea p r o( Y EA (b e2 a 8 M f A = 5
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3
— .W A L1- -B E C C1“ “ -- P A T T1
JT
a4
p
~
; . =
7~
0 2 55 07 51 01 21 51 72 0 0 .A T OI M AN U M
F i3 0C o m p ao c a l cs -n es tf uf sg l o bS Op o t e nw ie x p e rv af A = 2 0
3
F i3 C o m p ag l oS p o t e n
— W A1- -B E C1
1 “ .- P A ’1
I 1
I I I1 I 1 I I I I 1
I . O2 55 07 51 01 21 51 2 0A T O MM AN U M
L
o c a l cp -n es tf uf sw ie x p ev af A = 2 0
— W A L1 9- -B E C C1 9..
1 1 1I t I 1 I 1: ..
— W I L1 94.:...:
- -M O L D1 9.~ .,
- “ ” ”R A P A1 9: :..“ T
0 2 55 07 51 0l &l t1 7t 2 2A T OI M AN U M
3
F i3 2C o m p ao c a l c up o ts c ar f s g Sp o t e n tw ie x p e r iv a lf A = 2 0
3
O v e rt M o l dp o t ea pt b r et S S a R
e x p e r i mr e s uT hi n s u r po c ob et a
f o c uo l n e ue n ea u S i i f T l d
t i of re x p e ra s ei t r e aa a cr w
s t ad e f o r ma l a rC o n c eo t ❑a r b 1 w
t hs p h e rp o t e nh am ov a li a pt t t n p
t e n to P a t te a l5R a pe a 5 a W ar er
r e st hm e a s u rI g e nt ht hp o ta t r
t hd aa b oa w ea t W i la H op o ta s b
t hB e c c ha G r e e
N e u tt oc rs e cc a l cf t p oo T V a5 8
c o m pw ie x p e r id af C a Y i F 3 a 3 A i6e l ua rc a l c u lw it r e gp o to K d a
u sf os t r u cm a t eT m e a sh b r g a
a gt r e ds oo t s t r ue f fN o t p of t
e x p e r i mv a lf C p a r t iw b e- 4 M A h e
s e v ep o t e nd r e a sw ee s pt o M oW
P a t t e ra R a p aT s al e np ro f N ( S O
e x ct ha l es e va a m ab e3 M
S i m ic o m p af t t oc rs eo 1 a 2 a
g i vi F i g3 a 3 t o gw t r ef ip p6 6
o I g a ra t r e g( Sa c tp o to M aa Y
w h is t oa 1 M eT hn uh s i gs d e s
t hl a rd e v i as ei F i3 a 3 a n s u rw t g2
e rf e a to m i nu n d ea m ao v eI t c o 9
r e a s o na g r ew ie x p ei s o f t a cs
p o t e no M a da Y o u
I s u m mt n eg lp o t eo P a tR aa W
( ap a r t i ct l a tt wa pt f ot l oS S R
d a ta nt C r e sf A < 1 5E S 2 M a w a o b t t
p r e -p o t e n tO t o lg ls et W ip oh t
m oo v e rc o n s iw it U d t 2 M T d a f d
t i oi i n e c et l oi m od ea t p o t
3
o
+ P E1... “ -1A.. ~
“ . .. . , ’ . . . .......
E....
— M O L1- -E N G E1“ “ ” -B E C C1“ K A1
H
*
\+
● “ \ .* “ ~ .“
I,. I I 1 i 1 1 1 I 1
*
%* Z .
P E1W I L1R A P1W A1P A T T E
1 1 I I I 1 I I i 10.0 2.0 4.0 6.0 8.0 1 0 .L 2 .1 41 618.0 2
N E UE N()
F i3 3 .C o m p aw iC e x p e rt oc r o sd o 8 Sp o t e n tf on e u te n e rb ; t0 a 2 M
F O1M I1C O OM O L1E N G1B E C1K A1
1111t1 :11 :1 :, :
\1 :t1 :t :t :\* : .s :, :t :t ..\
— W I L1- -R A P1........... W A1- P A T1
0.0 2.0 4.0 6.0 8.0 1 01 1 1 16.0 2N E UE N E( M
F i3 4C o m p aw i8
p o t e n tf n e ue n e
,
e x p eb e0
t oc r od o 8 Sa 2 M
4 0
S H1M O L1E N G L1B E C1I G1
F i3 5p o t e n t
‘ “ “, ,~, “ .
...
8 \‘ -....., “ ., \.. .\
\
\
‘ . \. \$t :$ I 1 1 I 1 1 I I t1
T “.........\.........-“...“ “ .
+
- - - - -...........
S H1W I L1R A P1W A1P A ’1
.% 1 1 . -1 1 I [ 1 1 1 I I 1 1 1 1 t 1 I 1 [I , 1 1 1 1 , I t )
1 0I IN E U T RE N E( M‘
‘ C o m p a r i s ow i tI S oe w e r i m et oc r o sd o 8 S
f on e u te n e rb e t0 . 0M
4
\ : . . .h .
+xo
- - - - - -...........
I I , , I 1 r , I 1 t I , 1 I I I II 1 1 I I I I I It
‘- - - -- - - -- -- =
‘ .* ..
\+ P O E1 9x S H A1 90 G OIN 1 9~WILMORE, 1964 ‘, “
------RAPAPORT, 1979 ‘, ;’ ,........... W A L1 9. ,’. P A T T1 “
1 I # I 1 1 1 1 11 1 I I 1 f I J !I I 1 1 1 1 I I I +
r 1 0I IN E UE N E( M
F i3 C o m p aw i2 3
p o t e nf n e ue n ee x p et oc r od o 8 Sb e t0 .M
4
o .P e r f o ro G l oO p tP o t ei C a l co n + 5
R e a c t( PG Y o u
T e x a mt hg l oo p tm op o to S N m c i
t hs t r u c t
w ep e r f o r
F i g3
c r os e c t i
b e t w1 l c
5 r em a t er e gd e tc a l co n +
5i n c lc o m p ao N t os e la r
c a l c uw it p o t eo T aV a n ee
a 2 M eL ad i f f( 2a e va t
v a r ip o t e n tT w e aa g rw U m e ai a l e
g i ew h et B e c cp o t ei t u pp o t f a a t
p o t e n ti t l op aa - 2 h it e x pf 0 M
S i g n i fd i f f ea lo ca mt c a ls e la r
t ic r os e c t iT m oo b vo u ti t c o mi t h
B e c c hr e a cc rs e ca m oe n ea t r el
B e c c hs h ae l a sc rs e cf r- 2 M
T hd i f f e ri r e a cc rs e cs i F 3 s b m
f ei c a l c u l ao s p e cp a rr e ac rs eT q
t h ee f f eH a u s e r - Fs t a t i s tc a lw p e
f oe ao t hp o t e ni l l u si F 3 7a w a f t l
p o t e n t iT hC O M Na G N Ac os yw u tf t c
l a t iw in a t tb em at o p tp a rW f l
c o r r e c tw ei n c la n e ue n eb e5 M a c hf o
g o ip r o ta na l pi a d dt n e ua g aw p ra
a le n e r gE x p e r i m e n t a ld i sl ew i nf e
r e s i dn u c lm a ts m o ot c o nl er e p ru t
G i l ba nC a m e6
f o r ma C o6
p a rt aD r5c o n t r i b uw ee s t if l o w -N l eu a s s o
D Wc a l c u l aw it H a r6
l op o tO pm p a5z a t if op r o ta a l pf rH a rN a n
6w u tt
c a l c uc h a r g e d - pt r a n sc o e f fA g i ar e
s h aw au sf ot E g a m ms t rf u nw a s n o
t if a cb a so 5 N iy m e a s un 1 k T c oc
c u l a tw em ab c h a ni n pn et r a nc o ef
t hv a r is p h e rp o t e nl e aa o tp a rc o
4
I :,,I
!;
:
I ,:,I
!;
:...
..
.”
(f
fV
JW
IJ
..
’”
x-..
....,
..
x.
$”
*..
-t
&
JI
mUO.
!c.
rv
C.Mw-lo
P
Calculatedresultsfor the 58Ni(n,n’)reactionto the firstexcitedstateof 58Ni are shown in Fig. 38, togetherwith the Ni total crosssectionin the
MeV region. Calculationswith the potentialsof Delaroche,67 Strohmaier,68and66 58Harper, all of whichwere developedspecificallyfor Ni, are includedwith
tbe globalpotentials. As wouldbe expected,there is a tighterenvelopefor
the localpotentialsthan for the globalones. Thereis a cleargroupingof the
(n,n’)calculationsinto higher values (Becchetti,Wilmore,Rapaport,Walter,/Patterson, I)elaroche)and lower values (Moldauer, Engelbrecht, Kawai,
Strohmaier,and Harper).
A similargroupingof the calculationsinto“higher”and “lower”valuesis
seen in Fig. 39 for the (n,2n)cross sections,exceptthat the differencesare
larger,reachinga factorof 2. Realizingthe importanceof lowerenergyneu-
tron transmissioncoefficientsin (n,2n)calculations,the qualitativecorres-
pondenceof the (n,n’)and (n,2n)resultsis understandable.The situationis
less well definedfor the (n,np)calculationson the right side of Fig. 39,
where the resultsclustersomewhattighter. The major outriderin these cal-
culationsis the resultwith the Becchettipotential.
The resultsin Figs. 38 and 39 for the localpotentials,whilehavingsig-
nificantlyless spreadthan the globalpotentialresults,are alsodividedinto
the “high”and “low” (n,n’)and (n,2n)cross-sectionvalues. The experimental
data are similarlydividedand do not resolvethis issue.
Overall,these calculationsillustratethe uncertaintiesinherentin using
unoptimizedglobalpotentialsin reactioncalculations.Figs. 38 and 39 indi-
cate that the BeccheCtineutronpotentialis not appropriatefor 58Ni calcula-
tions and that the Moldauerpotentialshouldnot be used at higherenergies,
probablynot above 5 MeV. In theirpresentform the Patterson,Rapaport,and
Walterpotentialslead to over-predictionsof the 58Ni(n,2n)crosssectionand,
less definitively,the Engelbrechtpotentialresultsin underpredictionof the
(n,2n)cross section. The calculated(n,2n)is more sensitivethan the (n,np)
cross section,as well as the (n,y),(n,p),and (n$a)crosssections,whichare
not shown.
45
NiTOTAL CROSSSECTION
q*+ N2WSON, 1959x BILPUCN.19S3o PEREY,1972
— MOLDAUER, wtn------ ENCELSRIXHT.19s7‘-------BDXHEITT,1969‘— ICAWAL1979
OYX*.●
mJ-;.
●
I*
~~0.0 20 4.0 0.0 0.0 10KICLo 14.0 10.0 18.0
NEUTRON ENERGY (MeV)
58Ni(n,n’)58Ni Ex = 1.454MeV
+x0v
-----...-----
●
+x0v
---------—
+ GUSNTHER,1975x PEREY,i970o ROGEG 19’71v KORZH.197B
— DELAROCHILL9ES----S1’ROHMAIER,19S1......HARPER,W&? 1
●I/D Lo 20 S.o
NEUTRON ENEI%Y (McV;”
Fig. 38. Experimentaltotalneutronand (n,n’) cross sectionsfor Ni and 58Nicomparedwith calculationsfor 11 SOM potentials. See text for detailsof theHauser-Feshbachstatisticaltheorycalculations.
46
5f)Ni(n2n)57NiCROSSSECTION
80
+x0
v-----...........—
..4-”--,.....---”
...-””.-””,...-””
L.....
.,. .+@-J-----------------
~+x0v
......
.-.-...
..—
s 13.0 h lb lb tin ho lb.oNEUTRON ENERGY (MeV)
1
5tjNi(n,np)57aCROSSSJKTION
..>+ CLOVER,19S2x BARRALL.1909
— MOLDAUER.1963-----ENGELBRSCHT;19(77........ BECCHST17.1969 ..Z.....,-.-....”..-.....— KAWA~ I%% /..-
./
./.”/“....
+x
......
.........
1+GLOVEFL1962x BARRALL 1969
— DELAROCH& 19B5~ ------STROHMAIER,.19S1.....--HARPE& 19S2,
:
so----
20+~ d-
~
00
8.0 10.0 120 14.0 10.0 10.0NEUTRON ENERGY (MeV)
o
Fig. 39. Experimental(n,2n)and (n,np) cross sectionsfor 58Ni comparedwithHauser-Feshbachstatisticaltheorycalculationsfor 11 SOM potentials.
47
P. RareEarth-ActinidePotentials:165H0 238U 2429 Pu (P.G. Young)
Over the past severalyears,a numberof studieshave beenmade of stati-
callydeformednucleiin the rare earth and actinideregionsleadingto rather
simpledeformedopticalmodel (DOM)parameterizationsthat reproducea signifi-
cant body of experimentaldata. Examplesof some of these analysesare the69Nd-Sm isotopestudiesby Shamu et al. , the W-isotopestudiesby Arthur70 and
Delaroche,71 theHo-Tinanalysesby Younget al.72, and the actinidecalculations
by Haouat et al.73 74and Lagrange. The variouspotentialshave many similar-
ities, and, in some cases, the differenceseven in detailsare small. The
possibilityof a regionalpotentialdescribingboth rare earth and actinide
rotationalnuclei,at leastat some reducedlevelof accuracy,is exploredhere,
togetherwith the suitabilityof globalparameterizationsin this region.
To investigatea regionalpotential,the Haouat-Lagrangeactinidepoten-tial 73,74
9 which describesneutronscatteringresultsup to E = 5 MeV for sev-
eral Th, U, and Pu isotopes,was adaptedfor use with 165H~ This case was165H07;
chosenbecausea DOM parameterizationalreadyexistsfor that is similar
to ones for W isotopes70 and 16gTm,72as well as to the actinidepotential.
The large ground state spin of 165Ho (7/2-)precludesthe possibilityof
extensivestandardcoupled-channelcalculations,and certainlyany automated
fittingof suchcalculations.To carryout the analysis,the❑ethodof deriving62
a DOM potentialfrom an SOM analysis,demonstratedby Madlandand Young for
actinides,was employed. In this instance,an abbreviatedprocedurewas fol-
lowed,becausethe exercisewas largelyexploratoryand the goalwas to develop165a Ho potentialthatwas as similaras possibleto the actinidepotential. In
particular,the
to denoteSOM):
followingsimpletransformationwas assumedhere (usingprimes
and the samevaluesof
and DOM calculations.
‘DaD ~=07
‘iai‘w; “ ‘
(1)
diffusenessand realwell depthwere used in both the SOM
Starting with an average representationof the Haouat-Lagrangepoten-tia173,74 37writtenin the Lane form and includinga smallvolumeterm,an SOM
fi28 165was made to Ho total cross-section❑easurementsbetween7 and 30 MeV59
and to the measuredangulardistributionat 11 MeV. The onlyparameterper-
mitted to vary in the searchwas WD, assuminga lineardependencewith neutron
48
energy. The higherenergyexpressionthatresultedfor WD was ❑atchedat 6 MeV
to a lowerenergysegmenthavingthe sameenergydependenceas the actinidepo-
tential,after the appropriatescaling accordingto Eq. (l). The resulting
parametrizationis givenin TableVII as “SetA.”
Coupled-channelcalculationswere performedusing the ECIS78 code . Be-38
low 4 MeV, the first threemembersof the ground-staterotationalband (7/2-,
9/2-, 11/2-)were coupledin the calculations,using deformationsof 82 = 0.3
and 94 = -0.02.73 At higher energies,these levelswere replacedby ficti-
tiousO‘, 2+, 4+ levelsaccordingto the modelof Lagrangeet al.75 It was de-terminedempiricallythat this approximationleadsto errorsless than 0.8% in
the totalcrosssectionforEn 2 4 MeV.
TABLEVII
NEUTRONDOM PARAMETERSFOR 165H0
Haouatet al.,
1982a’3 andLagrange,
198274
‘R = 49.8-16q-O.3E
‘D = 5.3-8q+0.4E
‘D = 9.3-8rl
‘so =6.2
r. (fro)a (fro)
1.26 0.63
1‘S1O‘ev 1.26 0.52E>1OMeV
1.12 0.47
-----------------------------------------------------------------------------
Set A Same as Haouatexcept:
‘D = 4.7-8q+0.4E ES6 MeV
1
1.26 0.52
‘D = 7.1-8rI-O.046(E-6) E>6 MeV
‘v = -1.8+0.2E 1.26 0.63
------------------------------------------------------------------------------
Set B Sameas Haouatexcept:
‘D= 5.O-8q+0.4E E58 MeV
1
1.26 0.52
‘D = 8.2-8q-O.046(E-8) E>8 MeV
‘v = -1.8+0.2E 1.26 0.63
----------------------------------------------------------------------------
aAveragedover severalactinides.
49
Calculationsof the 165Ho totalcross sectionand elasticangulardistri-
bution at 11 MeV with the DOM versionof Set A are comparedwith measurements72and with calculationsusing the Younget al. DOM parameterizationin Figs.40
and 41, respectively.(TheSOM calculationsof both the totalcrosssectionand
elasticangulardistributionsshow the characteristicoverpredictionof maxima
and underpredictionof minima.) The resultsfrom the Set A DOM agreewith the
measurementsabout as well as the Young results,exceptfor a 2-3%overpredic-
tion of the total cross sectionnear 14 MeV. The agreementwith the elastic
angulardistributionat 14 MeV is improvedoverthatof Younget al.
The final iterationin this simpleprocedurewas to roughlyaveragethe WD165parameterizationfor Ho with that fromthe actinidepotential;the resultis
the averagepotentialSet B in Table VII. Calculationswith the Set B param-
etrization, also includedin Figs.40 and 41, generallyimprovedagreementwith
the total cross-sectiondata, but slightlyworsenedagreementwith the 11-MeV
angulardistributionmeasurement.
Calculationsof 238U and 242Pu neutrontotalcrosssectionswith the Set B
DOM parameterizationare comparedin Figs.42 and 43 withmeasurements59 of neu-
trontotalcrosssectionsand with the regionalDOM parameterizationsof Haouat-
Lagrange73,74 62and Madland. Values of ~z and (34from the Haouat-Lagrange
analysiswere used in the calculationswith Set B. Agreementwith the data is
slightlypoorerat low energieswith Set B as comparedwith the Haouat-Lagrange
actinidepotential. At energiesabove 2 MeV, however,Set B reproducesthe uT
data as well as or better than the Haouat-Lagrangepotential. The MadlandDOM
potentialappearsto best reproducethe totalcrosa-sectiondata for both 238U
andza Pu up to 10 MeV,whichis the limitof its rangeof validity.
50
-k-X0v
.-----
MARSHAK, 1970F&~L~~,:.1
SIVJPE61&1960YOUNG, 1982
[)SEXA DOMSET B DOM
1 1 1
01 I
5.0 10.0 15.0 20.0 2!5.0 :
‘\
\
\‘\\
\‘\\
v ‘.‘\
v ‘\ .
N.N.1.-\\‘.
+xov
------...........
I , I I 1 1 , I ,-2 I I I t 1 I 1 1[ I t I 1 1 I I I
10-’I I
Id’ Id
Lo
NEUTRON ENERGY (MeV)
Fig. 40. Comparisonof calculationswithfor measurementsof OT vs E for 165Ho.describedin the text and in TableVII.
severaldeformedopticalpotentialsThe Set A and Set B potentialsare
51
+ FERRER, 1977— YOUNG, 1982
[)-----SET A DOM......... SETB DOM
‘.0
Fig. 41. Comparisonof calculationswith severaldeformedopticalpotentialsfor measurementsof OEla ic(8) vs 0 for 11 MeV neutronsfor 16SH0. The SetAand Set B potentialsare?kescribedin the textand in TableVII.
NeutronEnergy(MeV)
+ Posr?tm 1981x SHAMU 19780 &#LBDiNG, 197S
‘- HAOUAT, 19S2.......... MADLAND, 1978
D &n 10.0 ls.o 20.0 wNeutronEnergy(MeV)
Fig. 42. Comparisonof experimentalneutrontotal cross sectionsfor 238Uwithcalculatedvaluesfrom 3 deformedopticalpotentials. The Set B parametrizat-ion is describedin the textand in TableVII.
52
1. ~~~~~~~~~, ~+MOORS, L979
%&w
#-x KAmEPBPELE&1978
‘b .- HAOUAT. 1982......... MADLAND, 1978
Slo<10-’ ld Id
NeutronEnergy(MeV)
+ NIVIORJ%L970
- HAOUAT. 1=-..-....MADLAND, 1978
n 6.0 tin M.o 20.0 25.0
Neutron Energy (MeV)
la
Fig. 43. Comparisonof experimentalneutrontotalcrosssectionsfor 242Puwithcalculatedvaluesfrom 3 deformedopticalpotentials. The Set B parametrizat-ion is describedin the text and in TableVII.
g--- ReactionTheoryCalculationsof n + 165H0Reactions(P.G. Young)
Preliminarycalculationshave been performedof neutron-inducedreactions
on 165H0using the COMNIJC63 and GNASH8code
were made
1.
2.
for the calculations:
Neutrontransmissioncoefficients
lationsare used.
Experimentalenergylevels,spins
systems. The followingassumptions
from deformedopticalmodel calcu-
166H0and paritiesup to 482 keV in
3.
4.
5.
(22 levels)and 590 keV in 165Ho (14 levels)are included.
A Gilbert-Cameron64 level-densityformulation,which reproducesob-
servedlevelspacingsat the neutronbindingenergy,is matched(num-
ber and energy derivative)to the experimentallevelsin (2) above.
Width-fluctuationcorrectionsare includedin the cross sectioncal-
culationsbelow0.5 MeV but are negligibleat higherenergies.
Gamma-raytransmissioncoefficientsare inferredfroma Tm measurement.
In particular,the shapeof a y-ray strengthfunctionwas determined
from a measurement76on 169Tm and the normalizationwas accomplished
from measurementsof <r > and <Do> for 165H0yo 3 as compiled by
Mughabghab,57 in the followingreamer:
a. A giant-dipole-resonanceshape and normalizationwas taken for
f (E ) fromthe systematicof Lone.77Ml Y
53
b. 78The assumed fM1(Ey)was subtractedfrom the measured total
f(Ey) for Tm, resultingin a tabulationfor the dominantf~l(Ey)
strengthfunction.
c. Weisskopfsingle-particleestimateswere used to obtainE2, M2,
E3, M3, E4, and M4 strengthfunctions.
d. The normalizationof the resultingtotalgamma-raystrengthfunc-
tion
from
166H0was determinedfrom <I_ > and <DO> measurementsonyo
the expression
<r > Bn
J(-_& .
)
Z f (E )E22+1 p(Bn-Ey)dEy ,2=0 o X9 X2 y 2
166H0whereBn is the neutronbindingenergyof .
The neutron total cross sectionsthat result from the deformedoptical
model analysesof Young et
perimentaldata in Sec. P.
forboth potentialsfrom 10
al.72are comparedwith the ‘SetA“ analysisand ex-
The agreementwith experimentis better than t 5X
keV to 30 MeV, and somewhatcloserat most energies.
The ‘5 Ho(n,y)radiativecapturecrosssectioncalculatedwith Younget al.72potential 59is comparedwith experimentaldata for neutronenergiesbetween1
keV and 4 MeV in Fig. 44. Here the agreementis generallywithint 20%, de-
pendinguponthe particularmeasurementsin the comparison.
Calculationsof the 165Ho(n,2n)crosssectionto the 6- isomericstateof164H0at E = 140 keV with the Younget al. potentialand both the Set A and SetxB potentialsof Sec.P are comparedwith experimentaldata in Fig. 45. The dif-
ferencein the calculationsfor the three potentialsis less than 10% at all
energies.
To test the theoreticalgamma-rayemissionspectrafrom the models, the
E@?!? of a spectrumfor thermalincidentneutronscalculatedwith the youngetal. potentialis comparedwith the measurementof Orphanet al.
78 in Fig. 46.
The experimentalspectrum,givenby the dashedhistogramwas obtainedby unfold-
ing spectraldata froma Ge(Li)detector. The unfoldinguncertaintiesand sharp
decreasein efficiencyof the pair spectrometerthat was used precludeddeter-
minationof the unresolvedspectrumbelow 1.5MeV
down to E = 220 keV).Y
The agreementbetweenthe
trum above E = 1.5 MeV is not too unreasonable,Y
encesdo appear.
54
(althoughlinesweremeasured
calculatedand measuredspec-
but some significantdiffer-
I I I i I !111 I 1 I I I 1111 I I I II1111 I I1
‘-10-”
AA
A
MENLOVE, 1967BRZOSKO,1971POENITZ,1975LEPINE,1972GIBBONS,1961FAWCETT,1972BLOCK,1961CZIRR,1970 ❑
ANAND. 1976YAML
I
A–iURO~1978x SIDDAPPA,1973
Y + MACKLIN, 19810 “- A KONKS, 1968c.
I I I II1!11 I I 1 II1111I IIII11!1I I10-2 10-’ 10°’
NEuTRoN ENERGY (MEV)
Fig. 44. Comparisonof the calculated163Ho[n,y) cross section [yO~g ‘t al072
potential)with experimentaldatabetween1 keV and 4 MeV.
04-
qo-
00.
1 I T
/
,’ x
------...........
TiMENLOVE,1979STEINER,1969YOUNG,1.982
[1SETA DOMSET B DOM
i [ 1 I I
8.0 10.0 18.0N;;TRON1;0NERGl!6.~MeV)
1.O
Fig. 45. Comparisonof calculationswith severaldeformedopticalpotentialsformeasurementsof a (metastable)vs E for 165H0. The setA and set B poten-
titilsare describ#d2?nthe textand in Thle VII.55
M1-
.-
- -1II1I1,1,
‘o I+10.0 ;.0
I 1 1 I6.0
GAMM::RA~-OENE%Y &EV).0
Fig. 46. Photon-emissionspectrafrom 16SHo(n,y) reactions with thermalneu-trons.The solid curvewas calculatedusing the Young et al.72potential;thedashedhistogramrepresentsthemeasurementof Orphanet al.78
Finally,Fig. 47 givesthe y-ray spectrumcalculatedat E = 50 keV, nown
representedin absoluteunits of b/MeV. The shape is very similarto the one
calculatedat thermalexcept some of the weaker linesare startingto become
more significant.
The comparisonspresentedabove indicatethat these preliminarycalcula-
tions agree quite reasonablywith the availableexperimentaldata. Further
optimizationof the gamma-raystrengthfunctionsmight be attemptedafternew
gamma-raymeasurementsare completed*at Los Alamos.
*InformationavailablefromS. Wender(P-3)and G. Auchampaugh(P-DO)of the LosAlamosNationalLaboratory.
56
~
Fig. 47. Calculated gamma-rayemissionspectrumfor ‘65H0(n,xy)
-&--1= reactions with 50-keV neutrons.
g
$> l’wzoG70u*-,lamVIVI0’?@g zu ~
7~ 1 I 1 I I I I0.0 1.0 6.0 7.0
GAMMiYRA~oENEkiY &EV)
R. GNASHOutputConversionCode forENDF/BFile 6: GNFILE6(P.G. Young)—A program(GNFILE6)has been developedthat convertsoutputfromthe GNASIi8
Hauser-Feshbachstatisticaltheorycode to an energy-anglecorrelatedrepresen-
tationin ENDF/B-VIFile 6 format. BecauseGNASHonly calculatesangle-indepen-
dent spectra,the codeutilizesthe File 6 LAW=l,LANG=2option,whichspecifies
that Kalbach-Mannsystematic79 are used to representthe angulardependenceof
the energy-angleemissionspectra. Accordingly,the GNFILE6code collectsthe
outgoing particle spectra, dcr/d&i,and
P(&i),for each outgoingparticle(i)at
GNASH calculations,and outputsthem in
includedin the outputare du/d&File 6
determinespreequilibriumfractions,
eachbombardingenergyincludedin the
the appropriateFile 6 format. Also
tablesfor outgoinggamma rays,which
are assumedto be isotropic.
The code presentlyhandles
cidentor outgoingparticles.
may be specifiedas histograms,
(E). The emissionspectraare
neutrons,protons,deuterons,and alphasas in-
Interpolationschemesfor the emissionspectra
linear(do/d&)-linear(8),or log (du/ds)-linear
automaticallythinnedin outgoingenergyaccord-
ing to an inputtedcriterion.Provisionis ❑ade to removea variable(inputted)
numberof discreteinelasticlinesfromthe File 6 spectrain orderto represent
the linesmore preciselyin ENDF/BFiles 3 and 4. In addition,the codescans
the discretegamma rays from the calculation,and automaticallyplacesall of
thosehavingcrosssectionsgreaterthanan inputtedminimumvalueinto the File
6 discrete-line representation,57
The code has been utilizedto constructENDF/Bfile6 tablesfromthe neu-
tron- 27and proton-inducedGNASHcalculationson Al, describedin Sec.F.
s. ModelingLevelsof Odd-MassDeformedNuclei(D.G. Madland)
A computercode NUCLEV has been developedto completethe low-excitation
rotationalband structureof odd-massdeformednuclei,given that some members
of each band are experimentallydeterminedin excitationenergy,spin,and par-
ity. Axialsymmetryis assumed. Then,the relevantequationfrom theparticle-
rotoris givenby
‘2 [J(J+ I)E(J,K)= SW + ~ - K2 + & ~ a(-1)‘+4 (J + ;)] (2)n L1. fiy2 L
where &K is the single-particle(quasi-particle)energy,I is
inertia,
symmetry
which a
that the
Finally,
The
mine the
J is the total angularmomentum,K its projectionon
axis,and a is the decouplingparameter. The lastterm
the moment of
the body-fixed
in Eq. (2),in
appears,arises from the Coriolisinteractions.It has been assumed80so-calledrecoilterm canbe absorbedintothe quasi-particleenergy.
bandmixingeffectshave,so far,been ignored.
solutionof Eq. (2) then requiresknowledgeof three statesto deter-
threeunknowns(&K,I,a)forK = ~ and knowledgeof two statesto deter-
mine the two unknowns(SK,I)for K > ~. If insufficientexperimentalinforma-
tion exists (theusual case),one can use Nilssonor Nilsson-likecalculations
to complete,as much as possible,the low-lyinglevel spectrum. It is noted
here that usuallythe first few membersof a given low-lyingband are themost
accuratelyknown experimentally.In such cases the best possiblevalues are
obtainedfor &K, I, and a (if K = ~) provided,of course, that one does not
then attemptto calculateband memberstoo high in spin valueswhereI = I(w).
Another reason to confinethe calculationof the discretelevel spectrumto
lower excitationenergiesis that more complexstatesthan those treatedhere
arise as the excitationenergyincreases.For thesereasons,the maximumexci-
tationenergyis confinedin the presentcalculationsto valuesbetween1 and 2
MeV for the rareearths,actinide,and transactinidenuclei.
For a specifiedvalue of the maximumexcitationenergyEEMAK, the code
NUCLEVcalculatesthe remainingmembersof eachbandup to excitationEEMAK. It
then producesa discretelevel spectrumby orderingall levelsin increasing
excitationenergy, computesthe angular momentum distributiontogeLherwith
58
first and secondmoments,the parity distribution,and the cumulativeenergy
distribution(discretenuclearleveldensity). Finally,if desired,a searchis
performedfor adjacentlevelsthatare withinsome specifiedenergyinterval,to
aid in searchesfor close-lyingpairs.
As a test example,calculationshavebeenperformedfor sevennuclei,with
E.EMAX= 1 MeV, that have been well studiedexperimentally.The resultsare
summarizedin the last columnof TableVIII,whichgivesRMS deviationsbetween
calculatedand measured sets of levels. In computingthe RMS, none of the
measuredlevelsused to determinethe parametersof Eq. (2)were included. The
rangeof RMS deviationsextendsfrom 2.5 keV (239Pu)to 19.9keV (171Yb). The
RMS deviationis, of course, influencedby how well the levelis measuredand by
how appropriatethe ❑odel is. In someof the casesof TableVIII,the magnitude
o:Ethe RMS deviationis dominatedby contributionsfrom one or two states. On
the basis of this test example,one would concludethat RMS deviationsof per-
haps a few keV can be achieved.
TABLE
COMPARISONSWITHEXPERIMENTALLEVELS
VIII
FOR EXCITATIONENERGIESBELOW1 MeV
Numberof NumberofNumberof Numberof KnownBand Band States BMs .
NumberofNucleusKnownBandsa
16768Er 9
1717oYb 9
1j:Hf 7
183W74 7
237U92 8
237#P 6
2;:PU 5
KnownBand Calculated StatesNeeded That Can Be DeviationDStatesa Band States for Parameters Compared (keV)
41 46 20 21 10.6
35 41 19 16 19.9
25 34 15 10 6.5
20 31 15 5 4.8
28 56 17 11 8.3
35 55 14 21 5.4
25 46 12 13 2.5
aTakenfromRef. 81.
bNot includingthe knownband statesused to determinethe parametersfor cal-culatingthe membersof each band.
59
I
T. NuclearStructureStudiesfor Gamma-RayLasers[D.G. Madland,E. D.Arthur,D. C. George,and D. Strottman(T-9)]
We summarizesome initial results in our investigationof the nuclear
physics issues of gamma-raylasers. We describehere what is known thus far
from existingexperimentaldata and whichtheoreticalmodelsone may employfor
systematicsearchesof candidatenucleiand for detailedcalculationof candi-
date level properties. We have earlierreported82 on simplenuclearphysics
considerationsthat indicatewhichmass regionsmay be most fruitfulto search.
A detailedsummaryof all of our initialresultsis givenin Ref. 83.
Some of the proposedschemesfor gamma-raylasersrequirethe identifica-
tionof a suitablenucleusin whichan isomericstate(ofsufficientlifetimeto
allow populationand preparationin a host material)lies nearbya state that
decays essentiallyinstantaneously.Because of present-day
radiationsourcesneededto drive the interleveltransitionto
the energy spacingbetween the two statesmust be less than
electronvolts (eV).
limitationson
producelasing,
severalhundred
As part of an effortto identifypossiblenucleiwith certainof the above
level characteristics,we completeda searchof the computerizednuclearstruc-
ture data library,CDRL82,84 85which is based on the 1978Tableof Isotopes
compilation.This librarycontainsdata (excitationenergy,spin,parity)for
41000levelsalthough,becauseof the vintageof the compilation(1977),current
dataare oftenlacking.
The criterionused to perform the searchwas initialidentificationof
isomericstates having lifetimesgreaterthan or equal to a specifiedinput
value. A halflife2 5 secondswas used for theseresults. Afteridentification
of such a state,the spacingsof nearbylevelswere examinedto determinewhich
ones (if any) fell within a specifiedexcitationenergywindow,AE. (TwoAE
valueswere specified:5 keV and 1 keV.) If one or more levelswere foundthat
lay nearbyto an isomericstateof sufficientlifetime,then the energy,spin,
and parity informationappropriateto such levelswas printed. These results
were examinedfurtherto eliminatelevelswhere spin or parityinformationwas
lacking,or wherean obviouslevelduplicationhad occurred.
Figure48 illustratesregionsof the periodictablewherecandidatenuclei
havingisomericstatesof lifetime> 5 s alongwith short-livedlevelsoccurring
within a spacingof 5 keV are indicated. Also shown (approximately)by the
shaded areas are regions of nucleardeformationwhere enhanceddensitiesof
60 I
nuclear levels should occur. Table IX lists the nuclei identifiedin this
search. For the nextpart of the search,the spacingcriterionwas loweredto S
1 keV. Figure 49 depictsthe candidatenucleiidentified.Of the nucleiap-
pearing in Fig. 49, 11’gHfis of particularinterestbecauseit exhibitsthe
closestlevelspacing(- 200 eV) of any nucleusidentified.The transitionfrom
the short-livednuclearstate involvesa 1.1 MeV gamma ray, which may be too
energeticfor the gamma-raylaser,but ideal for investigationof interlevel
transferprocesses,
120
100
80Proton
Number ‘040
20
0
Defofmdfonm
Regions
.
. A........................ s●
.
e’......-..”..,’..... c-
P..................
0.........................,,..,..#...”....”.”..#...#..“.!;<:&”{..””.“...”
P-.................
+;<+:”<:”................;.:.
I ! 1 1 I 1 1 1
() 20 40 bo &)o 100 120 140 160 180
Neutron Number
Figure48. Candidatenuclideswith 5 keV (or less)spacings.
TABLEIX
NUCLEIIDENTIFIEDIN THE SEARCHWITHAE S 5 keV
~lGa74 ~7Rb80
@b90 ~6Pd111
11047Ag 56Ban3EU152
63 65Tb158
~1Lu171 ~2Hf17g
18374W 82Pb203
83Bi201 ~5Am2Q
61
There are severaldifficultiesassociatedwith this search,most of which
are relatedto the vintage(1977)of the compilation.Experimentaltechniques
have progressedsignificantlyover the past 8 years so that a more up-to-date
compilationmightoffermanymorenuclearcandidates.Secondly,two data files,
one resultingfrom nucleardecay data and the other from reactiondata, tteie
merged to produceCDRL82. In the process,levelsappearingin theseseparate
fileshavingspacingsS 1 keV were consideredto be the same. Whilethispre-
sumptionis prudentfor most nuclearlevels,thereis a significantchancethat
level informationapplicableto the gamma-raylasercouldbe lost. In orderto
circumventcertainof theseproblems(especiallythose relatedto use of anti-
quated data), a secondsearchhas begun usingnuclearstructuredata from the
more recent (circa1982 for some nuclei)ENSDF85 evaluatednuclearstructure
file.
As a secondstep in the effortto determinewhichmass regionsmay be most
fruitfulto searchtheoretically,and to check our earlierconclusions83 based
upon simple theoreticalarguments,we have scannedboth the CDRL and ENSDF
,0.557 MeV3“ ,0.1186 fleV
:-
7
0.5553–l.02mI+ -0.4879 6“
T-0.1177-252 d
62
2- 1- 0. 16.8d2“-1- 0.0013 o.66/As
1●—0.24.4s
Agl10
7/2”-
F
.l.1059MeV 11/2+ ,—. 0.30949fleV-5.3 s25/2-~ --1.1057—25.1 d 9/2”
r
0.300946
-L 5/2-3/2- *
009900
9/2” 0 stableO0464B4
l/2- 0 stable
Hf17’183w
3“ 0.0s(?)5-
T
004663 152yo- 0.044(?)
(7)
1- 0. 16h242
Am
Fig. 49. CandidateshavingspacingsS 1 keV.
I
nuclear structure files for experimentallyknown isomericstates. We have
performedfour scans,on each file, for isomericstatehalflives,TI, thatare%
greaterthan 1 s, 1 rein,10 rein,and 1 h. For each of theserangeswe have
calculatedthe averagenumberof isomericstatesas a functionof the nuclear
mass numberA. Figures50 and 51 illustratethe resultsfor the rangeT, > 102
min for the CDRL and ENSDF files, respectively. These clearlyshow strong
dependenciesof the averagenumber of isomericstates on mass number. As we82,83expected, regionsof shell closurein neutronnumberN and protonnumber
Z} as well as deformedrare earth and actinidenuclei, containthe largest
numbersof isomericstates. In particular,the regionsN = (28,50,82),Z =
(28,50),the rare earths (150~ A ~ 190),and the actinidesand transactinides
(A > 220), exhibitwell-definedpeaks. However,the largestpeak (foreachof
the four halfliferanges studied)occurs for mass numbersA = 195-197,which
cclrrespondsto stable and long-livedisotopesof 760s, ?TIr, j’spt,79Au,and
S~Hg. These nuclei are representativeof the transitionregionbetweenthe
heavy deformedrare earths and the sphericalnuclei near doublymagic 208Pb.
Clearly,this regioncouldbe furtherinvestigatedfor possiblegamma-raylaser
Cc,nsiderafions.
3
2
1
0
Isomeric States (CDRL)
io 50 100 150
u200 250
Fig. 50. Average number of isomericlevelswith halflivesgreaterthan 10min as a functionof nuclearmass num-ber. The CDRL 1982 evaluatednuclearstructurefile84was used.
63
Fig. 51. Identicalto Fig. 50 exceptthat ~the ENSDFevaluatednuclearstructurefile86was used.
tu
c1.d
2
1
Isomeric States (ENSDF)
o 50 100 150 200 250
A
We now brieflydescribethe main theoreticalmodelswe envisionusing to
systematicallysearch for candidatenuclei and to determinecandidatelevel
properties.
Odd-ANuclei. Most descriptionsof odd-A nuclei begin with the Bohr-
Mottelsonansatzfor the Hamiltonian:
(3)
where the Ik are momentsof inertia,and Jk’ ‘k’ and jk are componentsof the
total,core,and single-particleangularmomentum,respectively.In particular,
referringto the 3-axisof the body-fixedsystems,‘3=Kandj3 = Q, whereas,
referringto the space-fixedsystem,‘3’
= M. The correspondingwave function
underthe assumptionof axialsymmetry(11= 12 = I) is
+~= r‘J; 1 [lI&xK + (-l)J-K D;-KX-KI ,1671
(4)
with XK = Z ajK$jK , where (5)j
64
4. are the single-particlewave functionsand the a. are givenby the NilssonJK JKmodel or similarcalculation.For an axially-asymmetricsystem,the wave func-
tion (4)mustbe summedoverK.
With axial symmetry,the matrix elementof H can be readilycalculated
usingEq. (4):
9<JKIHIJK>= $ [J(J+ I) -K2+<JKl~ -K21JK>-6 ~ ~(-l)J+*(J+ ~ )a] . (6)
9
The third term is referredto as the recoilterm, while
from the Coriolisinteractions,connectingK and -K in a
and is thereforenonzeroonly if K = ~. The quantitya,
eter,is givenby
a = Z (-l)j-*(j+ ~)(aj~)2 ,j
the last term arises
crossmatrixelement,
the decouplingparam-
(7)
function.wherethe a.l are expansioncoefficientsof a NilssonwaveJ%
In practicethe recoilterm is usuallyignoredby assumingthat its effects
can be lumped into the singleparticleenergy. However,in our application
where the accuratedeterminationof the candidatelevelenergyis crucial,this
term cannotbe ignored. It is especiallyimportantif severalvalencenucleons
exist,becausethe recoiltermthen containsone-bodyand two-bodyoperatorsand
cannotbe absorbedinto the single-particlepotential. Moreover,when pairing
is taken into account,even if
recoiltermbecomeseffectivelya
A secondrefinementleading
energyis the inclusionof band mixingeffectsdue to off-diagonalmatrixele-
mentsarisingfromthe Coriolisinteractions,<JK’[HIJK>.Thesematrixelements
existwhen K’ and K differby 1 and they may alter the energydependencefrom
that of Eq. (4). It is stressedhere that the magnitudeof such off-diagonal
matrix elements is not yet completelyunderstood.
thereforerequiredin thisarea.
there is only a singlevalencenucleon,the
many-bodyoperator.
to more accuratepredictionof candidatelevel
Odd-OddNuclei. In the simplestgeneralization
More theoreticalwork is
of Eq. (3),to includetwo
extranucleons,one has
H= & (Jkk 21k- j: - j~)z+ Vnp , (8)
65
where V isnpric case has
experimental
new is Vnp”
the residualneutron-protoninteraction.Only the axially-symmet-
been workedout in detail,due to uncertaintiesin Vnp and odd-odd
levelschemes. In thiscase,K = Qn + flpand the only termthatis
The matrixelementfor V is thengivenbynp
<JKIVJJK’>= a2ps2nlvnplQ;Q:>+ (-l)K+JtiK-K,<S2pqvnpl-w - c?:> .P
(9)
The first term is called the Gallagher-Moszkowski87 matrix element and the87secondthe Newby matrixelement. The Newbymatrixelementcontributesonly to
K= O bands owing to the rotationalinvarianceof V The magnitudesof thesenp”matrixelementsare, typically,100 keV and 50 keV, respectively.Clearly,an
accuratecalculationof the energyof a candidatelevel in an odd-oddnucleus
requiresa very good representationof V In addition,odd-oddaxially-asym-np”metric nuclei of interest,perhapsnear A - 180, no longerhave K = G?. This
means that the entireformalismsummarizedabovemustbe repeatedto obtainthe
analogous,althoughmore complex,expressionsfor the level energiesof such
nuclei. We note here ‘thatthe largestpeaks of Figs. 50 and 51, thosecorres-
ponding to A - 194-198,may includesuch nuclei. Given this possibility,the
axial-asymmetricmodelmay be very importantin the searchfor candidatelevels
for the gamma-raylaser.
u. Comparisonsof FourRepresentationsof the PromptNeutronSpectrumfor theSpontaneousFissionof 2Cf [D.G. Madland,R. J. LaBauve,and J. R. Nix(T-9)1. -..
Becauseof its importanceas
measurementsand calculationsof
the spontaneousfissionof 252cf.
a neutronstandard,
the promptfission
In particular,we
of N(E) against recentexperimentalmeasurementsof
we presentcomparisonsof
neutronspectrumN(E) for
test four representations
the differentialspectrum
and thresholdintegralcrosssections. Theserepresentationsare the Maxwellian
spectrum,two versionsof the Watt spectrum,the NBS spectrum,88 and the Los
Alamos spectrumof Madlandand Nix.89 For the Maxwellianspectrum,we obtain
the value of the MaxwelliantemperatureTM by least-squaresadjustmentsto the
experimentaldifferentialspectrumof Poenitz and Tamura’Oand also that of
Boldemanet al.91 Similarly,for the Watt spectrumwe performleast-squares
adjustmentsto obtain the Watt temperatureTw with the otherparameterof the
Watt spectrum,the averagekineticenergyper nucleonEf, determinedfrom ex-
periment. For the Los Alamosspectrum,least-squaresadjustmentsdeterminethe
nuclear level-density parametera, which is the singleunknownparameterthat
66
appears. The NBS spectrumhas been previouslyconstructedby adjustmentsto
eightearlierdifferentialspectrummeasurements.With theserepresentationsof
the spectrumso determined,we calculate15 thresholdintegralcross sections
for each representation,using ENDF/B-Vcross sectionsgenerally,and compare
the calculatedvalueswith the measuredvaluesof Grundlet al.92 and Kobayshi
et al.93
We considerfirst the differentialspectrumof Poenitzand Tamura. Our
least-squaresadjustmentswith respect
adjusted parameter values and minimum
Maxwellian(TM = 1.429MeV, X2 = 1.20),
f?ed Watt (TW = 0.897MeV, X2 = 1.57),
0.55). Here the modifiedWatt spectrum
resentingseparatelyneutron emission
to this experimentgive the following
values of X2 per degree of freedom:
Watt (Tw= 0.897MeV, X2 = 2.33),modi--1and Los Alamos (a = A/9.15MeV , X2 =
is the averageof two Watt spectrarep-
from equi-temperaturefragmentsof the
lightand heavy fragmentmass peaks. The valuesof E: and E: are againdeter-
❑ined from experiment. The NBS spectrumyields a value of X2 = 1.92. The
ratiosof thesespectraand the experimentalspectrumto the Maxwellianspectrum
are shown in Fig. 52. Clearly,the Los Alamosspectrumagreesbest with the
experiment,both in overallshape agreementand by factorsexceedingtwo in X2.
Secondly,we considerthe differentialspectrumof Boldemanet al. Our
least-squaresadjustmentswith respectto this experimentgive the following
correspondingvalues:Maxwellian(TM = 1.420MeV, Xz = 8.24),Watt (Tw= 0.926
MeV, X2 = 31.70),modifiedWatt (Tw= 0.922MeV, X2 = 23.42),and Los Alamos(a
= A/9.50MeV-l,X2 = 11.59). The NBS spectrumyieldsa valueof Xz = 6.09.The
ratiosof thesespectraand the experimentalspectrumto the Maxwellianspectrum
are shown in Fig. 53. Here the NBS spectrumagreesbestwith the experimentin
terms of X2. However,the Maxwellianand Los Alamosspectrayield X2 values
tb.atare withina factorof two of the minimumvalue.
Figure54 shows15 ratiosof calculatedto experimentalintegralcrosssec-
tions,as a functionof the effectivethresholdenergyof the reaction,for each
of the spectrathat have been adjustedwith respectto the Poenitzand Tamura
measurement,plus the NBS spectrum. We infer that the Maxwellianspectrumis
too hard in the tail regionand thatthe two Watt spectraare too soft. The NBS
spectrumis slightlyhard and the Los Alamos spectrumis slightlysoft. The
correspondingratios for spectraadjustedwith respectto the Boldemanet al.
experiment,plus
made here except
the best overall
the NBS spectrum,are shownin Fig. 55. Similarinferencesare
thatthe Los Alamosspectrumis just slightlyhard and it gives
agreementwith experiment.67
This
Data for
94work has been presented at the InternationalConferenceon Nuclear
Basic and Applied Science,May 13-17, 1985, Santa Fe, New Mexico.
1 I 1 I I I I 1 I 1 1 8 , I 1 1 1 I
252cf(sf)
!
“\.
-..I t 1 I 1 , , I I , , I t I I .11 I I
---- ModifiedWatt ~~–.– NBS ;1— LosAlamos I ~\
:a
10-’ 10° 10’LaboratoryNeutronEnergyE(MeV)
Fig. 52. Differentialspectrumcomparisonsfor adjustmentsto the PoenitzTamuraexperiment(Ref.89).
1.25 , , I I , , , [ , 1 0 f I
252Pdnd
–.– NBS13 \
— LosAlamos3:1:1
0.75 I I f I ! 1 1 I 1 1 :1! ! ! I , I
lo”’ 10° 10’Laboratory Neutron Energy E (MeV)
III
Fig. 53. Differentialspectrumcomparisonsfor adjustmentsto the Boldemaneexperiment(Ref.91).
and
t al.
68
1.30 , 1 ( 1 I , 1 IHa/-
252cf(sf) !///j\O’
1.15- I~E.=a)Q
g 1.00( -.——. —o.—~am
v 0.85 - —+ Maxwellian““:.&
%;--. * f, -*- Modified Watt........ * ,“* —“* NBS““y;\ ~: -..0k- :●.O =s%=~ LosAlamos
0.70 ..t I 4 ...* “(... x 1 ,
0 10EffectiveThre;holdE,~(MeV)
Fig. 54. Integralcross-sectioncomparisonsfor spectraadjustedto the Poenitzand Tamuraexperiment(Ref.90).
1.30 I I [ r # I 1 1 , t
252cf(sf)
.4 ‘“-”-”-”-”-”:—+ Maxwellian
~,““-v”””Watt
6
1
M $ -+- Modified Watt%5 “..8A~~ —“* NBS
“ 0.85-v.:.:-~-“...* .*““..~\J+...=..—o— LosAlamos-.\.. X . ....‘. ...w .. ---v .. =..... ‘..... ‘...... ‘A
. .. .
0.70I...1 I ! I I 1 1 1v 8 I
o
Fig. 55. Integralcross-sectionet al. experiment(Ref.91).
10Effective Threghold E~~(MeV)comparisonsfor spectraadjustedto the Boldeman
v. CoupledEnergy-AngleDistributionsof RecoilingNuclei(D.G. Foster,Jr.
and R. E. MacFarlane)
In previousreports95,96we have describeda new codesystemfor calculat-
ing the coupledenergy-angledistributionsof particlesand recoilnuclei. This
systemtakesadvantageof recentlyincreasedflexibilityin File 6 of the ENDF/B
system. Briefly,wheneverwe calculatea seriesof nuclearreactionswith the
GNASH code,8we store all of the individualincrementsof crosssectionsfor
subsequentreanalysis.A new code namedRECOILreadstheseincrementsand uses79a modificationof the Kalbach-Mannformalism to calculatethe resultingangu-
lar distributionsof the particlesemittedduring the subsequentdecays. By
summingthe resultingrecoilsover the successiveparticleemissionsand aver-
aging over angles,RECOIL constructsa Legendreexpansionof the angulardis-
tribution,as a functionof secondaryenergy,for each recoilspecies.
In makingthese calculations,we have modifiedthe Kalbach-Mannformalism
in two respects. The firstis to forceall of the Legendrecoefficientsto go
quadraticallyto zeroat zerosecondaryenergy,whilestilljoiningthe original
curves reasonablysmoothly. The second is to adopt curvesfor the first two
Legendre coefficientsfor neutrons that are differentfrom the curves for
chargedparticles. The curves for neutronswere derivedby fittingmeasured
angulardistributionsfor inelasticneutronscatteringfromiron;theseexhibit
substantiallymore forwardpeakingbelow 20 MeV than do charged-particlemeas-
urements.
The outputfrom RECOILconsistsof fragmentsof the desiredENDF records.
These are retrievedfrom intermediatestoragein the correctorderby a second
new code namedMAKE6,whichwritesthe resultsdirectlyin the requiredformats
forFiles3, 6, 12, and 15.
We have used RECOILand MAKE6to generatethe coupledenergy-angledistri-
butionsfor 56Fe from5.25 to 36 MeV, usingthe GNASHcalculationsfromthe 198023evaluationby Arthurand Young. Unfortunately,RECOILis so expensiveto run
that we could not afford to use a fine enoughmesh in averagingover angular
distributions,so the resultingrecoilangulardistributionsfor minor recoil
species are useless. Accordingly,we modifiedMAKE6to rejectangulardis-
tributionsthat are clearlyfaulty. We also added an inputparameterto sup-
press recoilangulardistributionsin which neitherof the first two Legendre
coefficientsexceeds a specifiedthreshold(typically0.1). Even with these
omissions,the resultingadditionsto the ENDF filetotalmore than7000 lines.
70
Takingadvantageof the flexibilitypermittedby the rules for File 6, we
treatedonly the (n,n’), (n,p),and (n,a)reactionsexplicitlyover the entire
range of primary energies. We treated the (n,2n) reactionexplicitlyfrom
thresholdto 20 MeV, then buriedit in MT = 99 above20 MeV, alongwith all the
other minor reactions. The resultingcross sectionfile for MT = 99 above 20
MeV thereforebegins with a subsectionfor each of the three lightparticles
(neutron,proton,alphaparticle),followedby eight subsectionsfor the minor
heavy recoils. Figure56 displaysthe resultingcrosssections,as
File 3. The “totalH cross section shown is incomplete,because
elasticcrosssectionhas been omitted.
,’,’,#
,’,’,’#
*.,...,.........,...,.,,..............
recordedin
the shape-
s-o m.o 15.0 20.0 Zs.o 30.0 3!5.0 40.0
Neutron energy,MeV
Fig. 56. Reactioncrosssectionsincludedin thiswork. The “total”crosssec-tiondoesnot includethe shape-elasticcontribution.
Figure57 illustratesa typicalparticlespectrumat the highestenergyin
our calculations.The spectrumis normalizedto have an integralof unity,as
requiredfor ENDF/B. The apparentlyempty portionat lower energieshas been
drainedof most of its crosssectionby transitionsthat leftenoughenergyfor
anotheremission,in this case to the (n,2n)or higher-orderreactions.Typi-
cally,the preequilibri~ fractionsaturatesat 1.0 for these very energetic
emissions.The sharpbend in the preequilibrium-fractioncurveis the resultof
a rathercrudetreatmentin GNASH.71
Figure58 shows the spectrumof 56Fe recoilsthat correspondsto Fig. 57.
Becausethe recoilbin-widthin RECOILis self-scaling,the apparentwidth of
the discretestructureis distortedby differencesin relativebin width. The
dashedand dottedlinesexhibitthe energydependenceof the firsttwo Legendre
coefficients.The negativevalues for 2 = 1 reflectthe factthatthe average
directionis backwardsin the center-of-massframe. At mwch lowerenergies,the
Q = 2 coefficientfrequentlyis largerthanthat for 2 = 1.m
1 1. ... .
......”~”””””””’”-””””””““...
/...+
........”’........’”./...
..=”/’/#/./
:’
:—..........Sg:yzc-z
k
I I a
0.0 5.0 10.0 SSo 30.0 350Neut~o”nener~~,MeV
Figure 57. Normalizedneutronspectrumand its associatedpreequilibriumfrac-tion for the (n,n’)reactionat 36 MeV.
- ~:rum
...,,,..,-t =2 .-~uJ
ca.-0,,,,,,.,.,........
............--$””’,C--..,”.....................................................................,....,..$,,...-$,””’”.-,-
..4Q+G-1
.2 i!-“ ----- -..-.
%,..-..‘... S
----------- -------
On 02 0.0
Recoilenergy,&VFig,58.SGFerecoilSpectrmand angulardistributioncorrespondingto Fig. 57”
72
w. Testsof the GNASHPreequilibriumModelat Low Energies(D.W. Muir)—In the courseof a seriesof calculations97 of neutronreactionson ‘gCo,
using a versionof GNASHnow operationalon the CRAY-1at Harwell,98 it was ob-
servedthat the preequilibriumcalculationdid not convergeproperlyat an in-
cidentneutronenergyof 8 MeV, while it did convergeat nearbyenergies,both
above and below this energy. In order to furtherexaminethis discontinuous
behavior,an identicalcode versionwas implementedon the Los AlamosCRAYma-
chines. Identicalbehaviorwas then seen in Los Alamos repetitionsof the
Harwellruns. Numericalexperimentationand analysisof the code has revealed
that the observedbehavioris a natural consequenceof the algorithmused in
subroutineRESOL to detect the onset of equilibriumin the solutionof the.99“master equations. While the problem can be avoidedwith existingGNASH
versionsby simply turningoff the preequilibriumtreatmentat low energies
(wherethe preequilibriumeffect is smallanyway),we have implementedan im-
provedconvergencetestin RESOLthateffectivelyavoidsthe problem.
II. NUCLEARCROSS-SECTIONPROCESSINGAND TESTING
A. NJOYDevelopment(R.E. MacFarlane)—The NJOY nuclear data processingsystem100 is now in use all over the
world, and with the increasinginternationalstandardizationon ENDF-typefor-
mats, NJOY use should expand even further. The developmentof NJOY has pro-
ceeded through a series of dated ‘versions”[e.g.,NJOY(6/83)]and numbered
“revisions”[e.g., (6/83-2)]. We are now in the process of releasingNJOY
(6/83-3).The majorchangesmade sincerevision2 are describedbelow.
Many changesweremade to handlethe new ENDF/B-VIformats;RECONR,BROADR,
UNRESR,THERMR,MODER,and GAMINRare all essentiallyVersion-VIcompatiblein
NJOY(6/83-3). See the discussionsof thermalchanges,the Reich-Mooreoption,
and photon-interactionprocessingin Sec.B, ChapterII of this report.
The effortsto improvethe transportabilityof NJOY have continued,and the
use of FORTRAN-77has increased(seeOPENZand PACKespecially).The “overlay”
type structurehas been changedto a “segment”structurethat seemsto be con-
sistentwith more systems. The use of localplottingroutinesin DTFR has been
reduced,and a FORTRAN-77versionof the “Draw Large Characters”routinehas
been written. Only low-levelroutines,such as ‘draw a vector”and “advance
pagenare neededto converttheDTFRplottinglogicto a new system,
73
In responseto the most commoncriticismof GROUPR,a more automatedway to
request the processingof a seriesof reactionshas been added. The single
inputcard “3/” will now causethe processingof all the reactionson the PENDF
tape (exceptthermal). Similarly,“6/” will requestall neutrontransferma-
trices(exceptthermal),and “16/”will generateall photonproductionmatrices.
Optionalquantitiessuch as thermaldata,averageinversevelocity,or delayed-
neutrondatamust stillbe requestedexplictly.
A new interactivemethodfor choosingthe energygrid forDoppler-broadened
cross sectionswas installedin BROADR. This methodcorrectssome smallinac-
curaciesnoticedby S. Ganesan(ReactorResearchCentre,Kalpakkam,India),and
it actuallyimprovesthe speedof BROADRfor heavy isotopes. In addition,the
inputinstructionsfor BROADRweremodifiedslightlyto providethe same control
over reconstructionand thiming used by RECONR. Test calculationshave shown
that the older method was perfectlyadequatefor producing❑ultigroupdata at
the 1/8 to 1/4 lethargylevel if reasonablytight toleranceswere used (1% or
better). However,the newermethodgivesimprovedpoint-cross-sectionresults,
and
640
and
some small changesmay be seen if very fine groupstructures(forexample$
groups)are used.
SeveralENDF/B-Velementalevaluationshave energyregionswhereresolved-
unresolved-resonancerepresentationsoverlap. These evaluationsare not
processedcorrectlyby NJOY (6/83-2). We havemodifiedRECONR,BROADR,UNRESR,
and GROUPR to detectsuch overlaps. In BROADR,the smoothunresolvedpart is
removedfrom the reactioncross sectionin the overlaprange,the remainderis
broadened,and the smoothpart is addedback onto the result. In GROUPR,the
resolvedpart of the cross sectionin the overlaprangeis separatedfrom the
unresolvedpart and used as part of the U. backgroundcrosssectionwhen com-
puting the effectiveself-shieldedvalue of the unresolvedpart of the cross
section.
In additionto theENDF/B-VIupgradesin THERMRdescribedelsewhere,sever-
al improvementswere made to the calculational❑ethods for thermaldata. A
number of these problemswere reportedby M. Mattes (Universityof Stuttgart)
and some were foundby lookingat detailedplots of thermaldata using an up-
gradedplottingcode. THERMRnow does a betterjob with both incidentand se-
condaryenergygrids. Figure59 showsexamplesfor two interestingmoderators.
People interestedin using NJOY for thermalneutroncross sectionsshouldup-
gradeto version6/83-3as soonas possible.
74
0.00 0.05 0.10 0.15 (Energy (eV)
Fig. 59 (a)
!0
~
(/)c-o‘r~\‘“:‘:’’/;-,,Lr ,,c1
,-. ;;-.,
Q‘, ,’;
---- , : ;---- %, ;.--” , : ; ,~,c ------ ‘. ,; ,’ ;00 --- ,. :;
0 /--------. : , : ;
“~s-, 1’ : ;
c) ---- , ‘, ,0,. :
., : , : : “
(% ,, : t , , :\,, ,: “;,, :,, ;; ;:,,, :,, , , ; : :# : ; , , ,
,, ‘“j , ,.u : , ,,
,,,:; ;
.;
,$ :,, , : ,.,,,: t, : ,, I
b,
y,, :1,
0 II:, p,,,
-10-3 10-2 10-’ 10°Energy (eV)
Fig. 59(b)
Fig. 59. Examplesof THERMRcalculations:(a) BeO at 600 K for three incidentenergiesnear 0.01 eV, (b) H in ZrH for an incidentenergyof 0.01 eV at tem-peraturesof 300,600, 800 and 1200K,
75
Two new volumesof the NJOY report,namelyLA-9303-M,VolumesIII and IV,101,102are now complete. Volume III describesthe GROUPRand GAMINRmodules,
which preparemultigroupcross sectionsfor neutronand photon transportand
responses,and the MODER module, which performsmode conversionand certain
other operationson ENDF/B and NJOY output files. Volume IV describesthe
ERRORRand COVR modules,which are concernedwith the covariancesof multigroup
crosssectionsand fission~ values. The new volumesprovidedetaileddescrip-
tionsof the theoryand methodsused in thesefivemodulesand theyprovidemore
complete(andmore up-to-date)descriptionsof the user inputthanthatgivenin
the generalNJOY user’smanual.100
B. Reich-MooreResonanceFormat(R.E. MacFarlane)
The use of the Reich-Mooreresonanceformathas been approvedfor nonfis-
sionableisotopesfor ENDF/B-VI.We haveborrowedsomecodingfromthe National
NuclearData Center (Brookhaven)ENDF-VI checkingcode PSYCHEand modifiedit
for RECONR, the
made to include
communities.The
D. Larsonof Oak
E. Cullenat the
resonancereconstructionmodule of NJOY. Provisionwas also
fissioncharnelsfor testingor for use in other evaluation
new optionhas been testingusinga sampleproblemprovidedby
Ridge NationalLaboratory.Resultsalso have been sentto D.
InternationalAtomicEnergyAgency (IAEA)for comparisonwith
otherReich-Mooreresults.
c. PhotonInteractionCrossSections(R.E. MacFarlane)
The existingphoton interactioncross-sectionlibrariesavailableat LOS
Alamos are based on the DLC-7E librar@ in ENDF/B-IVformat,as processedby
NJOY. Recently,there have been threedevelopmentsthat make it desirableto
upgradeour processeddata libraries. First, a new version of the evaluated
data libraryhas been releasedin ENDF/B-Vformat. This one is calledDLC-99/
HUGO,* and its contentsare describedin Ref. 103. Second,a new formatfor
photon interactiondata has been adoptedfor ENDF/B-VI. Third,we have always
feltthatthe GAMINRmodulewas too slow.
Basedon thesedevelopments,we decidedto updatethe GAMINRmoduleof NJOy
to handlethe ENDF-6 formatand to be more efficient. The efficiencygainwas
obtainedby taking advantageof the fact that incoherentphotonscatteringis
* The DLC-7Eand DLC-99librariesare availablefromthe RadiationShieldingIn-formationCenterat the Oak RidgeNationalLaboratory.
76
proportionalto the chargenumberZ at high energies. The energyabovewhich
proportionalityholds increaseswith Z, and in a series of calculationsfor
graduallyincreasingZ, the new code simplyrescalessome of the resultsfrom
the previousstepto get the high-energygroupsfor the currentelement.
We also convertedthe DLC-99/HUGOlibraryto ENDF-VIformatand supplied
the resultto theNationalNuclearData Centerat the BrookhavenNationalLabor-
atory.
The new versionof GAMINRwas testedon all threelibraries,and the modi-
ficationsare now availablein NJOY (6/83-3). Multigrouplibrariesfor the
DLC-99 evaluaticmswill be generatedin 12 and 24 groupsin the near future.
D. ENDF/B-VIThermalData (R.E. MacFarlane)—As a part of the developmentwork for the ENDF-6 format,we examinedthe
representationsused for thermalneutron scatteringdata in the previousver-
sionsof ENDF/B. The followingproblemsand shortcomingswere noticed.
1. It is oftennecessaryto computeincoherentinelasticscatteringfor energy
or momentumtransfersoutsidethe rangeof the tabulatedS(CY,~).This kind
of extensionis normallydone using the “short-collision-time”approxi-
mation,which requiresa table of effectivetemperatureversusmoderator
temperature.Theseeffectivetemperatureshavebeen computedfromthe same
frequencydistributionmodelsused to generateS(a,~),and the temperatures104are given in ENDF-269. They currentlymust be transferredto the input
of the processingcodesby hand. It wouldbe betterto add a supplementary
tableto the formatfor MF=7,MT=4.
2. Incoherentelasticscattering(polyethylene,ZrHx)is currentlyrepresented
as a temperature-dependenttabulatedcross sectionin File 3 (MT=2)and an
angular distributionin File 4. A more accurateangular distribution
(especiallyfor Monte-Carlo)can be obtainedif one knows the effective
bound cross sectionand the Debye-Wailerintegral. Once again,thesedata
are given in ENDF-269and must be transferredto the processingcode by
hand.
3. Coherentelasticscattering(Be,BeO, graphite,UC, U02) is representedin
the same way. It is currentlypossibleto reconstructthe exact angular
77
distributionfromFile 3 by locatingBraggedgesand subtractingcrosssec-
tions to get structurefactors(thismethodwas developedforNJOY). When
this is done,the existingFile 4 is no longerrequired. It turnsout that
an even ❑ore compactrepresentationusingFile 7, MT2 insteadof File 3,
MT2, is desirable.
4. Temperaturedependentcross
The values in the file may
sectionsare givenusinga rarelyused format.
not be consistentwith thosecomputedfromthe
standardFile 2 + File 3 data for the evaluation. Cross-sectiontabula-
tionsshouldbe removedfromthe thermalfiles.
5. Some compoundevaluations(BeO,Benzine)givethe molecularS(a,~)in File
7 rather than the S(a,~) for one atom in the compound(H in H20). Such
evaluationsrequirecross-sectionand effectivetemperaturedata for the
secondaryatom.
Repairs for these problemswere incorporatedinto a formatproposalfor
File 7 in ENDF-6. Thisproposalhas been accepted.
In order to transferdata from the old formatto the new, a simpletrans-
lationcodehas beenwritten. It takesas much informationas possiblefromthe
old ENDF/B-111thermal evaluations(tapes 320, 321, ...),and requestsuser
input for the balanceof the information;thatis, new MAT numbers,new comment
cards,boundatom crosssectionand Debye-Wailerintegralfor incoherentelastic
scattering,parametersfor SCT approximationin mixed moderations(BeO),and
tablesof effectivetemperaturesfor the SCT approximation.
This conversionprocesshas been carriedout for severalexistingevalua-
tions. The work will be completedin the near future,and the resultswill be
made availableto the Cross-SectionEvaluationWorkingGroup (CSEWG)through
NNIlc.
Conversiondoes not removeshortcomingsin the originaldata. Some of the
outstandingproblemsincludethe following.
1. Upperenergiesfor the
2. Some of the free atom
thermaltreatmentsare
crosssectionsin File
generallytoo low.
7 do not agreewith the cross
sectionvaluesin the latestevaluationsfor the materials.
78
3. Gridsfor u and P are sometimes too coarse.
4. Some S(a,f3)values are set to zero in the files when they get ‘small.”
Unfortunately,the definitionof “small”is too large,and thesezeroslead
to problemsin computedcrosssectionswhen attemptsare made to extendthe
calculationsto higherenergytransfers.
Some of these problemsshouldprobablybe workedon beforethe ENDl?/B-VI
filesare released.
E. Cross-SectionProduction(D.C. George,R. E. MacFarlane)—In order to supportvariousQ-Divisionprograms,neutroncrosssectionsin
69- and 80-groupMATXS libraryformatswerepreparedfor the followingmaterials:
Material
Re-185Re-187Nb-93Ta-181W-182,183,184,186U-235U-238
Temperature
1200,2100,31001200,2100,31002100,31002100,31001200,2100,310031003100
(Jo1010
101-1010101-1010101-1010101-1010101-1010101-1010
In addition,temperature-dependentcrosssectionsfor the MCNPMonte-Carlocodes
werepreparedfor the followingmaterials:
Material
H-1H-1H-1Li-6Li-7Be-9cNa-23KCrFeNiSm-149Xe-135Mn-55Zr
Temperature ScatteringLaws
300,400,500, 600, 800 H20, Benz300 Poly300,400,500, 600,800, 1200 ZrH300, 1200300, 1200300,600,800, 1200 Metal,BeO300, 600,800, 1200,1600,2000 Graphite300, 1200300, 1200300, 1200300, 1200300, 1200300, 1200300, 1200300, 1200300,4000,600,800, 1200 ZrH
79
ScatteringLaws
(continued)
Material Temperature
Mb 300, 1200Mo 300, 1200Eu-151 300,900Eu-153 300,900Ta-181 300, 1200v 300, 1200,1800R&i85 300, 1200Re-187 300, 1200U-235 300, 1200,1800U-238 300, 1200,1800Pu-239 300, 1200,1800
A speciaIcross-sectionlibrarywas preparedforESS-Divisionto be used to
computeneutronscatteringin the soilof Mars and to describethe transportof
the scatteredneutronsthroughthe Martianatmosphereto an orbitingneutron
detector. This system shows promise of being able to map the occurrenceof
water on Mars. A futurelibrarywill includethe low temperature(200K) scat-
teringcrosssectionsforwaterneededformore realisticcalculations.
Becauseof the variousimprovementsto NJOY describedelsewherein thisre-
port, we have begun a programto recomputecross sectionsthatmay be particu-
larlyaffected. We are also tryingto completethe processingof all the eval-
uationspreparedfor ENDF/B-Vrevision2. Some recentjobs under thisprogram
follow.
Material Format
H-1 PENDF,69x24GENDFH-2 PENDF,69x24GENDFH-3 PENDFHe-3,He-4 PENDFBe-9 PENDF,69x24GENDFc PENDF,69x24GENDFcl 69x24GENDFMg 69x24GENDFAr PENDFZr PENDF,69x24GENDFPu-239 PENDF,69x24GENDF,80x24GENDFPu-240 PENDF,69x24GENDF,80x24GENDF,ACER
80
III.NEUTRONACTIVATION,FISSIONPRODUCTS,AND ACTINIDES
A. DelayedNeutronSpectrafromFissionPulses[T.R. England,M. B. Butler,—E. D. Arthur,A. Sierk (T-9),C. W. Maynard(Univ.of Wisconsin),andF. M. Mann (HanfordEngineeringDevelopmentLaboratory)]
Currentwork is directedtowardan improvementin precursordata suitable
for aggregate,time-dependentcalculationsin summationcodes. This includes
directfissionyield distributions,delayedneutronemissionprobabilities(Pn)
and precursorspectra. Calculationsrequiresimilarinformationfor the pre-
cursorparents.
Most recent effortshave been on a reevaluationof Pn valuesand on ex-
pansion of the individualprecursorspectra. The fissionyields in use are
describedin Ref. 105, with the exceptionof 238U fast fission,in which the
proton pairing parameterhas been reducedby approximatelya factor of two.
1. Pn Values.
The current evaluationincludes data through mid-1985. The evaluated
measureddata (82 nuclides)are also used to derivefittingparametersfor the
Hermann-Kratzequation106 and the resultsused to estimateunmeasuredPn values
for 28 nuclides. The evaluationprocess is describedin Ref. 107. Table X
lists the currentlyevaluatedand estimatedPn’s; the estimatedvalues can be
identifiedby the lack of an uncertainty.The actualuncertaintyis probablya
factorof two or more,but the 28 precursorshavingestimatesaccountfor only a
fewper centof the totalcalculateddelayedneutronrate (~lOxat equilibrium).
In addition,TableX lists the sourcesof spectraand the time-groupassignment
in the conventionalsix groups. The basisof the groupassignmentis discussed
in Ref. 108; however,group assignmentsare not used in the currentcalcula-
tions. Instead,we use the precursorsand theirparentsin explicitsummation
calculations.The additionaldata needed for such calculationsare based on
ENDF/B-Vand listedin Ref. 109,with the exceptionof more recentPn, yieldand
delayedspectradata.
2. Numberof Precursors.
Currentlywe are using 110 precursorsand their parents--about228 nu-
elides. Based on energetic derived from mass tables,there shouldbe > 270108precursors. These additionalprecursorsare generallyvery short-livedand
have smallyields.We haveexaminedthe effectof theseprobableprecursorsonly
81
on the totaldelayedneutronrate at equilibriumand find that they would in-
crease the calculatedrate by only 1-2%. We will examinethese for fission
pulses,and particularlyfor their
duringthe nextT-2 ProgressReport
CSZZAAASHL(s)
—
Zn 300790 0.313Ga 310790 3.00Ga 310800 1.66Ga 310810 1.23Ga 310820 0.60Ga 310830 0.31Ge 320830 1.9Ge 320840 1.2Ge 320850 0.250Ge 320860 0.247As 330840 5.3As 330850 2.03k 330860 0.9AS 330870 0.30Se 340870 5.60Se 340880 1.50Se 340890 0.427Se 340900 0.555Se 340910 0.27Br 35087055.7Br 35088016.0Br 350890 4.38Br 350900 1.80Br 350910 0.600Br 350920 0.360Br 350930 0.176Kr 360920 0.360Kr 360930 1.29Kr 360940 0.210Kr 360950 0.780Rb 370920 4.53Rb 370930 5.86Rb 370940 2.76Rb 370950 0.380Rb 370960 0.204Rb 370970 0.170Rb 370980 0.110Rb 370990 0.145Sr 380970 0.40Sr 380980 0.65Sr 380990 0.6Sr 381000 0.618
Pn VALUES
Pn
0.35210.2280+/-0.2290+/-11.0000+/-20.4000+/-50.0000+/-0.0040*2.77529.3856+/-10.15080.0870+/-62.0320+/-8.6692+/-
contributionto high-energydelayedneutrons
coverage.
TABLEX
AND SOURCEOF DATAa
Uncert. Gp.
—
50.2670 40.3800 40.8300 41.6900 56.8500 5
44
8.0000 66
0.0440 37.9284 41.9957 4
43.8296+/-19.93970.152CJ +/- 0.02200.8530+/- 0.012010.5219+/- 3.29985.475215.50682.5600+/- 0.20006.3400+/- 0.500014.1000+/- 1.090024.9000+/- 2.360018.3000+/- 1.870043.7318+/-12.334624.04760.0327+/- o.oo381.9900+/- 0.19006.3300+/- 2.49006.4000+/- 3.70000.0101+/- 0.00071.3700+/- 0.090010.2000+/- 0.67008.7900+/- 0.560014.2000+/- 0.940027.1000+/- 1.960013.5000+/- 1.030016.0000+/- 2.20000.0055+/- 0.00260.3030+/- 0.05400.4770+/- 0.14800.7380+/- 0.0490
63455612345565465334566665555
---—- Source ---—-
Pn
TheoryMeas.Meas.Meas.Meas.Meas.TheoryTheoryMeas.TheoryMeas.Meas.Meas.Meas.Meas.Meas.Meas.TheoryTheoryMeas.Meas.Meas.Meas.Meas.Meas.TheoryMeas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.
Spec.
TheoryMeas.1Meas.1 +aug.Meas.1 +aug.TheoryTheoryTheoryTheoryTheoryTheoryTheoryMeas.1+aug.TheoryTheoryTheoryTheoryTheoryTheoryTheoryMeas.2Meas.1Meas.2+aug.Meas.2+aug.Meas.2+aug.Meas.2+aug.TheoryTheoryTheoryTheoryTheoryMeas.2Meas.1+aug.Meas.2+aug.Meas.1+aug.Meas.2+aug.Meas.2+aug.Meas.2+aug.TheoryTheoryTheoryTheoryTheory
82
TABLEX (Cont.)a
Cs ZZAAASm(s)
Y 390971Y 390970Y 390981Y 390980Y 390990Y 391000Zr 401040Zr 401050Nb 411030Nb 411040Nb 411050Nb 411060MO 421090Mo 421100Tc 431090Tc 431100Ag 471210Ag 471220Ag 471230Cd 481280In 491271In 491270In 491280In 491291In 491290In 491301In 491300In 491311In 491310In 491320Sn 501330Sn 501340Sn 501350Sb 511340Sb 511350Sb 511360Sb 511370Te 521360Te 521370Te 521380Te 521390I 531370I 531380I 531390Sr 381000
I 531400I 531410
1.113.70.652.01.40.8002.5730.4931.5004.802.8001.000104092.7721.400.830.81.50.391.0531.3003.760.842.50.990.1110.580.1110.280.121.471.040.41810.2001.820.820.47819.03.51.60.58024.56.502.380.618
0.8600.46
Pn Uncert.Gp.
—
0.1110+/- 0.0370 40.0560+/- 0.0053 33.4800+/- 0.9800 50.2420+/- 0.0190 41.0400+/- 0.1870 40.8190+/- 0.0590 50.0481 40.3571 +/- 0.7700 5000021* 40.0078* 30.9962* 40.1633 40.0292 40.5545 40.0199* 40.0972 40.0770+/- 0.0050 50.1880 +/- 0.0120 40.5560+/- 0.0350 50.0295 40.7000+/- 0.0800 40.5820 +/- 0.0500 30.0600+/- 0.0090 42.2500+/- 1.4300 42.9400 +/- 0.4500 41.5600+/- 0.1240 60.9450+/- 0.2850 51.7600+/- 0.2500 61.6000+/- 0.3320 66.5200 +/- 0.6850 60.0722* 4
18.9000 +/-l4.4OoO 45.2786 50.1160+/- ooO120 2
17.8900 +/- 1.5400 429.8225 +/- 3.9095 420.479 5
1.1700+/- 0.5400 22.7800+/- 0.6600 37.0000+/- 2.3500 44.4045 57.0500 +/- 0.5400 25.4300 +/- 0.5400 39.94oo +/- o.8000 40.7380 +/- 0.0490 5
9.3500+/- 0.9900 421.5000+/- 3.9000 5
---— Source---—Pn
Meas.Meas.Meas.Meas.Meas.Meas.TheoryMeas.TheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryMeas.Meas.Meas.TheoryIN127Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.Meas.TheoryMeas.TheoryMeas.Meas.Meas.TheoryMeas.Meas.Meas.TheoryMeas.Meas.Meas.Meas.
Meas.Meas.
Spec.
TheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryTheoryIN127TheoryTheoryIN129Meas.1INL30Meas.1IN131TheoryTheoryTheoryMeas.1+aug.TheoryTheoryMeas.1+aug.TheoryTheoryMeas.1TheoryTheoryTheoryMeas.1Meas.1Meas.1+aug.Theory
Meas.1+aug.Meas.1+aug.
83
TABLEX (Cont.)a
CsZZAAAS HL(s) Pn Uncert.Gp.
.— —I 531420 0.200I 531430 0.401Xe 541410 1.72Xe 541420 1.22Xe 541430 0.96Xe 541440 1.10Xe 541450 0.9& 55141024.9@ 551420 1.69(% 551430 1.78Cs 551440 1.001Cs 551450 0.59(k 551460 0.340@ 551470 0.546Ba 561470 1.755Ba 561480 3.325Ba 561490 0.695Ba 561500 0.962La 571470 5.00La 571480 1.3La 571490 2.408
— —5.534152.35230.0324+/- 0.00670.3970+/- 0.04601.38832.39533.23180.0375+/- 0.03900.0960+/- 0.00741.6300+/- 0.11003.1800+/- 0.220013.8500+/- 0.920013.5000+/- 1.180034.9000+/-11.50000.0190+/- 0.00170.0120+/- 0.01800.4350+/- 0.12306.80250.0470+/- 0.02900.1110+/- 0.0081O.1OO8*
i54444424445554354344
---—- Source---—-Pn Spec.
Theory TheoryTheory TheoryMeas. TheoryMeas. TheoryTheory TheoryTheory TheoryTheory TheoryMeas. TheoryMeas. Meas.1Meas. Meas.1+aug.Meas. Meas.1+aug.Meas. TheoryMeas. TheoryMeas. TheoryMeas. TheoryMeas. TheoryMeas. TheoryTheory TheoryMeas. TheoryMeas. TheoryTheory Theory
aPn and itsuncertaintiesare listedin per cent. UnderPn Source,the notationof measurementrefersto an evaluationof measurements, and theoryrefersto useof the Herrmann-Kratzequationusingfittedparametersbasedon the measuredPn’s.Under SpectraSource, Meas. 1 refers to normalizedspectrareceivedfrom G.Rudstam,and Meas. 2 refersto normalizedspectrareceivedfromK. Kratz. Ineithercase,+aug. refersto an augmentationof thesespectrausingthe nuclearmodel code BETA, as discussedin the text. Theoryalso usesthe BETA codefortheoreticalspectra. The asterisk(*) followingthe Pn value identifiesthosetheoreticalvalues using Wapstra 1983 mass values. All other nuclidesuseWapstra1981or M611er-Nixmasses.
3. PrecursorSpectra.
Presentlywe havenormalizedmeasuredspectrafor 30 nuclidesand we expect
to add an additional4 or more. These30 accountfor 80 to 90% of the totalde-
layedneutronemissionat equilibriumand aftera few secondsdecayfollowinga
fissionpulse,dependingon the fissioningnuclide. “
Current calculationsuse measuredspectrasuppliedby G. Rudstam*110 or
K. -L. Kratz,*lllmodifiedas notedbelow,and theoreticalcalculationsusing
the BETA code112 for unmeasuredspectra.
*The actual data files were suppliedby G. Rudstam,SwedishResearchCouncilsLaboratory,University,
84
Studsvik,Sweden,in 1981 and by K. -L; Kratz,Johannes-GutenbergMainz,Germany,in 1983.
Thereare a numberof problemswith spectra. Measuredspectragenerallydo
not includethe completeenergyrange. Thus, the 3He spectrometersare gener-
ally deficientat energiesbelow - 70 keV, and hydrogenrecoilspectrometers
coveronly - 1 MeV. Becauseof the low count rateat highenergies,the meas-
ured spectrawith eitherspectrometergenerallycut off at 3 MeV or less. The
measurerreportsresultsnormalizedoverthe measuredenergyrange,not absolute
values.This presentsa difficultywhen the spectrafrom differentexperiments
stressingdifferentenergyrangesare to be combined,or when theoryis used to3extendthe spectra. We have generallyassumedthatthe He spectrometerresults
are the most accurateover an energy rangethat can differfor each emitter.
Other resultsare first normalizedto the 3He data using ratiosof integrals
over a Small, 3commonenergyrangeand then added to the He datato extendits
range. The resultingcombinedspectra are then renormalizedover the total
erlergyrange. This procedureis necessarilysubjectiveand requiresa detailed
examinationand individualdecisionfor each emitter.
Beforeany spectrawere combinedor extendedby theory,we comparedthe He3
data of Rudstamand Kratz. Figures60 and 61 are typicalof the approximately
ten precursorscommonto each measurer. They are sufficientlysimilarso that
there is little reason to choose one over the other, and uncertaintiesare
sufficientlylargethat we see no reasonto combinethesesourcesintoa compo-
sitespectrum. The choicemade is identifiedin TableX.
We thenexaminedthe rangeof measuredenergiesusingdifferentmass tables
and any availableleveldensities,spins,and paritiesof the precursor’sdaugh-
ter and granddaughternuclidein the BETA code.112 This portionof the study
was focusedat an augmentationof the high-energyspectra,if necessary,of the
measureddata. Figures62-65 are typicalof the range of comparisonsof the
theoreticaland measuredspectrausing the mass tables (Q and Sn, the neutron$
separationenergy)that best agree with the measuredspectra. The BETA code
cannotprovidethe fine energystructure;it generallyappearsto underpredict
the low energyand overpredictthe high-energydelayedneutrons. Partiallythis
is a resultof the normalizationover a largerenergyrange. However,it could
also be that the beta-strengthfunctionand leveldensityneed improvement.In
any case,we are using the BETA code resultsonly for unmeasuredspectraand to
add a high-energytail to some of the measuredspectra. The tail is firstre-
duced to an approximatevalue near the end of eachmeasurement.To date it has
been reducedessentiallyto the lastmeasuredvalue,but, in the future,it will
85
0.020
0.015
0.010
0.005
O.ooc
37-RB– 96GCOMPARISONOF EXP.
SOLID=KRATZD_RUDSI’AM
1j .. ,
..
.,
I I I I I I I I 1 I I I500 1500 2000 2
&wH (KeV)
Fig. 60. Normalizeddelayedneutronspectrafor nuclide‘6gRb.
0.015
0.010‘
0.005
0.000
37-RB– 98GCOMPARISONOF EXP.,...:;:: SOLID=KRAIZ
DO%RUDS’I!AM
1...;
. .
L.
:..:
I I I i I i I I I I I I I I I I 1 I I I I [ I1000 1500 2
E’IiiliGYtKeV)
Fig. 61. Normalized delayedneutronspectrafor nuclidegag~~.
10
If)
0.05
0.04
0.03
0.02
0.01
::,.$.
A::,.;;::..-;;:“;
. .:.
,- :.
-, ;-;,-1,, .-::.,
I
\
-,
..,-:.‘-.
L,.
-,,.
‘-,..‘-l-,. .
37–RB-92GSOLID-EXP
Pm
DASH-MOD AP83MASSES;
..‘:.
“-..“..,-,-
“--,-.“-. %
0.00+--‘ -----
I I I I0
ENERGY(Ii$”Fig. 62. Normalizeddelayedneutronspectrafor nuclide9263R~.
0.020
0.015
0.010
0.005
0.000
1000
W–m- 94GSOLID-EXPP ‘mDASH-MOD AP83MASSES;
---‘“-%.
I I I I I I I I I I I [ I Io
i I I I I I I I I I1000 1500 2000 2500 3000 3500
ENERGY(&V)Fig. 63. Normalizeddelayedneutronspectrafor nuclideg%’~~.
87
O.olo-
0.oo5-
0.000-,
51-SB–135G
!?&ii?:E&RMss@
------------ .I I I I I
o ‘ 500III1II1IIII[I I I I I r I I I I I l-r I I I I 1 I I I
1000 1500 2000 2500 3000 3500 4CENERGY(E@
Fig. 64. Normalizeddelayedneutronspectrafor nuclide135gSb.
0.035-
0.030-
0.025-
Y0.020-.
y
0.015-
0.010-
0.005-
0.000--
)0
55-CS-144G
RRz..fw&%fssm
i,:%,,,!,.-
i,
--------- --------------
1 I I I I I I I I I I I InAI I i I I I I I I 1 1
0 500 1000 1500 2000 2500ENERGY(KEN)
Fig. 65. Normalizeddelayedneutronspectrafor nuclidelh%c~.
88
be based on a small rangenear the end of the measurements.The pointof addi-
tion is subjective,basedon uncertaintiesand plotsof the measurement.Twenty
of the thirtymeasuredspectrawere extended;the point of additionand the
fractionalreductionare listedin TableXI.
TABLEXI
MEASUREDPRECURSORSHAVINGEXTENDEDSPECTRA
Nuclide Joined Frac. Nuclide Joined Frac.— —KeV — KeV
31Ga 80G 1060 0.6427 31Ga 81G 1690 0.775933As 85G 2520 0.4662 35Br89G 2290 0.533935Br 90G 2830 0.5423 35Br91G 2940 0.302235Br 92G 3000 0.8393 37Rb93G 1230 0.251437Rb 94G 2460 0.9625 37Rb95G 121O 0.141237Rb 96G 2220 0.1060 37Rb97G 2110 0.034237Rb 98G 2470 0.0965 50Sn134G 1620 0.522251Sb135G 1910 0.6393 531 139G 1610 0.3473531 140G 1760 0.2566 531 141G 1680 0.425555CS143G 1260 0.3210 55CS144G 1430 0.1771
Becauseof the recentinterestin higherenergies,it has beennecessaryto
recalculatethe spectrafor 70 unmeasurednuclides. Our previousresults,noted
in Ref. 108,extendedonly to 5 MeV or less. Basedon comparisonssuchas those
in Figs. 62-65, we have used QP
and S values derived from Wapstra mass
tables,*113n 114whereavailable,and fromM611er-Nixotherwise.
Presently,we are addinglow energyspectra,havingbeenmeasuredrecently115 116with a hydrogenrecoilspectrometer and otherdatameasuredby Reeder and
Kratz.1’7 In addition,we anticipatereevaluatingthe Pn valuesand incorpor-118atingsome recentmeasurementsby Reeder.
4. SummationCalculations.
Before any of the improvementsin fissionproductyields,Pn and spectra
data were made, it was shownin Ref. 108 thatsummationcodecalculationscould
greatlyextendthe low- and high-energyrangeof aggregate,evaluatedspectra,
and they could increasethe number of fissionablenuclideshaving evaluated
spectra. The earlierwork was basedon interestin improvementsin equilibrium
spectra. Time-dependent,aggregatespectrafollowinga fissionpulse are even
more difficultto measureand requireeven more accurateprecursordata, es-
peciallyfissionyields,
*W,3pstra81 refersto abut not published.
for use in summationcodes.
preliminary1981 set of massesdistributedfor comment
89
We have used a modifiedversionof the CINDER-10code119 for computing
aggregatepulse spectra. Prior to the extensionsof spectranoted above, a
typicalpulse result is shown in Fig. 66. For high-energyneutrons,a better
representationis given in Fig. 67, where the fractionof neutronsabove the
abscissaenergy is plotted. The rapid drop between2-3 MeV resultsfrom the
lack of any precursorspectraabove3 MeV. This, in fact,was the motivation
for the extensions.Figure68 comparesthe new resultsat 20 secondsaftera
pulse with the old. Here 20 measured spectra were extended,but no other
changesweremade.
The values labelledtime O on Figs. 66-68shouldactuallyapplyat - 10-4
s. There could be neutronsemittedfrom the highlyexcitedfissionfragments
duringthe firstfewmicrosecondsfollowingfission.
Similarresultshavebeen computedfor otherfuels.
107
106
105
104
103
Id
101
10°
TIMEDEPENDENTSPECI’RA FOR ‘5U F!! PULSE
.,...-. ‘.--. #--,-
~q
IF,.*-.,,L .-
~,,,:”:o-~,-.,,.
Fig. 66. 235U delayedneutronspectra(1.3E+ 16 fissionpulse).
ix)
90
10°
10-’
10-2
10-4.
10-5
10+
-u F~ FISSIONPULSE
\{~ ,,101
I I I I I I I I II I I I I I I I I I I I I I i I I500 1000 1500 2000 2500 3000 3500 4
ENERGY(KeV)
Fig. 67. Fractionof totalon pulsespectra).
delayedneutronsabove abscissaenergy (based
10°~
lo-’= 235U Pm DN FRAC AT 20 S
\
..... EXTENDOD-.. m 20NucuDEm....
lo-’=... OR161NALRAC.‘...
.,,‘.‘1...
10-2 ‘,:..‘.,..‘1‘1:‘,:-..-----
10-7 ------! 1 I I I 1 I0 1000 2000 3000 4-(DO
Fig. 68. 235U fractionof total delayedneutronsabove abscissaenergy.
91
5. Confirmationof Spectra
The high-energyaugmentationof 20 measuredspectrais
68, but it has very littleeffecton the measuredportion
someapplications,the energiesabove- 2 MeV are important
pendentconfirmationof at least the orderof magnitudeof
of an aggregateexperiment.
very evidentin Fig.
of the spectra. For
and we needan inde-
theseresults, short
A.‘Sierk120used a completelystatisticaland evaporationmodelto get ap-
proximatespectra. Mass chainyieldsand theirdistributionvs Z were assumed
to be describedby a Gaussian. The ft valuewas fit to an approximationfor
halflives(separatelyfor odd-oddand odd-evennuclei). The rateof beta decay
to excitedstateswas approximatedand the emissionspectrumwas assumedto be a
simple evaporationmodel. In actualcalculations,true halfliveswere applied
where they were known,and the same sourcesof massvaluesemployedin the BETA
codewere used.
Consideringthe numberof approximations,it was not clearthatthisstudy
could confirmthe more detailedsummationcalculations,seen in Fig. 68; how-
ever, as demonstratedin Fig. 69, the resultscomparevery well, differingby
only a factorof three in the integralvalue at 5 s, the only time compared.
This is within the estimatedfactor of five uncertaintyin the statistical
calculation.
10910’
107
106~05
104
103
ld
ld
TIMEDEPENDENTSPECTRAFOR‘5UFASTPULSE(5 s COOLING TIME)
3
1 k-. /;::
‘.‘..‘.,‘...‘.‘.
$.‘.,
RATIOOFT-~-91NTECRALS418‘.●.‘.‘.‘.
1‘.‘!‘.
loOLl—l— .,‘.
~~- 1 4 I0 1000 2000 3000 4000 5000 6000 7000
ENERGY (KeV)
Fig. 69.235U delayedneutronspectra.
B. ENDF/B-VIYields(M.B. C. Butlerand T. R. England)—
In a preliminaryENDF-VIevaluation,105ENDF-VMfissionproductyieldswere
modifiedby extendingthe yieldsalongmass chains. For the 50 yieldsetscur-121
rentlyin ENDF-VM,the pairingmodel was used to extendyieldson the neutron
rich side of the mass chains66-172. The influenceof pairingon the distribu-
tion of the yieldswas also taken into accountby the use of both neutronand
proton pairing factorsin the yield extension. This process resultedin in-
creasingthe numberof yieldsper set froman averageof - 1100to an averageof
- 1200. The new yield sets were testedby executingthe OKLA code,which em-
ploysvariousconservationprinciplesin the integraltestingof yielddata. In
terms of satisfyingthese basic conservationlaws,the 50 extendedyield sets
appearsatisfactory.
With the exceptionof modifyingthe pairingused for 238U fast fission>
thiseffortwas primarilydirectedtowardgettinga completeset of yieldsin an
EN_OF/Bformat.
c. Beta and GammaFission-ProductDecayEnergyComparisonswithRecent—JapaneseMeasurements(Pulse)[T.R. England,R. J. LaBauve,W. B. Wilson,and M. Akiyama(Universityof Tokyo)]
For 238U and 232Th fast fission,we havemade severalcomparisonswith the
recent Japanese measurements. Figures 70-73 illustratethese comparisons.
When the JapaneseNuclearData Committee(JNDC)1.5 nuclidedecayenergies
replacethosein ENDF/B-V,the agreementis remarkablyimprovedoveruse of only
ENDF/Bfiles. Also,the Japanesecalculationsusingonly theirfile (whichuses
ENDF/B-Vyields)are nearly identicalto those using ENDF/B-V+ JNDC nuclide
energies.
Similarly,we have seena gooddegreeof improvementwhen comparingENDF/B-
V + J?JDCenergieswithUS measurementsfollowing235Uand 239Pu thermalfission.
93
BetaDecay Heat for”% (RI lse)
T T Experiment (Aktyam& eL al)J.
— CalculaUo!xENDF@-V+ JNDCEnergle#
............ CalculaUoruENDF/B-VONLY------ ~lculntlowJNOC—.- Calculatioru ENDF@-lV
—. —.—. -
1 I I I I1111 I I I I I1111 1 I I I I111J 1 I 1 I Ill
102 103 104CoolingTime(s)
n-..Fig. 70. Comparisonof Japanese&decay heat for ‘JzTh (pulse)with calculations.
.
1.4,1.3i
1.21
.1
Gamma Decay Heat for 23’Th (Pulse)
iExperiment (Aklyanm et. al)
i%
— (hlculatioru ENDF@-V + JNDCEnergtes
.-w-- Calculation SNDF@-V ONIX. . ------ Cdculatlon: JNDC
—.. Cdculatiom ENDFfi-lV
....-....~......
%
....--””””- ...,%,......T...
....—.-
.//
020.11o! I I 1 I I I Ill I I I I I 1111 I i I I i I Ill I I I 1 11(
102 103 104CoolingTime(s)
. . .
t
Fig. 71. Comparisonof Japanesey-decayheat for ‘2LTh (pulse)with calculations.
94
BetaDecayHeatfor“SU (Pulse)1-
i Experiment(Aklyama,etal)
— &lculaUon:ENDF~-V+JNDCEnergies---- CalculaUomENDF@-VONLY
4
------CdculatiomJNDC—.- CaleulaUomENDFfi-IV
I I I I I I 111 I 1 I I i 111[ I I I I
102I I I 11[ I I I I [1-r
103 104Cooling‘IIme(s)
Fig. 72. Comparisonof Japanese (kdecay heat for 238U (pulse)with calculations.
1.4 IGamma DecayHeatfor‘W (Pulse)
I Experiment(Aklyamqetal)
— CdculaUomENDF~-V+ JNDCEnergiee
-----CdeulatiomENDF@-VONLY------CdculaUomJNDC—-- CalculatlotuENDF@-IV
I 1 I I 1 Ill] I I I I I i 1[[ I I 1 I I 1111 I I I I Illr102 103 104
CoolingTime (s)
Fig. 73. Comparisonof Japanese y-decay heat for 238U (pulse)with calculations.
95
D. Evaluationof10,11
B(a,n) Cross Sections [W. B. Wilson and R. T. Perry(TexasA&M University)]
The (a,n) cross section, measured by Walker122
for ‘a% below 5 MeV, has
been used in SOURCES123 124code calculations of thick target B(a,n) yields,
producing values about 40% higher than yields measured for 3.5-5.5 MeV a’s onboron 125,126,127
. Calculations of (a$n) neutron spectra for commercial high-
level waste problems128
with B require individual IOB and 11B cross sections
extendingabove 6 MeV, as well as product level branching fractions. The avail-able IO,ll,nat
B(a,n) cross-sectiondata have been accumulatedas follows:
(a) the ‘atB(a,n) data of Walker;122
(b) cross sections and product nuclide level branching fractions calcu-
lated with the GNASH code;8
(c) the 1lB(cr,no)cross sections calculated from the 14N(n,ao)reciprocal
reaction cross section of ENDF/B-V85 from the evaluationby Young and
Foster;129
(d) the 10’11B(a,n) cross sections stripped from the thick target yield
data of Bair and del Campo125
using the a stopping cross-sectionfunc-
tions of Ziegler.130
Cross sections obtained from these sources, as shown in Fig. 74, appear to be
divided into a group of higher-magnitudedata containing (a), (b), and (c) above,
and the lower-magnitudestripped cross sectionsof (d).
The followingobservationsmay be made
(a) Yields calculatedwith the Walker
(b) The GNASH calculationsshould be
on these data:
data are higher than measured yields.
expected to produce relativelyaccu-
rate partial cross-sectionratios a(a,n2)/o(&,n) (i.e.,product level
Q branching) but less accurate cross-sectionmagnitudeswhen used to
describe light nuclei.
(c) The 14N(n,ao)cross section used in the reciprocalreaction calculation
is an evaluation of widely varying data and closely follows the high-129
est values.
96
(d) Yields calculated with
(ajn) yields of BairIO,ll,nat
B(cr,n)yields,
the cross sections stripped from the 1O,llB
and del Campo agree well with all measured
as shown in Table XII.
The cross-sectiondata stripped from the Bair and del Campo yields have been in-
cluded in the SOURCES data library,as have level branching fractionscalculated
from partial cross sectionsproduced in the GNASH calculations.
35C
300
250
200
150
100
50
0
GNASHcalculations
012345678a Energy, MeV
Fig. 74. Boron (a,n) cross-section
9 10 11 12
data.
97
TABLE XII
COMPARISONOF MEASURED (a,n) THICK TARGET YIELDS AND VALUESCALCULATEDWITH CROSS SECTIONS STRIPPEDFROM YIELDS
MEASURED BY BAIR AND DEL CAMPOa
(alpha$n) thick target yields$ n/ 1.e+6 alphas=== === === === ==== === === === === === ===== === === === === ==. .== == ---- ------
boron-10 boron-n natural boron=== === === === === =.. = =================== ===================
E, MeV Meas Cal c Zdi++ Meas Calc Xdiff Meas Calc Zdi++====== ====== ====== ---------- ----====== ====== -——-= ====== =..=== ---—-
S.s 0.331 O.sbl -1-9.1 3.803 S.456 - 9.1 3.150 2.840 - 9.84.0 0.7S8 0.786 -I-3.7 7.618 7.254 - 4.84.5
6.238 5.967 - 4.31.924 1.948 + 1.2 12.64 12.26 - 3.0 10.63 10.21 - 4.0
5.0 3.S52 3.574+0.6 18.4X 18.04 15.64- 2“1 bi9.6
15.16 - 3.15.3 4.762 21.47 1s.15 - 7.4
C21.0 18.15 -13.65.!5 5..674 5.696 + 0.4 24.0S 23.66 - 1.6 20.59 20.09 - 2.46.0 8.578 S.604 + 0.3 29.24 28.86 - 1.3 25. S5 24.83 - 2.16.5 12.29 12.32 + 0.2 SS.92 3s.5s - 1.1 29.S!5 29.X2 - 1.87.0 16.78 16.82 + 0.2 37.52 37.16 - 1.0 33.62 33.11 -1.5
aAll measured yields are from J. K. Bair and J. G. del Campo,125unless other-
bwise noted.-See G. V. Gorshkov,V. A. Zyabkin, and O. S. Tsvetkov,Ref. 126.‘See J. H. Roberts,
Iv. APPLICATIONS
Ref. 127.
A. Initial Loading Calculationsfor the RI SAFR Design [(R. J. LaBauve,D. C.George, and E. Specht (RockwellInternational)]
As part of the US Departmentof Energy’s directive that the national labor-
atories provide assistance to private companies in their fast reactor research,
development, and design, Los Alamos National Laboratory has cooperated with
Rockwell International (RI) by performing a series of calculations for the131initial loading of the RI design for SAFR, a heterogeneousfast breeder reac-
tor. This report gives results of calculationscompleted in FY1985 and indi-
cates additionalwork needed to assure a safe start-up of the reactor.
The basic one-sixth core, hexagonal-Z model used in our calculationswas
taken from data sent to us by Argonne National Laboratory (ANL) for the oxide
version of SAFR; ANL is assisting RI in the SAFR core design. Due to the fact
that this model is set up
than we feel was needed for
simplifiedthis Hex-Z model
our Hex-Z model by keeping
for depletion calculations,it contains more detail
our initial start-up calculations. Consequently,we
for our application. Our R-Z model was derived from
volumes (actually,areas) equal in going from hexa-
gonal to annular regions. The R-Z model is shown in Fig. 75, and the Z-plane at
98
mid-core (Z = 132.1 cm) of the Hex-Z model is shown in Fig. 76. These models
were used in the preliminarycalculationsdescribedbelow.
The nuclear cross-sectiondata we used were derived from ENDF/B-V132 data
processed by NJOYIOO into the 80-group MATXS6133 fine-group library. The
TRA.NSX133code was used to produce the 12-group library in the ISOTXS134 format135requiredby DIF3D, the code used for two-dimensionalR-Z and three-dimension-
al Hex-Z calculations. Initially, TRANSX was run to generate 80-group cross
sections for each of nine different compositionsused in the models. Table XIII
gives the correspondence between TRANSX regions and the zones show in the
figure for the R-Z model. A DIF3D 80-group run was made using the R-Z model to
generate 80-group fluxes for subsequent use in a second TRANSX calculation to
collapse to 12-groups. The 80- and 12-group energy structures are given in
Table XIV. The last TRANSX step produced 12-group homogenized cross sections
for the nine compositions and also microscopic cross sections for what are
referred to as “IB,” “OC,” and “RRM ❑aterials, using Zone 1 (IBO1) and Zone 3
(OCOI and OC02) fluxes to collapse the cross sections for the “IB” and “OCH
materials, respectively;Zone 9 (RRO1) fluxes were used for all TR’! materials1OB 11
except 7 B, and C for which Zone 8 (CRI1 and CR12) fluxes were used.
264.2,OIDCRO1 I I 1 I I I I I I I
RCRI1ZZ31B02=CR02 FIRKDIMlllCR12
r
RRfl
I I I I I I I I I IIn -em m mLrn3 m. . . . m ml
id “m N@CJ 4.
N r-)-r m hNn 403.c
R K-- —
Fig, 75, R-Z inodelof SAFRt99
0 IBO13Ocol
3IB021 OC02i CR02URBO13 RRO1u RR02
132.10
Fig. 76. Hexagonalplane at 132.1 m--mid core.
TABLE XIII
REGION CORRESPONDENCEFOR CROSS-SECTIONCOLLAPSE
~ANSXRetionIks@natioqfi-ZaeN~n Hex-ZZoeN~n
ARA-LowerAxialReflector
ARKUpperAxialReffector
IBO1-InnerBlanket#l
IB02-IrmerBlanket#2
OCO1-OuterCOxelH
oco2-outercoxe#2
CRO1-ControlRd.s#l(out)
CR02-ControlRds#2 (out)
CIU1-ConrrolRods#1(in)
CRU-ControlRods#2(in)
ABO1-AxialBlanket#l
AB02-k&ilBhmket#2
RBO1-RadialBlanket#1
RRO1-RadialReflector#l
RR02-RadialReflector#2
100
ARscARscLBscIBscOcsCOcsc
CRoscCRIscCRIscABsc
ABscRBscRRlsc
RR2Sc
9
9
1
1
3
3
3
3
8
8
1
1
1
9
9
6
6
1
2
3
3
7
7
8
8
4
4
5
9
10
TABLE XIV
BOUNDARIESFOR 80-GROUPSTRUCTURE
(&IQ
02’03
H06070809101112131415161718
;:21
z24
z27282930
%33343536
;?3
%
QLyz
1.6905X107 421.4918X107 43L3499XI07I.1912XI07 :LOOOOX1O7 467.7880X106 476.0653X106 484.7237X106 493.6788Xl&a 502.8650X106 512.2313X1($ 521.7377x105 531.3534Xl@aLI943X106 :1.O54OX1O6 569.3014X1O58.2085Xl@ ::7.2440XlC# 596.3928Xl& 605.6416X1($ 614.9787Xl&a4.3937x@ %[email protected]&a :2.3518Xl@;.:;g;;$ E
68l:[email protected]@ $%6.7379Xl@ 715.2475Xlti ;;4.0868X10’$a3.1828X1C+ 742.8088X1C+2.6058XI04 ;22.4788X1($ 772.1875XlC# 781.9305X1O4 79L7036Xl@ 80
Emin 1.3888Xl@a
a12-groupboundaries.
A series of preliminaryDIF3D problems was
1.3710XI018.31535.CU353.05901.12544.I399X1O-11.5230X10-1
run to study effects of changes
in mesh size, cross-section group structure, and geometry, and also to deter-
mine control rod worth. Results are summarized in Table XV. Note from the
table that for 80-group, R-Z geometry, going from a 14-cm core mesh sPacing to
a !;-cmspacing resulted in only a 4-mini-k change, so we compromisedat a 7-cm
mesh for the base 80-group, R-Z problem from which we derived the fluxes input
to TRANSX. Also, surprisingly,only a 2-mini-k differenceis observed between
R-Z and Hex-Z geometry; whereas a 2-mini-k difference is also observed between
the 12- and 80-group R-Z problems. The latter is probably due to the fact that
we collapsed using fluxes from only one blanket and one core region (the inner
101
—
ones), as indicated in Table XIV. Finally, note the
going to more planes for the Hex-Z problems. We did,
model for the loading sequencesdescribedbelow.
R-Z
R-Z
R-Z
R-Z
Hex-Z
Hex-Z
Hex-Z
TABLE XV
negligible difference in
however,
RESULTS OF PRELIMINARYDIF3D PROBLEMS
~~ %f~80 out 1.0279 60.s
80 out 1.0241 120.s
80 mid-way 0.9833 85.s
12 mid-way 0.9850 10.s
12 mid-way 0.9873 54.s
12 out 1.0179 54.s
12 mid-way 0.9871 110.s
use the 22-plane
“14-cm’’mesh
“S-cm’’mesh
“7-cm’’mesh,baseproblem
IsotopicXsecused
12z-plsnes
12zpIant?s
22z-pIanes
Alterationswere
figurations and also
made in the model to simulate several initial loading con-
to include detector locations. Low-level flux detectors
were assumed to be located in Ring 12 and a detector and/or source was assumed
to be located at the center (Ring 1). The reactor was assumed to be initially
loaded symmetrically from center out, and the assemblies in the rings not yet
loaded were assumed to consist of 95% Na and 5% HT9.
The altered R-Z and Hex-Z models are shown in Figs. 77 and 78, respective-
ly. Note that the sizes of the source and detector regions are exaggerated to
show up the figures. The compositionsof regionsRBO1, RRO1, and RR02, shown in
Fig. 78, were changed to 95% Na and 5% HT9 in the DIF3D problems.
for the hexagonal plane at mid-core (Z = 132.1 cm), Rings 1-6 are
loaded normally,but Rings 7 and 8 are shown to be loaded with RBO1,
95% Na in this case.
In Fig. 78,
shown to be
5% HT9, and
Results of this series of DIF3Dcalculationsare shown in Table XVI. The10
response of the detectors was simulated by calculating B(n,(x)and 235U(n,f)
reaction rates. The reaction rates are in units of reactions/see-nucleusfor an
assumed power of 15 watts. Note that the reaction rates at the LLFDs are down
by a factor of 103 from the centralvalue, but would be down by a factor of 105
if the radial blanket and radial reflectorswere in place during loading. Also
given in Table XVI are values of keff for the various loading configurationsand
“multiplication”values based on a relative keff obtained for the fully loaded
reactor with CR-1 withdrawn and CR-2 positioned at mid-core (see Table XV).
102
264.2OIODET I 1 1 t 1 1 11 1 1 I 1=ICRO1I??ZCRI1mIBo2 IIRKIDiUlCR02EacR12
.-e. “
*
162.6
132.0 /42-213 . 01121.9
101.6
81.3g7. g
198.1pg.: - pol m~ RB02 flB02
-1
OC02 RBO1 RRO1
17B02 RB02-----
1 J
I flRFI
RR02-/
I ! ! ! 1 Iu)
I I 1W(I3
Im 1 I 1 j
+ . . . . cum m. . . (n ml .—
rnz mo R Ui . . .rlw NM -$m- (% -m.
mm.- ——
Fig. 77. SAFR R-Z model for loading sequence.
❑ SOR31801EiocolZICRO1Ss1002Z30C02SlRf3013CR023RR01JRR02❑ OET
Fig. 78. Mid-core plane (Z = 132.10 cm) of Hex-Z model withRings I-6 loaded normally and 95% Na, 5% HT9 in other rings.
103
Although the calculationsdescribed in this report will be very useful in
planning SAFR initial start-up, they are incomplete and need to be extended.
Note in Table XVI the rather large changes in keff from problem to problem
caused by loading entire rings and/or fully withdrawing/insertingthe control
assembly blanks. Full core problems need to be run to observe the changes
caused by incrementalpositioning of the control rods and by adding one or two
fuel assemblies at a time as criticalityis approached. Also, because eigen-
value calculationsfor keff less than about 0.8 are not very useful, the prob-
lems shown in the table begin with normal loading
tions for loadings up to this point should also
performedwith a source located near the center.
RESULTS
Rez~ PositionofContig. CR-1 f=-2 %
TABLE XVI
up
be
through Ring 5.
done, but these
OF FIVE LOADING CONFIGURATIONS
13erectorReactionRates ReactionRateRatiosIOB(n,~) 235U(n,f) IOB(n,e) ‘5U(n,f) ‘w
1 out out .7894 2.9X10-18 1.4X1O-1’3 5.9XI04 4.8X104 4
2 out out .8645 2.4X10-18 L2XI0-18 8.1X104 6.7X104 7
2 in out .7547 2.6X10-18 1.3X1O-18 7.7X1O-4 6.4X104 3
3 in in .8144 L8X10-18 9.OXIO-’9 1.OX1O-39.IX104 5
3 out out .9415 1.7X1O-*8 8.7X10-19 LOXIO-3 9.1XI04 21
4 in out .9337 1.7XI0-18 8.6X1O-19 2.3X10-3 2.1X1O-3 17
4 out out .9957 -
4 in in .8670 1.6XI0-18 8.4X10-19 L6X10-3 L4XI0-3 7
5 in in .8941 1.1X1O-2O 6.1X10-21 1.3X1O-5 L3X1O-5 10
4(R-Z) in in .8692
Reactorcontigurationdescriptions:
1 Hexringsl,Z3,4,510adednormally.Inrings6,7,8fuel/axialbLmketassernbli=replacedwithdummy
as.semblieswith5%ITf9and95%Na.RadialbkrketandracfialreflectorswaealsorepIacedby5%HT9
and95%Na.IlYsinring6.
2 Sameasinl,butfuel/axialblanketassembliesloadedinring6.
3 .%rnessi nl,butfuelhxialblarrkta.wembtiesloadtxtinrings6and7.
4 Smeatil, butfuWnidbl*t~wrnbfi= loadedinrings6,7,and8.
5 FuUm~witirtidblti&mdmfl@~lmd2inpl=
“M”=”multipfiatiod’=@efiY(~ti-KeKhwhere~f=.9871formctor ~figu~ti~gswi~~-1
outandCR-2midway.
Reactionratesareinreactionakc-nucleusforapowwofls Watts.
R=ctimmtemtimmvdueat&ti~dwnW value.
Calcula-
must be
104
B. CalculationalSupport for MST-5 IsotonicallyTailored Ceramics Irradiation—Experiments (R. J. LaBauve)
In a cooperativeproject, Los Alamos National Laboratoryand Oak Ridge Na-
tional Laboratoryare planning a series of experimentsin which two isotonically
tailored ceramics [A1203 and “sialon” (Si3A1303N5)]will be irradiated in the
Oak Ridge High Flux IsotopeReactor (HFIR). These experimentsmay be considered
to be a first step in a program to develop ceramics for applicationsin which
the materials are exposed to high fluences of fusion neutrons. The purpose of
the HFIR experiments is to simulate a typical fusion “first wall” spectrum,
particularly to determine the gas-production/displacement-per-atomratio in the
irradiatedsamples. The isotopic content of the samples (e.g., concentrationof15N in sialon) irradiatedin HFIR will be varied to stimulatethe irradiationof
the ceramic in the first wall spectrum.
Our calculationalsupport for this project consistsessentiallyof modeling
the experiments and predicting results based on calculations using the REAC
code136 132and ENDF/B-V data. Specifically, we calculate the isotonically
tailored ceramic in the specimen in HFIR spectrumand compare results with those
calculatedfor the non-tailoredspecimen in the first wall spectrum. To date we
have identified several important reactions and have calculated the integral
cross sections of these in the HFIR PTP (peripheraltest position, near central
plane) and STARFIRE first wall spectra. Results, shown in Table XVII, are
further comparedwith earlier calculationsmade for the Oak Ridge Reactor (ORR).
Graphical comparisons of the cross sections for three of the more important
reactionswith the PTP and first wall spectra are shown in Figs. 79-81.
c. T-2 Macintosh ComputerNetwork (D. C. George)—
The arrival of the Apple Laserwriterprinter spurred developmentof the T-2
Network, linking the Apple Macintosh computers via an Appletalk network. The
Laserwritercan nowbe shared among all network members. The Laserwriterprint-
er support software was installed on appropriate software including MacWrite,
Microsoft Word and MacPaint. The Laserwriter’sTimes, Helvetica, Courier, and
Symbol fonts and Paragon’s Scientific and Cursive fonts were installed in the
word processing applications. The generation of mathematical equations was
investigatedand procedures for generatingvery readablemathematicalprose were
developed.
105
TABLE XVII
SPECTRUMAVERAGE CROSS SECTIONS
Reaction
14N(n,p)14N(n,d)14N(n,t)
14N(n,&)
160(n,~)
170(n,&)
27Al(n,p)
27Al(n,~)
‘a%i(n,p)
‘aV3i(n,&)
Threshold ORR Spectrum I-IFII?SpectrumEnergy(MeV) Average(rob) Average(rob)
0.0 35.8 439.15.72 0.367 0.8244.32 1.02 0.1730.17 96.5 17.382.67 11.0 1.70
0.0 105. 77.272.09 4.94 0.8054.19 0.75 0.1424.01 8.07 1.3992.75 3.46 0.624
1stwall SpectAve.(rob)
52.996.564.91
33.0521.81
81.1413.5219.7239.0227.91
Note: ORR andHFIR/STARFIRE1st Walldifferencesnotduetospectrumdifferencesonly.ORR calculationsreportedpreviouslyusedENDF/B-lV data,whereasENDF/B-V was used in theHFIR and 1st Wallcalculations.
a)>.-+0—
.-+
i10-8
lo-? IIIHIH,IIIHIM,1111111,llllnll,11111111!1111111~IlllllilIllflmwIIIIIVIIIVImTkTnml10-’1 10-’ 10-7 10-5 10-3 10-’ 101
Energy (MeV).
Fig. 79. Cross section for 1700(n,~) compared with the HFIR PTp and ST~lRE
first wall spectra.
106
‘L’- ~‘Solid – Cross SectionDash – PTP Spectrum
. Averoge Cross Section - 0.805 mbChain Oosh - Ist Wall Spectrum
: 10-’---,---Average Cross Section - 13.517 mb
>-:-.;--—-
> ‘..-,-->.-
-+- -L--; ----u L----‘—- I I— .- —-.-! —/.~ - — —
<10-3/-—-------
;-------nn
ii
10-7
L--- .-,
i,------,---------.
;,-----
10-’1 I I I I4
I I
Fig. 80. Cross section forfirst wall spectra.
6 8 10
Energy (MeV).27Al(n,p] Cowared with
12
the HI?IR
a)>.-+u—a)Yn
E.-+
10°Solid – Cross SectionOash – PTP SpectrumAveroge Cross Section - 0.142 mbChain Dosh - 1st Well Spectrum
4 .—
,------- , I.—.-— --------- -—-~
L. ------,,,----------
‘1L----------‘,.------
lo-’& I I I I I
Fig. 81.HFI:RPTP
4
Cross sectionspectra.
6 8 10
Energy (MeV).for 27Al(n,a) compared with
12 14
the STARFIRE first wall and
107
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
108
K. F. Liu, J. S. Zhang, and G. W. Shuy, “Comment on ‘Fusion of PolarizedDeuterons’,“ Phys. Rev. Lett. ~, 1649 (1985).
G. M. Hale and D. C. Dodder, “A=4 Level Structure from an R-Matrix Analysisof the Four-Nucleon System,” B. Zeitnitz, Ed., Proc. IOth Int. Conf. FewBody Problems in Physics, Karlsruhe, West Germany, 1983 (North HollandPress, 1983),p. 207.
H. M. Hofmann and D. Fick, “Fusion of Polarized Deuterons,” Phys. Rev.Lett. ~, 2038 (1984).
G. M. Hale, “Work on Polarized d+d Reactions Since the Madison Workshop,wLos Alamos informaldocument LA-UR-2232 (1985).
B. P. Ad’~astions ~H(d,pl~’c~:dV. $. A~tonenko,and D. E. Fomenko, “Study of the Reac-zH(d,n) He with a polarizedDeuteron Beam. Measurementof the Analyzing Power,” Yad. Fiz. 33, 601 (1981) ISov.J. Nucl. Phys. ~,313 (1981)].
G. M. Hale, “R-Matrix Analysis of the7Li System with Peripheral Channel
Overlap Exchange Effects,” Proc. Int. Conf. on Nucl. Data for Basic andApplied Sci., Santa Fe, New Mexico, May 1985 (Gordon and Breach). (Pro-ceedings to be published as well in RadiationEffects.)
F. M. Mann, “Transmutationof Alloys in MFE Facilities as Calculated byREAC,” Hanford Engineering Development Laboratory report HEDL-TME 81-37(1981).
P. G. Young and E. D. Arthur, “GNASH: A Preequilibrium-StatisticalNuclearModel Code for Calculations of Cross Sections and Emission Spectra,” LOSAlamos ScientificLaboratoryreport LA-6947 (November1977).
M. Blann and J. Bisplinghoff,“Code ALICE/Livermore1982,” LawrenceLiver-more National Laboratory reportUCID 1914 (1982).
S. Pearlstein, “Neutron-InducedReactions in Medium Mass Nuclei,” JournalNucl. Energy ~, 81 (1973).
J. B. Cumming, “Monitor Reactions for High Energy Proton Beams,” An.u.Rev.Nucl. Sci. 13, 261 (1963).
R. E. MacFarlane and L. Stewart, “ENDF/B-VIFormat Proposals,”in Los Ala-ITIOSNational Laboratory report LA-10288-PR, “Applied Nuclear Science andDevelopment Semiamual Progress Report October 1, 1983-May31, 1984” (Jan-uary 1985), p. 46.
E. D. Arthur, “Calculationof Neutron and Gamma-Ray Emission Spectra Pro-duced by p+27A~Reactionsjft in Los Alamos National Laboratory report LA-10288-PR, “Applied Nuclear Science Research and Development SemiannualProgressReport October 1, 1983-May31, 1984” (January1985),p. 3.
D. Wilmore and P. E. Hodgson, “The Calculationof Neutron Cross Sectionsfrom Optical Potentials,”Nucl. Phys. 55, 673 (1964).
13.
16.
17.
18.
llJ.
20.
21.
22.
23.
Zf,.
25.
26.
27.
28.
29.
.-W. F. McGill, R. F. Carlson,T. H. Short, J. M. Cameron, J. R. Richardson,I. Slaus, W. T. H. van Oers, J. W. Verba, D. J. Margaziotis,P. Doherty,“Measurementsof the Proton Total Reaction Cross Section for Light Nucleibetween 20 and 48 MeV,” Phys. Rev. C ~, 2737 (1974).
C. M. Perey and F. G. Perey, “DeuteronOptical Model Analysis in the Rangeof 11 to 27 MeV,’tPhys. Rev. 132, 755 (1963).
C. M. Perey and F. G. Perey, “Compilationof PhenomenologicalOptical ModelParameters 1954-1975,” Atomic Data and Nucl. Data Tables 17, 1 (1976).
G. M. Crawley and G. T. Garvey, “InelasticScatteringin the 2s-ld Shell,”Phys. Rev. 167, 1070 (1968).
S. M. Grimes, R. C. Haight, and J. D. Anderson, “Measurementof Sub-CoulombBarrier Charged Particles Emitted from Aluminum and Titanium Bombarded by15-MeVNeutrons,”Nucl. Sci. Eng. ~, 187 (1977).
J. L. Kammerdiener,“Neutron Spectra Emitted by 239Pu, 238U, 235U, Pb, Nb,Ni, Al, and C Irradiatedby 14-MeV Neutrons,” Lawrence Livermore NationalLaboratory report UCRL-51232 (1972).
G. Morgan, “Cross Sections for the Al(n,xn) and Al(n,xy) Reactions between1 and 20 MeV,” Oak Ridge National Laboratoryreport TM-5241 (1976).
F. E. Bertrand and R. W. Peelle, “TabulatedCross Section for Hydrogen andHelium Particles Produced by 62 and 29 MeV Protons on zyAl,~!oak Ridge Na-tional Laboratoryreport ORNL-4455 (1969).
E. D. Arthur and P. G. Young, “EvaluatedNeutron Induced Cross Sections for54s56Feto 4(JMeV,” Los Alamos ScientificLaboratory report LA-8626-MS (ENDF304) (December1980).
A. Prince, “Optical Model Calculations for the Chromium, Iron, and NickelIsotopes in the Energy Range of 0.5 to 100 MeV,” K. H. B6ckhoff,Ed., Proc.Int. Conf. Nucl. Data for Sci. Technol., Antwerp, Belgium, September 6-10,1982 (D. Reidel Publ. Co., Boston),p. 574.
G. S. Mani, “Spin Assignments to Excited States of SGFe Using Inelastic
Proton Scattering,tiNucl. Phys. A 165, 225 (1977).
S. M. Grimes, R. C. Haight, K. R. Alvar, H. H. Barschall,and R. R. Borchers,“Charged-ParticleEmission in Reactions of 15-MeV Neutrons with Isotopes ofChromium, Iron, Nickel, and Copper,” Phys. Rev. C ~, 2127 (1979).
F. E. Bertrand and R. W. Peelle, “TabulatedCross Sections for Hydrogen andHelium Particles Produced by 62-MeV Protons on sGFe,~lOak Ridge National
Laboratory report ORNL-4456 (1969).
R. L. Clarke and W. G. Cross, “Elasticand InelasticScatteringof 14.1-MeVNeutrons from Ni and Zr,” Nucl. Phys. A ~, 320 (1967).
P. H. Stelson, R. L. Robinson, H. J. Kim, J. Rapaport, and G. R. Satchler,“Excitation of Collective States by the Inelastic Scattering of 14.1-MeVNeutrons,”Nucl. Phys. 68, 97 (1965).
109
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
K. Dickens, “Gamma-Ray Production Due to Neutron Interactionswith Nickelbetween 1 and 20 MeV,” Oak Ridge National Laboratory ORNL-TM-4379 (1973).
S. Tanaka, M. Furukawa,M. Chiba, “NuclearReactions of Nickel with Protonsup to 56 MeV,” Journal Inorg. and Nucl. Chem ~, 2419 (1972).
Sheldon Kaufman, “Reactionsof Protons with 58Ni and 6oNi,” Phys. Rev. 117,1532 (1960).
E. D. Arthur, “Calculationof Proton-InducedReactions on Copper at E S 50MeV,” in Los Alamos National Laboratory report LA-10513-PR,“Applied Nu-clear Science Research and DevelopmentProgress Report June 1, 1984-May31,1985” (September1985),p. 9.
J. C. Legg and J. L. Yntema, “PossibleSpin Dependence in Proton InelasticScattering,”Phys. Rev. Lett ~, 10055 (1969).
Y. Holler, A. Kaminsky,R. Langkan, W. Scobel, M. Trabandt, and R. Bonetti,‘Recompound Emission in the Reaction 65cu(p,xn) and the Nucleon-Nucleon
ScatteringMechanism,”Nucl. Phys. A 442, 79 (1985).
E. D. Arthur and C. A. Philis, “New Calculationsof Neutron Induced CrossSections on Tungsten Isotopes,” in Los Alamos National Laboratory reportLA-8630-PR,“AppliedNuclear Data Research and DevelopmentJuly l-September30, 1980” (December1980),p. 20.
A. M. Lane, “Isobaric Spin Dependence of the Optical Potential and Quasi-elastic (p,n)Reactions,”Nucl. Phys. ~, 676 (1962).
J. Raynal, ‘Optical Model and Coupled-ChannelCalculationsin Nuclear Phy-sics,’tInternational Atomic Energy Agency report IAEA SMR-9/8 (1970).
H. Marshak, A. Langsford, T. Tamura, and C. Y. Wong, “Total Neutron CrossSection of Oriented IGSHO from 2 to 135 MeV,” Phys. Rev. C ~$ 1862 (1970).
T. Kruse, W. Maofske, H. Ogata, W. Savin, M. Slagowitz,M. Williams, P.Stoler, “Elastic and Inelastic Proton Scattering from Heavy CollectiveNuclei,W Nucl. Phys A 169, 177 (1971).
H. Kamitsubo, H. Ohnuma, K. One, A. Uchida, M. Shinohara, M. Imaizumi,S.Kobayashi, and M. Sekiguchi,“Elastic Scatteringof 55-MeV Protons by HeavyNuclei,” Phys. Lett. ~, 332 (1964).
J. Frehaut and J. Jary, “Systematiquedes Sections Efficaces de Reactions(n,2n)pour des Series d’IsotopesSepares,”Proc. Int. Conf. on Neutron andNucl Data, Harwell, 1978, p. 1038.
E. D. Arthur, “Calculationof Neutron Cross Sections on Isotopes of Yttriumand Zirconium,’:Los Alamos Scientific Laboratory report LA-7789-MS (April1979).
J. C. Dousse, E. D. Arthur, D. M. Drake, J. Gursky, J. D. Moses, N. Stein,and J. W. Sunier, “CoincidentNeutron-ProtonEmission from Proton Bombard-ment of ‘7Sr and 91Zr,” Phys. Rev. C ~, 92 (1985).
110
4!5. P. Luksch and J. W. Tepel, “Nuclear Data Sheets for A = 87,” Nucl. DataSheets 27, 389 (1979).
46. E. D. Arthur, “calculationof n+ 239Ew Cross Sections up to Neutron Ener-gies of 20 MeV,W in Los Alamos National Laboratory report LA-9841-PR,“Applied Nuclear Data Research and Development Semiamual Progress ReportOctober 1, 1982-March31, 1983” (August 1983),p. 15.
4-?. J. Frehaut, A. Bertin, R. Bois, E. Grytakis, C. A. Philis, “(n,2n) CrossSections of 2H and Zsgpu,fiProc. Int. Conf. on Nucl. Data for Basic andApplied Sci., Santa Fe, New Mexico, May 1985 (Gordon and Breach), (Pro-ceedings to be published as well in RadiationEffects.)
48. E. D. Arthur, “Improved (n,f) Cross Sections Using Measured Fission Proba-bilities,”Trans. Am. Nucl. Soc. 46, 739 (1984].
49. pa G. young, “Global and Local Optical Model Parameterizations,”Proc.OECD, NEANDC Specialists Meeting on the Use of the Optical Model for theCalculation of Neutron Cross Sections Below 20 MeV, Paris, November 13-15,1985, to be issued.
50. P. A. Moldauer, “Optical Model of Low Energy Neutron InteractionswithSphericalNuclei,” Nucl. Phys. ~, 65 (1963).
51. F. G. Perey and B. Buck, “A Non-Local PotentialModel for the ScatteringofNeutrons by Nuclei,” Nucl. Phys. 32, 353 (1962).
52. C. A. Engelbrecht and H. Fiedeldey, “Nonlocal Potentials and the EnergyDependence of the Optical Model for Neutrons,” Ann. Phys. ~, 262 (1967).
53. F. D. Becchetti, Jr., and G. W. Greenlees, “Nucleon-NucleusOptical-ModelParameters,A > 40, E < 50 MeV,” Phys. Rev. 182, 1190 (1969).
54. D. M. Patterson, R. R. Doering, and A. Galonsky, ‘An Energy-DependentLane-Model Nucleon-Nucleus Optical Potential,” Nucl. Phys. A 263, 261(1976).
55. J. Rapaport, V. Kulkarni, and R. W. Finlay, “A Global Optical-ModelAnaly-sis of Neutron Elastic Scattering Data,” Nucl. Phys. A 330, 15 (1979).
56. R. L. Walter and P. P. Guss, “A Global Optical Model for Neutron Scatteringfor A>53 and 10 MeV<E<80 MeV,” Proc. Int. Conf. Nucl. Data for Basic andApplied Sci., Santa Fe, New Mexico, May 1985 (Gordon and Breach), (Pro-ceedings to be published as well in Radiation Effects.)
57. S. F. Mughabghab, M. Divadeenam, N. E. Holden, “Neutron Resonance Param-eters and Thermal Cross Sections,”Neutron Cross Sections,Vol. 1, AcademicPress, New York (PartA-1981), (Part B-1984).
58. 0. Bersillon, “SCAT2: Un Programme de Modele Optique Spherique,”in Commis-sariatsa l’EnergieAtomique report CEA-N-2227 (1981).
59. Experimental data provided from CSISRS compilationby the National NuclearData Center, BrookhavenNational Laboratory,Upton, New York.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
112
M. Kawai, presented at NEANDC Topical Discussions,Geel, September 1979;see also Y. K. Kuchi and N. Sekine, “Evaluationof Neutron Nuclear Data ofNatural Nickel and Its Isotopes,” J. Nucl. Sci. Tech. ~, 337 (1985).
S. Igarasi et al., “Evaluation of Fission Product Nuclear Data for FastReactors,” Japanese Atomic Energy Research Institute report JAERI-M 5752(1974).
D. G. Madland and P. G. Young, “Neutron-NucleusOptical Potential for theActinide Region,” Proc. Int. Conf. on Neutron Physics and Nuclear Data forReactors and Other Applied Purposes, Harwell, published by OECD, p. 349.
c. L. Dunford, “A Unified Model for Analysis of Compound Nuclear Reac-tions,” Atomics Internationalreport AI-AEC-12931(1970).
A. Gilbert and A. G. W. Cameron, Can. J. Phys. ~, 1446 (1965).
J. L. Cook, H. Ferguson, and A. R. Musgrove, “Nuclear Level Densities inIntermediateand Heavy Nuclei,” Aust. J. Phys. ~, 477 (1967).
R. C. Harper and W. L. Alford, “Experimentaland TheoreticalNeutron CrossSections at 14-MeV,”J. Phys. G: Nucl. Phys. ~, 153 (1982).
P. P. Guss, R. C. Byrd, C. E. Floyd, C. R. Howell, K. Murphy, G. Tungate,R. S. Pedroni, R. L. Walter, J. P. Delaroche,and T. B. Clegg, ‘Cross Sec-tions and Analyzing Powers for Fast-NeutronScattering to the Ground andFirst Excited States of SgNi and GoNi,~~Nucl. Phys. A 438, 187 (1985).
B. Strohmaier,M. Uhl, and W. Reiter, “Neutron Cross Section Calculationsfor szcr, ‘s~, 56Fe, and sgSGoNi for Incident Energies to 30 MeV,” IAEAAdvisory Group Meeting on Nuclear Data for RadiationDamage AssessmentandRelated Safety Aspects, Vienna, October 1981.
R. E. Shamu, E. M. Bernstein,J. J. Ramirez, and Ch. Lagrange, “EffectsofDeformation on Neutron Total Cross Sections of Even-A Nd and Sm Isotopes,”Phys. Rev. C ~, 1857 (1980).
E. D. Arthur, P. G. Young, A. B. Smith, and C. A. Philis, “New TungstenIsotope Evaluations for Neutron Energies Between 0.1 and 20 MeV,” Trans.Am. Nucl. sec. ~, 793 (1981).
J. P. Delaroche, G. Haouat, J. Lachkar, Y. Patin, J. Sigaud, and J.Hardine, “Deformations,Moments, and Radii of lgz~183>184S186Wfrom Fast
Neutron Scattering,”Phys. Rev. C ~, 136 (1981).
P. G. Young, E. D. Arthur, C. Philis, P. Nagel, M. Collin, “Analysis ofn+165Ho and 169TMReactions,” Proc. Nuc1. Data for Sci. and Tech. Int.Conf., Antwerp, Belgium, September 1982, p. 792.
G. Haouat, J. Lachkar, Ch. Lagrange, J. Jary, J. Sigaud, and y. patin,“Neutron Scattering Cross Sections for 232Th, 23SU, 235U, 238U, 239Puj andzQzpu Between o-6 and 3.4 MeV,” Nucl. Sci. Eng. ~, 491 (1982).
Ch. Lagrange, “Results of Coupled Charnel Calculations for the NeutronCross Sections of a Set of Actinide Nuclei,” NEANDC(E) 228 <L>, October1982.
I
7.5.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
81.
88.
89.
Ch. Lagrange, O. Bersillon, and D. G. Madland, “Coupled Channel Optical-Model Calculationsfor Evaluating Neutron Cross Sections of Odd-Mass Acti-nides,” Nucl. Sci. Eng. &3, 396 (1983).
S. Joly, D. Drake, and L. Nilsson, “Gamma-rayStrength Functions for 1°4Rh,IToTm,and 19SAU,”Phys. Rev. C ~, 2072 (1979).
M. A. Lone, “Photon Strength Functions,”in Proc. Third Int. Symp. NeutronCapture Gamma-Ray Spectroscopyand Related Topics, BrookhavenNational La-boratory and State Univ. of New York, September 18-22, 1978, R. E. Chrien,Ed. (PlenumPress, New York, 1979),p. 161.
V. J. Orphan, N. C. Rasmussen,and T. L. Harper, “Line and ContinuumGamma-Ray Yields from Thermal-Neutron Capture in 75 Elements,” Gulf GeneralAtomic report GA-10248 (1970).
C. Kalbach and F. M. Mare, “Phenomenologyof Continuum Angular Distribu-tions I. Systematic and Parameterization,”Phys. Rev. C 23, 112 (1981).
A. Bohr and B. R. Mottelson, Nuclear Structure, Vol. II (W. A. Benjamin,Inc., New York, 1975), p. 201.
C. Michael Lederer and Virginia Shirley, Eds., Table of Isotopes, SeventhEdition (John Wiley and Sons, Inc., New York, 1978).
D. G. Madland, “Search for a Suitable Isomer for the GRASER Program,” inLos Alamos National Laboratory report LA-10288-PR, “Applied Nuclear Sci-ence Research and Development Semiannual Progress Report October 1, 1983-May 31, 1984” (January1985),p. 26.
D. Strottman, E. D. Arthur, and D. G. Madland, “Nuclear Structure Con-siderations for Gamma-Ray Lasers,” Los Alamos National Laboratory informaldocument LA-UR-85-2701(May 1985).
R. J. Howerton, “ENSL82 and CDRL82: The 1982 Version of Evaluated NuclearStructure Libraries ENSL and CDRL,” Lawrence Li.vermoreNational Laboratoryreport UCRL-50400Vol 23. Addendum (1983).
Evaluated Nuclear Structure Data File, Version V, available from the Na-tional Nuclear Data Center, Brookhaven National Laboratory, Upton, NewYork.
C. J. Gallagher,Jr., and S. A. Moszkowski,“Couplingof Angular Momenta inOdd-Odd Nuclei,” Phys. Rev. 111, 1282 (1958).
N. D. Newby, Jr., “Selection Rules in the Odd-Even Shift of Certain Nu-clear RotationalBands,~’Phys. Rev. 125, 2063 (1962).
J. Grundl and C. Eisenhauer, “Fission Rate Measurements for MaterialsNeutron Dosimetry in Reactor Environments,”Proc. First ASTM-EURATOM Sympon Reactor Dosimetry, Petten, Holland, Sept. 22-26, 1975, Part I, p. 425.
D. G. Madland and J. R. Nix, “New Calculation of Prompt Fission NeutronSpectra and Average Prompt Neutron Multiplicities,”Nucl. Sci. Eng. 81, 213(1982).
113
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101!
W. P. Poenitz and T. Tamura, “Investigationof the Prompt-NeutronSpectrumfor Spontaneously-Fissioning252Cf,” Proc. Int. Conf. on Nuclear Data forScience and Technology,Antwerp, Belgium, 1982, Reidel, Dordrecht (1983),p. 465.
J. W. Boldeman, B. E. Clancy, and D. Culley, “Measurementsof the PromptFission Neutron Spectrum from the SpontaneousFission of 2s2Cf,” submittedto Nucl. Sci. Eng. (November1984).
J. Grundl, D. Gilliam, D. McHarry, C. Eisenhauer, and P. Soran, in memo-randum to Cross Section Evaluation Working Group (CSEWG) Subcom. on Stan-dards (May 1983).
K. Kobayashi, I. Kimura, H. Gotoh, and H. Tominaga, “Measurementof AverageCross Sections for Some Threshold Reactions of Ti, Cr, and Pb in the Cali-fornium-252SpontaneousFission Neutron Spectrum Field,” Annual Reports ofthe Research Reactor Institute, Kyoto University, Vo. 17, p. 15-21, 1984(unpublished).
D. G. Madland, R. J. LaBauve, and J. R. Nix, “Comparisonsof Four Repre-sentations of the Prompt Neutron Spectrum for the SpontaneousFission of252Cf,” Proc. Int. Conf. on Nuclear Data for Basic and Applied Sci., SantaFe, New Mexico, May 1985 (Gordonand Breach).
D. G. Foster, Jr., and R. E. MacFarlane, “Coupled Energy-AngleDistribu-tions of Recoiling Nuclei,” in Los Alamos National Laboratory report LA-10288-PR, “Applied Nuclear Science Research and Development SemiannualProgress Report October 1, 1983-May31, 1984” (January1985),p. 36.
R. E. MacFarlane and D. G. Foster, Jr., “Advanced Nuclear Data for Radia-tion Damage Calculations,H Jour. Nucl. Mat. 122 and 123, 1047 (1984).
D. W. Muir, !~calculationof SgCO Cross Sections using GNASH and Comparisonwith PreviouslyPublishedResults,”pp. 5-6 in “NuclearPhysics TheoreticalGroup Report No. 50, Progress Report for the Period May 1984 to May 1985,”Oxford University Nuclear Physics Laboratory report 39/85 (June 1985).
D. W. Muir, “Implementationof GNASH and Auxiliary Codes on the HarwellCRAY-1,”Atomic Energy Research Establishment,Harwell, report AERE R 11877(July 1985).
c. Kalbach, “PRECO-B: Programme for Calculating Preequilibrium ParticleSpectra” (unpublished). See also C. Kalbach, “The Griffin Model, ComplexParticles,and Direct Nuclear Reactions,f’Z. Phys. A283, 401 (1977).
R. E. MacFarlane,D. W. Muir, and R. M. Boicourt, “The NJOY Nuclear DataProcessing System Volume I: User’s Manual,” Los Alamos National Laboratoryreport LA-9303-M,Vol. I (ENDF-324)(May1982).
R. E. MacFarlane and D. W. Muir, “The NJOY Nuclear Data ProcessingSystem,Volume III: The GROUPR, GAMINR, and MODER Modules,” Los Alamos NationalLaboratory report LA-9303, Vol. III (ENDF-324) (to be published in 1986).
114
1(-)2.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
11:3.
l~(k.
11s.
D. W. Muir, R. E. MacFarlane, “The NJOY Nuclear Data Processing System,Volume IV: The ERRORR and COVR Modules,” Los Alamos National Laboratoryreport LA-9303-M,Vol. IV (ENDF-324)(December1985).
R. W. Roussin, J. R. Knight, J. H. Hubbell, and R. J. Howerton, “Descrip-tion of the DLC-99/HUGO Package of Photon Interaction Data in ENDF/B-VFormat,” Oak Ridge National Laboratory report ORN’L/RSIC-46(E~F-335)(December1983).
J. V. Koppel and D. H. Houston, “ReferenceManual for ENDF Thermal NeutronScattering Data,” General Atomics report GA-8774, revised and reissued asENDF-269 (July 1978).
T. R. England and B. F. Rider, “Status of Fission Yield Evaluations,”R. E.Chrien and T. W. Burrows, Eds., Proc. NEANDC SpecialistsMeet. on yieldsand Decay Data for Fission Product Nuclides, Brookhaven National Labora-tory, Upton, New York, October 24-27, 1983 (BrookhavenNational Laboratoryreport BNL 51778).
K. -L. Kratz and G. Herrmann, “Systematic of Neutron Emission Probabili-ties from Delayed Neutron Precursors,”Z. Physik 263, pp. 435-442 (1973).
F. M. Mann, M. Schreiber,R. E. Schenter, and T. R. England, “Evaluation ofDelayed Neutron Emission Probabilities,”Nucl. Scie. Eng. ~, PP. 418-431(August 1984).
T. R. England, W. B. Wilson, R. E. Schenter, and F. M. Mann, “AggregateDelayed Neutron Intensitiesand Spectra Using AugmentedENDF/B-V PrecursorData,” Nucl. Sci. Eng. ~, pp. 139-155 (October 1983).
T. R. England, W. B. Wilson, R. E. Schenter, and F. M. Mann, “E~F/B-VSummary Data for Fission Products and Actinides,” Electric Power ResearchInstitutereport NP-3787 (ENDF-332)(December1984).
G. Rudstam, “Six-Group Representation of the Energy Spectra of DelayedNeutrons from Fission,”Nucl. Sci. Eng. 80, 238-255 (February1982).
K. -L. Kratz, “Review of Delayed Neutron Spectra,”Proc. ConsultantsMeet-ing on Delayed Neutron Properties,Vienna, Austria, March 26-30, 1979 [In-ternationalAtomic Energy Agency report INDC (NDS-107/G+ Special) (1979)].
F. M. Mare, C. Dunn, and R. E. Schenter, “Beta Decay Properties from a Sta-tistical Model,” Trans. Am. Nuc1. SOC. ~, 880 (1980). [See also Phys.Rev. C ~, 524 (January 1982).]
A. H. Wapstra and G. Audi, “The 1983 Atomic Mass Table,” Nuc1. Phys. A 432,No. 1 (January7, 1985].
P. M611er and J. R. Nix, “Atomic Masses and Nuclear Ground-StateDeforma-tions Calculatedwith a New Macroscopic-MicroscopicModel,” Atomic Data andNuclear Data Tables ~, No. 2, pp. 165-196 (March 1981).
R. C. Greenwood and A. J. Caffrey, “Delayed-NeutronEnergy Spectra ofgs,gTRb and lasslqscs,~~Nucl. Sci. Eng. ~, pp. 305-323 (1985).
115
I
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
P. L. Reeder, L. J. Alquist, R. L. Kiefer,“Energy Spectra of Delayed Neutrons from the93, -94, -95, and Cesium-143,” Nucl. Sci.
F. H. Ruddy, and R. A. Warner,SeparatedPrecursorsRubidium-Eng. 7&, pp. 140-1!50(1980).
Sequence of amual progress reports from the Institutefor Chemistry,Uni-versity of Mainz, Germany, 1973-1984.
R. A. Warner and P. L. Reeder, ‘Delayed Neutron Data from TRISTAN,”Proc.Int. Conf. on Nucl. Data for Basic and Applied Sci., Santa Fe, New Mexico,May 1985 (Gordonand Breach).
T. R. England, R. Wilczynski, and N. L. Whittemore, “CINDER-7:An InterimReport for Users,” Los Alamos Scientific Laboratory report LA-5885-MS(April 1975). (CINDER-1Ois a major modificationof CINDER-7,but is docu-mented only in a series of T-2 progress reports.)
A. Sierk, Los Alamos National Laboratory memorandum, T-9, September 24,1985, to T. England and E. Arthur; subject:Delayed Neutron Spectra.
D. G. Madland and T. R. England, “The Influenceof Pairing on the Distribu-tion of IndependentYield Strengths in Neutron-InducedFission,” Los AlamosScientificLaboratoryreport LA-6430-MS (July 1976).
R. L. Walker, “The (a,n) Cross Section of Boron,” Phys. Rev. 76, 244(1949).
W. B. Wilson, R. T. Perry, J. E. Stewart, T. R. England, D. G. Madland, andE. D. Arthur, “Development of the SOURCES Code and Data Library for theCalculation of Neutron-Sourcesand Spectra from the (a,n)Reactions,Spon-taneous Fission, and ~ Delayed Neutrons,” in Los Alamos National Labora-tory report LA-9841-PR, “Applied Nuclear Data Research and DevelopmentSemi-amual Progress Report October 1, 1982-March31, 1983” (August 1983),pp. 65-66.
R. T. Perry and W. B. Wilson, “On the (a,n) Neutron Production in BoronContainingSystems,”Trans. Am. Nuc1. SOC. K, 763 (1984).
J. K. Bair and J. G. del Campo, “Neutron Yields from Alpha-ParticleBom-bardment,”Nucl. Sci. Eng. 71, 18 (1979).
G. V. Gorshkov,V. A. Zyabkin, and O. S. Tsvetkov, “NeutronYields from theReaction (a,n)-in Be, B, C, O, F, Mg, Al, Si, and Granite IrradiatedwithPolonium & Particles,”Atomnaya Energiya ~, 65 (1962) (p. 654 of Englishtranslation).
127. J. H. Roberts, “Neutron Yields of Several Light Elements Bombarded withPolonium Alpha Particles,” US Atomic Energy Commission report MDDC-731(1944).
128. B. H. Weren and J. E. Faulkner, “(a,n) Neutron Source in CommercialHigh-Level Waste,” Trans. Am. NUC~. SOC. ~, 608 (1983).
116
129. P. G. Young and D. G. Foster, Jr., “An Evaluationof the Neutron and Gamma-Ray ProductionCross Sections from Nitrogen,”Los Alamos ScientificLabora-tory report LA-4725 (ENDF-173)(September1972).
130. J. F. Ziegler, Helium Stopping Powers and Ranges in All ElementalMatter,.Vol. 4 of The Stopping and Ranges of Ions in Matter series (PergamonPress,New York, 1977).
131. R. T. Lancet, J. C. Mills, “SAFR: A Marriage of Safety and Innovation inLMR Design,” Tran. Am. Nucl. Soc. 50 (TANSAO 50 1-644), p. 336 (1985).—
132. R. Kinsey, Comp., “ENDF-201: ENDF/B Summary Documentation,” BrookhavenNational Laboratory report B~-NCS17541 (ENDF-201), 3rd Ed. ENDF/B-V(1979).
133. R. E. MacFarlane, “TRANSX-CTR:A Code for InterfacingMATXS Cross SectionLibraries to Nuclear Transport Codes for Fusion System Analysis,” LosAlamos National Laboratoryreport LA-9863-MS (February1984).
134. R. D. O’Dell, “Standard Interface Files and Procedures for Reactor PhysicsCodes, Version 11,” Los Alamos Scientific Laboratory report LA-6941-MS(September1977).
135. K. L. Derstine, “DIF3D: A Code to Solve One-, Two-, and Three-DimensionalFinite-DifferenceDiffusion Theory Problems,” Argome National Laboratoryreport ANL-82-64 (April 1982).
117
136. F. M. Mare, “Transmutationsof Alloys in MF’EFacilities as Calculated byREAC,” Hanford Engineering Development Laboratory report HEDL-TME 81-37(August 1982).
