GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION · 2015. 3. 30. · S. S. Kapoor, S. K. Kataria,...
Transcript of GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION · 2015. 3. 30. · S. S. Kapoor, S. K. Kataria,...
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B . A . R X > - 5 4 7 . . . : • " • • • ' "-~?::Wi±
GOVERNMENT OF INDIAATOMIC ENERGY COMMISSION
STUDIES OF K 5tRAY EMISSION IN THE THERMALFISSION OF U« s AND SPONTANEOUS FISSION OF Ci'«s*
V . : ' ' . - ; ; • • • > • - • - ; - ' • • - ' - ; ' ' - . : - .
I. S, Kapoor, S. E . Kataria,^ S. R. S. Morthy, D. M. Nadkarni,
Nuclear Physics Division '
| ^
:T( FofiJiciB
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n . A . R . C . -547
GOVERNMENT OF INDIAATOMIC ENERGY COMMISSION
ini
U
STUDIES OF K X-RAY EMISSION IN THE THERMALFISSION OF U2 3 5 AND SPONTANEOUS FISSION OF
byS. S. Kapoor, S. K. Kataria, S.R.S. Murthy, D. M. Nadkarni,
V.S. Ramamurthy, P. N. Rama Rao and R. RamannaNuclear PhyBics Division
BHABHA ATOMIC RESEARCH CENTREBOMBAY, INDIA
1971
*Report on work performed under research contract No. 535/RB withInternational Atomic Energy Agency, Vienna, on "FundamentalStudies of the fission process in heavy nuclei"
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CONTENTS
SECTION I
SECTION II
a.
General Outline of the Project
x Experiments
Experimental
i. Experimental Arrangementii. Electronics
iii. Counting Rates
b .
c .
SECTION in.
a.
b .
c .
d.
e .
Analysis of the data
Results
K X-ray Half Liv 38 Versus FraAtomic Number
Introduction
Principle of the method
Experimental
i. Layoutii. Electronics and data taking
Alpha-X-ray data
Analysis of Results
i. Background correction
ii. Determination of observed K X-rayintensities from specificed Z fragments
iii. Determination of X-ray half livesVersus Z
Page
1
5
5
579
10
15
20
20
21
23
23
24
26
27
23
30
31
f. Discussion of the Results
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SECTION IV
a.
b.
c.
d.
Page
: Studies of K X-ray Multiplicity from 41Cf252 fission Fragments
Introduction 41
Experimental Set-up 42
Electronic Arrangement 42
Data Analysis 46
i. Heavy-Heavy or Light-Light X-ray 51Coincidence Data
iL Light-Heavy X-ray Coincidence Data 53
Results and Discussion 54
SECTION V : Summary 63
REFERENCES 67
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I. GENERAL OUTLINE OF THE PROJECT
It is known from earlier investigations'1' of the fragment
deexcitation process that soon after scission, the fission fragments
each having about 16 MeV excitation energy are accelerated to large
kinetic energies owing to Coulomb repulsion between them. Promptly
thereafter, a greater part of the excitation energy is dissipated by
neutron emission. The residual excitation-energy is then emitted in
the form of gamma rays. Approximately 8-10 MeV of energy is
carried away by about 8-LO gamma rays. About 85 fo of the total gamma
rays are emitted with a half life of about 10 sec, and the remaining
15% have half-life in the region of 10 sec. . A small fraction of
about 6% of these gamma transitions undergo internal conversion
primarily in the K and L shells giving rise to conversion electrons
and characteristic X-rays. In recent years, the studies of the radia-
tions emitted in the nuclear fission process have been a subject of con-
siderable interest. It has been so mainly due to the recognition of the
fact that the fragment nuclei emitting these radiations span the neutron
rich region far away from the line of {^-stability, and cover a large
region of nuclear periodic table as shown in Fig. 1. This region is
not easy to reach by other conventional means and fission process
provides a natural means of studying the nuclear spectroscopy of
these nuclei. Detailed investigations of the radiations originating from
fragment nuclei of known mass and nuclear charge have been made
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possible only recently, with the availability of high resolution lithium-
drifted Silicon and Germanium detectors, the multiparameter data acqui-
sition system and the on line computers. With the availability of these
facilities, recent efforts* " ' are aimed at studying the fission gamma
rays, conversion electrons and K X-rays as a function of the mass and
nuclear charge of the emitting fragment.
In this project, detailed investigations of the K X-rays emitted
in the thermal neutron induced fission of U and in the spontaneous
fission of Cr" were undertaken by carrying out three different types
of experiments. The first experiment involved a three parameter study
of the kinetic energies of the pair fragments and the coincident K X-rays
for the case of thermal fission of U235 . We will refer this as EjEgE^
experiment, where the fragment kinetic energies Ei, E? of the two
fragments and the X-ray energy E are recorded event by event using
the multiparameter data acquisition system. These data have provided
information on the K X-ray yields as a function of average fragment
inass and total kinetic energy. Details of this experiment are given in
section II. The second series of experiments described in Section III
were aimed to obtain information on the K X-ray emission times as a
function of the nuclear charge of the emitting fragment for the thermal
fission of U"5# The experiments on the correlated emission of the K
X-rays for the case of spontaneous fission of Cf252 described in
Section IV, provided information regarding the average multiplicity of
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K X-rftys and light-heavy correlation in the X-ray emiseion process.
All these investigations were carried out using lithium drifted silicon
detector system for X-ray energy measurements and with the four
parameter data acquisition system obtained under contract from IAEA.
The results obtained from all these studies are summarised in Section V.
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Cf2M FragmentsU*36 Fragments
N
M 54 56 58
F I G 1
The region of the periodic chart spanned by
Of252 and U256 f ission fragmants.
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II. E.E E EXPERIMENTS
a) EXPERIMENTAL
(i) Experimental Arrangement
A schematic diagram of the experimental arrangement is
shown in Fig. 2. The Bource foil holder assembly was specially designed
to mount the fragment detectors also in the same holder at a small dis-
tance of 0. 5 mm and 3 mm from the source foil. The source foil con-
sisted of about 100 Ugm/cm of U 3^ electrosprayed onto an area of 1 sq.
cm of a thin VYNS foil coated with a very thin film of gold, which was
first adhered to the foil-detector holder assembly. Since in this system,
the fragments are stopped within 0. 5 mm on one side, this arrangement
has the following advantages: (i) it eliminates the uncertainties asso-
ciated with the determination of solid angle of detection of X-rays
emitted from flying fragments, (ii) it improves the fission counting
rate enabling the experiments to be carried out with a low flux and
consequently with a low background. The X-ray energy was measured
with 0. 6 cm2 x 3 nun Si(L,i) detector cooled to liquid nitrogen tempe-
rature and coupled to a cryogenic FET amplifier. The energy resolu-
tion of the X-ray detector system in terms of FWHM of 26. 25 Kev
line of Am2 4 1 was 0. 88 Kev for low count rates for the system used in
this work. During the experiment the actual energy resolution attain-
able was about 1 Kev due to a slight deterioration of the system reso-
lution caused by highly saturated background pulses.
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FiG-2
SOURCE ANDDETECTORS,,ASSEMBLY^
-1 MIL AL $&£ rBERRYLIUM WINDOWS
- ! MIL ALUMINUM
CRYOSTAT WITH COOLEDSi (L i ) DETECTOR ANDFET ASSEMBLY
STAINLESSSTEEL
SPRING WIRECONTACT —
SOURCE U"235 —
TOP PLATEOF CHAMBER
FRAGMENT .•*DETECTORS AJ*
A
-VYNS BACKING
-PERSPEX
e e
DETAILS OF ASSEMBLY OFSOURCE AND DETECTORS
Schematic diagrani of the e_: erirfE •••tal arrangeTS:n'tfor the E..B-E oxperiraent.
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A colllmated neutron beam from thp C1RUS reactor was used
for this work. To reduce the fast neutron and / -ray content of the
beam, the beam from the reactor core passed through 15 cms of
quartz and 25 cms of BiBmuth and finally through a Steel collimator
which reduced the beam size to 1.25 cms. The thermal neutron flux
at the foil was about 5 x 10"n/cm /sec. The vacuum chamber housing
the foil-detector assembly was made to have very thin entrance and
exit windows of aluminium for the incident neutrons, to minimise the
beam scattering and therefore the background field in the region of X-
ray detector. The source foil detector assembly was placed in line with
and making an angle of 45° with the collimated neutron beam, and the
x-ray detector was placed at right angles to the beam direction at a
distance of about 3. 0 cmB from the source foil. The x-rays were
viewed through two 10 mil Be windows, one in vacuum chamber and
the other in the cryostat. Since in this arrangement the X-rays were
viewed through the fragment detector, thin wafers (thickness 350 microns)
of diffused junction silicon detectors were employed to have small atte-
nuation for the fragment X-rays,
(ii) Electronics
The block diagram of the electronic arrangement is shown in
Fig. 3. The pulses from the fragment detector system after suitable
amplification were fed to a single channel analyser to cut off the alpha
pulses. The at c. analyser was externally strobed by the zero cross-
over output of the bipolar pulses from the amplifier of the second frag-
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X-RAYDETECTOR
A PARAMETER! RECORDINGSYSTEM
DELAYEDnCOINC.
FRAGMENTDETECTOR
FRAGMENTDETECTOR
oo
BLOCK DIAGRAM OF ELECTRONIC ARRANGEMENT FOR E, E 2 E x EXPER;M=MT
FIG. a
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ment detector system. This arrangement provided timing pulses corre-
sponding to fragment-fragment coincidences. The timing pulses from
the X-ray detector system corresponding to zero cross-over and the fis-
sion timing pulses were fed to a double coincidence unit of resolution
time iUsec. The EjE£ double coincidences were scaled down by a
factor of 256 and these sealer output pulses and the triple coincidence
EjE2Ex pulses were fed to an OR gate, the output of which gated the 4
parameter system in the external delayed coincidence mode. The pulses
from the respective linear amplifiers containing the information on the
energies Ej, K^ and Ex were fed to the three ADC's (1, 3 and 4) of the
multiparameter system and a flag signal from sealer output was fed to
ADC 2. In this way, the pulse heights corresponding to either Ej E£
coincidences or EiE^Ex coincidences were recorded event by event on
a paper tape. A high precision pulser fed at the input of the x-ray
detector was first calibrated into energies using the e. m. radiations
from a A m ^ ' source. A careful channel versus energy calibration
was obtained at the start of each run and further checked at the end. In
the present set of experiments about Z. 5 x 105 events containing roughly
equal number of EiE2Ex and EjE, events were recorded. The record-
ing of E,E2 data was required to obtain an accurate mass calibration.
(iii) Counting Rates
The fission counting rates in the individual detectors D^ and D2
and the coincident EjE2 counting rates were about 1Z0, 30 and 30 per
sec respectively. The triple coincidence EJE2EJJ. counting rate was
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about 5 per minute. The singles background rate in the X-ray detector
was about 200 per sec in the fragment X-ray energy region and about
1500 per sec in all the energy range. The chance coincidence rate in
the X-ray energy region with a resolution time (2 T ) of 1 Usec was
therefore only 10% of the total triple coincidence rate. In this senee,
background effects were rather small since the major source of back-
ground in the triple coincidence data originates from the unavoidable
true coincidences with the compton scattered fission gamma rayB. How-
ever, the background counting rate of about 1500 per second mainly of
the saturated pulses in the x-ray detector had the effect of somewhat
deteriorating the actual x-ray energy resolution obtainable during the
experiment to a value of about 1. 1 keV.
The radiation damage of the fission detectors was continuously
monitored by recording their leakage currents and fragment kinetic
energy distributions. The time for which continuous recording of data
could be carried out was limited to 15 days during which the detector
oD, was exposed to about 1. 5 x 10 fission fragments since after this
the effects of radiation damage became significant. During a period of
15 days ahout 1. 2 x 10^ triple coincidence events and roughly equal
number of double coincidence events were recorded on the paper tape of
the 4 parameter system.
(b) ANALYSIS OF THE DATA
The data on the punched paper tapes were transferred on to a
magnetic tape with the 160 A satellite computer. The data were then
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properly decoded, and written on another tape in CDC 3600 computer
compatible format. This tape was used for further analysis of the data.
Fragment masses were obtained from the double kinetic energy
data through the energy-momentum conservation relations. In order
to take into account any small shifts in the fragment kinetic energy dis-
tributions during each run the double coincidence data of nearly each
day were first separately sorted out to obtain the kinetic energy distri-
butions. The first moments P^ and PJJ of the pulse height distributions
for each set of data were used for the calibration of pulse heights into
fragment kinetic energies. The energy to mass conversion was carried
out by means of an iterative process which incorporated mass dependent
(11)energy calibration proposed by Schmitt et al and neutron corrections
based on the results of Maslin et al* ' . Using this procedure the eva-
luation of prompt fragment masses for each event was individually done
and transcribed onto a magnetic tape. The pulse heights for the x-ray
channel in each event was also converted into x-ray energy and recorded.
After these transformations of the data, the unbiased mass distributions
for the cases when no x-rays were recorded was sorted out. The
observed mass distribution was found to be wider because of mass dis-
persions introduced due to neutron emission and experimental effects.
The experimental effects are attributable mainly to significant experimental
dispersion in the fragment kinetic energies introduced by the source
thickness, the proximity of the source foil, with the fragment-detector
and the detector resolution. The observed mass distribution was
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corrected for mass dispersion effects by the method of Terrel .
The removal of mass dispersion corresponding to
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3000
in5 2000
CD(X<
Q
1000
SCHMITT ET AL
PRESENT DATA
160
I
140 130
PROMPT FRAGMENT MASS120
FIG. 4
The frvL, icv I -if, c i r i t r i b u t i o r . •;.:. .i ..-."'exper iment c c a ^ a r e d '.vi!;h t h e r eoa l ' . o of
.i,- t :
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the heavy and the light fragments respectively are moving towards the
fragment detector which is placed very close to the source foil and
towards the X-ray detector. In this case the fragment motion is limited
to only about 0. 1 cm and hence the change of the solid-angle due to
varying emission times of X-rays is not appreciable. The following
results have been obtained from the analysis of only such events.
The unbiased mass distribution Y(M) and the distribution
Y(MT JJ) in coincidence with light or heavy fragment K X-rays are re-
lated by the following relation.
YX(ML. H> / Y = Px T (*>
where p (MT JJ) *8 ^ e average number of K X-rays emitted from
the masses M^ or MJJ. 7) (M), T(M) are the average detection effi-
ciency and the transition coefficients for the K X-rays characteristic
of fragment mass M, and -TL is the solid angle of X-ray detection.
The solid angle _Q_ of X-ray detection was determined by
comparing the number of L-X-rays detected per alpha decay of U
in the given experimental setup with the calculated number'14' of L>X
rays emitted per alpha decay. In the present arrangement the X-ray
intensities specially those from light group, were attenuated in passing
through the fragment detector. The transmission T of the X-rays of
different energies was calculated using the known values of the frag-
ment detector thickness and the absorption coefficients' ' for silicon.
The transmission was also measured for the experimental arrange-
ment by measuring the L X-rays in coincidence with natural Cephas
of U^3* present in the foil, with and without the fragment detector
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being present and was found to be in agreement with the calculated
values. T̂ was calculated from the known photoelectric and total absor-
ption cross sections in silicon.
(c) RESULTS
The mass distributions Y (M) and Y^(M) in coincidence
with the photon energies in the region of 10-21 keV and 21 to 45 keV
corresponding to the light fragment X-ray and heavy fragment X-ray
regions respectively were first sorted out. The mass distributions
YC(M) in coincidence with compton scattered gamma rays were sorted
out by fixing the energy window in the region 50 to 60 keV. Since a known
fraction of events under the light and heavy X-ray peaks corresponds to
compton scattered gamma background, the observed mass distributions
Y;r(M), Y (M) were appropriately corrected using Yc(M) to obtain the
mass distributions Yx (M) and Y (M) in coincidence with K X-rays
alone.
The K X-ray yield per fragment PxtMj^ pj) was then obtained
using Eqn. (1). The analysis was carried out separately for the two
fragment kinetic energy groups of 150-170 MeV, 170-190 MeV and for
all fragment kinetic energies respectively. The values of PX(M) versus
final fragment mass (after neutron emission) obtained for the three
cases are shown in Fig. 5 for the heavy fragment group. In calculating
the final fragment mass from initial masses the neutron number 2) (M)
for different K. E. intervals obtained by Maslin et a r were used. The
total K X-ray yield per fission for the light and heavy groups obtained
for different total kinetic energies are shown in Fig. 6. For the average
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AVERAGE K.E.
K.E. INTERVAL 170-190 MeV-
K.E. INTERVAL 150-170 MeV.
130 WOFRAGMENT MASS ( M f )
150FIG.5
160
K X-rcv yields per frf\/;ment versus ?v •".after noj."rc%: emission for the thret. 'rr.•
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UJ
U_ 0-4
a»!. as01
DCX
0-2
0.1
0-1/J SacHEAVY FRAGMENTSLIGHT FRAGMENTS
-aI
100 130 150 170 190 210 230
TOTAL KINETIC ENERGY (MeV)
K X-ray yieldsfragrant groupsenergy.
FIG.f
fmrr-ent for t^e ll^'.nta function of the tot.sl
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fragment K. E., the K X-ray yields for the light and heavy fragment
groups are found to be 0.11 + 0. 02 and 0. 30 \_ 0. 01 respectively.
The observed increase in the total K X-ray yield from the
heavy group as the kinetic energy decreases is consistent with lie
(16)results of Wyman et al for 0-1 neec interval . This behaviour can
•
be ascribed primarily to the change in the fragment maBB distribution
with kinetic energy. For example, as the kinetic energy decreases the
mass distribution becomes broader with the consequent increase of
the fractional heavy fragment yields in those regions which are away
from the closed shells (Z = 50, N = 82), and where the X-ray yields
are higher.
The present results on the variation of K X-ray yield per
fragment versus fragment mass for the total kinetic energy show the
(A- ft ft*already known feature ' of low yields in the region of closed
shells Z = 50 and N = 82 and increasing yield as one moves away
from the closed shells into the regions of permanently deformed nuclei
at N = 88. Furthermore' although the X-ray yield variation with mass
for the two kinetic energy groups are found to follow essentially the
same behaviour, there is an indication that for the high kinetic energy
group, the yields are somewhat larger than for the low kinetic energy
group in the deformed region. On the other hand for fragment masses
less than 136 the X-ray yields for low kinetic energy case are con-
sistently greater than that for high kinetic energy group. The increase
in the yields in the deformed region for.uigh kinetic energy case may be
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ascribed to the presence of a larger initial angular momentum in this
case leading to a higher population of states undergoing rotational
transitions with a larger probability of internal conversion. In the case
of nuclei in the spherical region where most of the internal conversion
originates not from the transitions between rotational states but from
the single particle transitions in odd A or odd-odd nuclei, the dependence
on initial fragment spin is not expected to be significant. The higher
X-ray yield for low kinetic energy group (high initial excitation energy)
can be the reBult of a larger number of transitions expected as the re-
sidual excitation energy after neutron emission is also expected to be
greater in this case.
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III. K X-RAY HALF LIVES VERSUS FRAGMENT ATOMIC NUMBER
(a) INTRODUCTION
It has been pointed out earlier ' that the electron vacancies
that give rise to X-rays from fission fragments arise primarily from
internal conversion of nuclear transitions during the deexcitation of frag-
ment nuclei. Once such a vacancy is created, the electron transitions
giving rise to X-rays take place very quickly ( & JO sec). Thus the
time of emission of X-rays following fission-is determined by the life-
times of the nuclear transitions being converted. Consequently a study
of K X-ray emission times from individual fragment nuclei can provide
useful information needed to characterize these transitions. A few
studies'1*' °) have been carried out in the past to determine average time
of emission as a function of fragment masses. Due to the effects of
mass resolution, these times of emission represent only a suitably
weighted average over a number of neighbouring nuclei. With a high
resolution Si(Li) detector X-ray spectrometer it is now possible to
determine the average X-ray yields originating from fragments of dif-
ferent nuclear charges and therefore to infer the X-ray emission times
emitted from fragment nuclei of specified nuclear charges.
In this work the spectra of the K x-rays emitted from U236
fragment nuclei were measured with a high resolution Li drifted silicon
detector for the time intervals of 0-110 nsec and 110 nsec - 1000 nsec
after fission. In each time interval the x-ray spectra were measured
for the two cases of the emitting fragment moving towards the x-ray
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detector and away from it. From the analysis of these spectra, the
observed intensities of the K x-rays from different Z fragments were
obtained for the above cases. From the observed ratios of the x-ray
intensities in the time, interval 0-110 nsec for the cases of emitting
fragment moving towards and away from the x-ray detector, the average
x-ray emission times for different fragment nuclei were determined. A
comparison of the spectra in the two different time intervals gave infor-
mation regarding the presence of any relatively long half life components
for X-ray emission originating from any fragment nucleus.
(b) PRINCIPLE OF THE .METHOD
The Fission detector D, the source foil S and the X-ray detec-
tor Dx are placed in line with each other as shown in the schematic
diagram of Fig. 7 where d, dj, do are the distances of the x-ray detector,
fission detector and the Berylliuin window from the Bource foil respec-
tively. If Nj and N2 are the number of X-rays detected in the cases
of emitting fragment moving away from D and towards D respectively,
the ratio Nj /N2 is equal to -fl- j / XLg where -TL j- and -O- 2 are the
effective solid angles of x-ray detection in the two cases respectively.
The solid angles Si-l and - ^ - 2 will depend on d, dJt d2, area of x-ray
detector aad the average x-ray emission times, and to a lesser degree
also on the area of source foil and the fission detector. It is apparent
that as the x-ray emission timen increase, the average point of emis-
sion moves away from the foil. Consequently -H- j / _Q-2 increases
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SCHEMATIC EXPERIMENTAL SETUP FOR X-RAY HALFLIFE MEASUREMENT
Be WINDOW
X-RAY OETECTOR
FISSION OETECTOR
i
rv
FIG.7
t ic diagran of z':.\- experimentfl sctjo forlial+'-lil'e .iQfisur- :er. , .
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with the increase in the emission timee. Therefore from the observed
values of Nj /N2 the average X-ray emission times can be determined
aB a function of the decay constant A and fragment velocity ft . The
exact calculations of -TL j, / XL^ as a function of the decay constant X
and the fragment velocity ft were carried out for the present geometry
with a Monte Carlo programme using computer CDC-3600. The average
life times T for x-ray emission from fragment nuclei of specified
nuclear charges were then determined by a comparison of experimental
values of Nj /N2 and the calculated values of -TL . / SX^,
(c) EXPERIMENTAL
(i) Layout
235 2
A source of U of thickness 200 u.g/cm was coated on a
VYNS film by the electrospraying technique. The source foil and a
surface barrier fission detector were mounted inside a vacuum chamber
having a 10 mil Beryllium window, such that the foil, fragment detector
and the Be window were in line and parallel to each other (Fig. 7). The
fragment detector and the beryllium window were at distances of 1 cm
and 1.5 cms respectively frozn the foil. A collimated neutron beam
from the CIRUS reactor was usnd for this work. To reduce the fast
neutron and gamma ray content of the beam, the beam from the reactor
core passed through 15 cms of quartz and 25 cms cf Bismuth and finally
through a steel collimator which reduced the beam size to 1. 25 cm.
The thermal neutron flux at the foil was about 5 x 10 n/cm2/sec. The
vacuum chamber housing the foil detector assembly was made to have
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very thin entrance and exit windows for the incident neutrons to mini-
mise the beam scattering and therefore the background field in the
region of the X-ray detector. The x-ray detector was a 1. 1 citfi x
0. 3 cm Si(Li) detector cooled to liquid nitrogen temperature and coupled
to cryogenic FET preamplifier. The energy resolution of the x-ray
detector system in terms of FWHM of 26. 25 keV line of Am2 4 1 was 0. 8
keV for low count rates. During the experimental runs, the actual
energy resolution attainable was about 1 keV due to a slight deterio-
ration of the system resolution caused by the highly saturated background
pulses and any long drifts. The X-ray detector was placed at right
angles to the beam direction at a distance of 3. 0 cms from the source
foil. The X-rays were viewed through two 10 mil Be windows, one of
the vacuum chamber and the other of the cryostat and the x-ray detec-
tor was optimally shielded to minimize background.
(U) Electronics and data taking
A block diagram of the electronic arrangement is shown in
Fig. 8. The bipolar outputs of the fragment detector amplifier and the
X-ray detector amplifiers (both in delay line shaping mode) were fed
to two zero cross over (ZCO) units to provide timing pulses. The gain
of the fission detector amplifier was suitably adjusted to avoid trig-
gering of the zero cross over unit by the natural alpha pulses. The
ZCO outputs were fed to a fast coincidence unit of resolution time
(2 t ) equal to 110 nsec and also to a slow coincidence unit of 2 t equal
to 1 u sec. For the purpose of x-ray pulse analysis with optimum .
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DDL SHAPING
FRAGMENTOETECTOR
"V. BIPOLARL \ . 0 U T w
DDL SHAPING
X-RAYDETECTOR
""NsBIPOLAR
V . DELAYEDL^*\OUTAMP/* '
ACTIVE FILTER
z.coUNIT t
2.CO
UNIT
COINC2T«110 ns
BASE LINERESTORER
i
m> t
I
COINC
h
GATE
APf> Anr? Ann AIVA1 i
i
0
BLOCK DIAGRAM OF ELECTRONIC ARRANGEMENT FOR X-RAY EMISSION TIME EXPERIMENT
Flft.f
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resolution, the output of the x-ray preamplifier was fed to an active
filter amplifier with a Gaussian pulse shaping network followed by a
base line restorer, which provided a delayed unipolar output for pulse
analysis. The unipolar outputs of the X-ray detector amplifier and the
fragment detector amplifier were fed to the two ADCs of the 4 parameter
system, which was gated with the slow coincidence output. The output
of the fast coincidence unit was fed to the third ADC to flag the fast
coincidence events. In this way, the pulse heights corresponding to
the kinetic energy of the fragment and the energy of the x-ray and the
timing label pulse were recorded event by event. A high precision
pulser fed at the input of the X-ray detector was first calibrated into
energies using the e.rn. radiations from a Am source. A careful
channel versus energy calibration was^obtained at the start of each run
and further checked at the end, the energy calibration and the system
stability was further monitored during each run by simultaneously
recording a fixed pulser output.
The singles fission count rate was about 27 per sec. The frag-
ment X-ray coincidence rate was about 8 and 11 per minute in the reso-
lving time of 110 nsec and 1 lAsec respectively. In the continuous
running of the experiment for about a month, about 2. 5 x 10 events of
the fragment-X-ray coincidences were recorded.
(d) ALPHA-X-RAY DATA
The present method of determination of emission times re-
quires that the geometry of the set up and in particular the distance
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between the foil and the X-ray detector be known accurately. Since
the measured distances could be subject to slight uncertainties, the
•olid angle of X-ray detection was also determined experimentally by
counting the number of L X-rays per alpha decay of U2 3 4 present in
the source foil wherein 54 keV transition to the ground state of Th2 °
is almost'totally converted in the L subshells. The spectrum of the L.
x-rays in coincidence with alphas was recorded on a pulse height ana-
lyser with the same electronic arrangement by gating the analyser with
the coincidence pulse. From the alpha-x-ray coincidence data, the
experimental solid angle of x-ray detection was determined in the fol-
lowing manners: The total number N. of L x-rays emitted per alpha,
decay was first calculated from the known branching ratios of alpha de-
cay and the measured valued ' of 0. 48 for the average L fluorescence
yield. The observed spectrum of L x-rays was corrected for the detector
efficiency and the total cumber NTJ of L x-rays reaching the detector
per alpha decay was calculated. The solid angle -*"*— of x-ray detection
was then obtained from the relation Si- = NA/NB . This solid angle
corresponds to the X-ray emission at the source foil itself, and was
experimentally determined to be equal to (£0068 £ . 0001).
(e) ANALYSIS OF RESULTS
The peak to valley ratio in the singleifragment pulse height dis-
tribution was observed to be about 10 to 1. On the basis of the recorded
fragment pulse heights, the identification of the fragments into the
light and the heavy group could therefore be carried out without any
significant intermixing.
-
-28 .
The sorting out of the recorded data on the magnetic tape was
carried out with a CDC 3600 computer. Fig. 9 shows the observed
spectra of the K x-rays in the time interval of 0
-
-29-
.' • LIGHT FRAGMENTS MOVING TOWARDS• * . X-RAY DETECTOR
1OOO|- * '. • (a)
• (0-HOnsec Data)
• (110-1000 nsec Data)
500
\
0
u
k HEAVY FRAGMENTS MOVING* TOWARDS X-RAY DETECTOR
1C00• (0-110 nsec Data)
, , . • (110-1000 nsec Data)
»•• •500
200_ I I
100 150 200 250CHANNEL NUMBER
FIG.S
The spectra of K X-rays emitted in the two timeregions of 0-110 nsecs. and 110-1000 nseca. forthe cases of (a) l i^ht fragment moving towardsthe X-ray detector and (b) heavy fraf^ent movingtowards the X-ray detector.
-
-30-
coincidences being leBS than 2%.
(ii) Determination of observed K X-ray intensities from specified
Z fragments
The observed number N(E) of K X-rays per unit energy
interval per fission can in general be expressed a»
where
N (Z) = Number of K X-rays per fission reaching the detectorfrom element Z,
R • = Ratios of the areas of the {, th X-ray component to thesum of all components for element Z,
= Standard deviation of the energy resolution function.
£ z >^ = Energy of the (/th component belonging to eleixient Z.
T| (E) = X-ray detection efficiency.
In order to determine NfZ) the spectrum for the light and
heavy X-ray groups were separately analysed. The background cor-
rected spectrum of each group was fitted to Eq. (1) with a least square
fitting code using the CDC-3600 computer and with the energies and
relative intensities of K
-
-31-
source served as a counter check for the calculation of T\(E). In the
fitting procedure the variance
-
oUi
ui2
35
(b)
IN=50
Io .
5a:
atLUQ. 8aUJ
I 6ID
a(A 4
2 -
Q EMITTING FRAGMENT KOVING TOWARDS X-RAV DETECTOR
§ EMITTING FRAGMENT MOVING AWAY FROM X-RAV DETECTOR(a)
_ n» I ft rx. -is-w
33 41 43 45 49 51FRAGMENT ATOMIC NUMBER
53 57 59 61
(a)- The observed intensities ffx(z) of the K X-rays per fission versus f rag asn« unumber in the tine interval of 0-110 naecs. for the cases of the eraittin..; fratner.tmoving towards and a'vay from the X-ray detector, (b )-The nven^e X-w.y e:niscicn
-
-33-
Monte Carlo method. In these calculations the X-rays were assumed
to be emitted exponentially with a single decay constant'X and -H--,
S\. 2 were determined for a range of values of X and fragment velo-
cities B . These calculations took into account the finite size of the
source foil and the stopping of the fragments in the beryllium window
and the fragment detector. The Doppler change in the solid angle re-
sulting from an anisotropic emissioti in the laboratory system due to
the motion of the emitting fragments was also incorporated in the cal-
culations using the relation XL = -TLO (1 + ji cosO)2 where Q ie the
angle of x-ray emission with respect to fragment direction. Fig. 11
shows the calculated values of -TL^/S^., versus d where d is related
to life- time "T by d = C &T.
The calculated solid angle for T = 0 was found to be equal to
0. 0067 in excellent agreement with the value obtained from the analysis
of alpha-X-ray data. Also the calculated ratio - ^ - 2 / -O-j for f = °o
is euqL to 0. 27, which is in agreement with the value 0. 26 for the ratio
Nv,/N where Nv, and NYO are the intensities for the two c isesJtj XT XJ •*•£
from Z = 52 in the time range of 110-1000 nsec. These agreements
provide an experimental check on the accuracy of the geometry used
for solid angle calculations.
From a comparison of the experimental results of Fig. 10(a)
and the calculated ratios (Fig. 11) for appropriate j3 , the average X-
ray emission times T* versus Z were obtained and theBe are shown
in Fig. 10(b) and Table I. From the data of Fig. 10(a) and (b) and the
-
GM5
UJ
<UJ
xiO10
oUJ
ill
aifl
8
6
4
2
(b)
N=50
\
p o -tf-1-I
COI
Q EMITTING FRAGMENT MOVING TOWARDS X-RAY OETECTOR
B EMITTING FRAGMENT MOVING AWAY FROM X-RAY DETECTOR
33 35 37II > I
ta)
41 43 45 " 49 51FRAGMENT ATOMIC NUMBER
53 59 61
( a ) - The observed in tens i t ies K -̂fz) of the K X-rays per fission versus, fraf-.aanljnumber in the time interval of 0-110 nsecs. for the cases of the emittin:., frairrtetmoving towards and away from the X-ray detector . (b)-The a v e r s e X-xtiy einissicn•times T vers'js the fragment atomic nunber.
-
-33-
Monte Carlo method. In these calculations the X-raye were assumed
to be emitted exponentially with a single decay constant 'X and - ^ - I .
-Tl_ 2 were determined for a range of values of X and fragment velo-
cities B . These calculations took into account the finite size of the
source foil and the stopping of the fragments in the beryllium window
and the fragment detector. The Doppler change in the solid angle re-
sulting from an anisotropic emission in the laboratory system due to
the motion of the emitting fragments was also incorporated in the cal-
culations using the relation _TL- = -TLO (1 + B cosO)2 where 0 is the
angle of x-ray emission with respect to fragment direction. Fig. 11
show8 the calculated values of -TL^/S^., versus d where d is related
to life time ¥ by d = C &T.
The calculated solid angle for T = 0 was found to be equal to
0. 0067 in excellent agreement with the value obtained from the analysis
of alpha-X-ray data. Also the calculated ratio -^-z' -^1 ioT "^ = °°
is euqL to 0. 27, which is in agreement with the value 0. 26 for the ratio
Nv,/N whsre Nv, and N,,., are the intensities for the two cases*1 Xj X I fa
from Z = 52 in the time range of 110-1000 nsec. These agreements
provide an experimental check on the accuracy of the geometry used
for solid angle calculations.
From a comparison of the experimental results of Fig. 10(a)
and the calculated ratios (Fig. 11) for appropriate p , the average X-
ray emission times T versus Z were obtained and these are shown
in Fig. 10(b) and Tible I. From the data of Fig. 10(a) and (b) and the
-
£=0.22
CALCULATED RATIO OF SOLID ANGLES VERSUS
d (CMS)
The calculated ratios _/2-;2/l.j versus ci
•ftI
dsXX>0Cms
-
calculated value of JTL for different T~ and B the' K-X ray yield
per fission were derived and these are shown in Fig. 12(a). For the
sake of comparison, we have al6o shown in the same figure the K X-ray
yield per fission determined in an independent earlier experiment^ ',
where the X-rays from the fragments stopped in a time less than 5x10 "^sec
were measured. The observed good agreexnent between the two indepen-
dent measurements shows the validity of the present method of deter-
mining the solid angle for x-ray detection from flying fragments and
consequently the X-ray emission times. The fragment charge yield curve
estimated by Wahl et al'1 8 ' is also shown in Fig. 12(a) . The K X-ray
yields per fragment obtained from 'iie present data on K-X rays yield
per fission and the above charge yield curve are shown in Fig.22(a). The
K X-ray yields per fragment obtained from the present data on K-X rays
yield per fission and the above charge yield curve are shown in Fig. 12(b).
(f) DISCUSSION OF THE RESULTS
The observed features about X-ray emission times are broadly
speaking, as follows:
(i) Small X-ray emission times of the order of 0.1 nsec in the
region of N = 50 in the light fragment group. The very small X-ray emis-
sion times and the X-ray yields in the region can be attributed to the
presence of wide level spacings in this region giving rise to faster decay
and low interval conversion, (ii) Comparatively long emission times
for 43TC, 52Te and 5gCe. In the present setup, from the ratio of
one could get only the lower limit of the emission times for these
-
z111
IU.oc 0.5UJQ.
U>
O .081-
.06UJ
a.
JL
(b)
111FRAGMENT CHARGE YIELD
EXPTL.K X-RAY VIELO
ffl33 41 43 45 49 51 53
FRAGMENT ATOMIC NUMBER
• 2
15 55
o:.10 CL
oUJ
.05 UJ
©
o55 57 61
( a ) - F X^ray yield per f leal on versus fragment atomic number The dotted bars referto the resul ts of Hef.17» .Also shown in the figure i s the charge yield curveestimated by Wahl et a l v " " ^ (b)« K X-ray yield per fragment versus atomic number.
-
-37-
nuclei as the sensitivity of the technique is limited for emission
times after 3 nBec. For the case of 52Te, a significantly large fraction
of K X-ray intensity is observed in the time interval 110-1000 nsec
showing the presence of predominantly delayed component and these
observed fractions are given in Table n. The half life for this delayed
component has been estimated to be about 200 nsec, if only a single de-
layed component is assumed. For the case of fragment nuclei 43TC,
5gCe no significant yie'd in the 110-1000 nsec time interval is observed
above the background thereby implying that the long life component is
either of very small intensity or the average emission time is less than
about 100 nsec. Isomeric half life for all known isotopes in the region
N = 50-58 are found to vary from days to seconds. It may be therefore
inferred that the isomeric transition half lives have significantly de-
creased in the case of neutron rich fragment nuclei (Z = 43, N ^ 62) due
to the onset of permanent deformation with the addition of extra neutrons.
For the case of 55CS, a noticeable yield above the background is
observed in the time region 110-1000 nsec data, the presence of an
intense fast component and a less intense slow component with emission
time of the order of 100 nsec is concluded in the case of X-ray emission
from 55CS. (iii) For the remaining fragment nuclei, average X-ray
emission times are around 1 nsec.
The broad features of the K X-ray yield per fragment charge
plotted in Fig. 12(b) are found to be similar to those for emission from
Cf252 fragr f̂~ --=
-
-38-
for U^3° fission'1'' . These features are the observed increase in the
X-ray yield as one moves, away from the closed shell region of N = 50,
Z = 50 and N = 82, a significantly lower yield for 5^Xe as compared to
the neighbouring odd Z nuclei and an increasing yield for N £> 88.
These observations on the relative probability of internal conversion
process in fragment nuclei for different Z have been earlier' ' '
qualitatively correlated with the expected properties of the low lying
states in these neutron rich nuclei.
-
-39-
TABLE I
Results from 0-110 nsec data
K X Ray YieldAtomic number per fission Mean Emission Time
Z (0-110 nsec) (nsec)
35
36
37
38
39
40
41
42
.43
44
.003
.009
.015
.016
.020
.018
i 026
.017
.006
.001
j_ .001
+_ .002
+_ .002
+ .002
+_ .002
+ .001
+_ .002
+ .002
+ i 001
+ .001
0.2 +_
0. 2 +
2. 2 +
0. 8 +
0. 2 +
0.4 +
0.8 +
1.4 +
7. 3 +_
0. 4 +
. 1
.1
.7
.5
.1
.1
.2
.3
.2
.1
Light Group Yield 0. 13
50
51
52
53
54
55
56
57
58
59
Heavy Group Yield 0.32
004 +
008 +_
015 +_
063 +_
034+_
076 +_
054+_
034+_
022 £
008 +
.002
.002
.002
.003
.003
.002
.003
.002
.002
.001
0. 1 +
0. 5 +
4.3
0.4 +
1.0:+
2.0J;
1.2+_
0. 8+_
4.8
0. 1 +
. 1
. 1
.1
.2
.7, 5.3.2.2
. 1
-
-40.
TABLE II
Results of 110 - 1000 nsec data
Fragment Observed K X Ray Yield (110-1000 nsec)Atomic Number Intensity per 104 Yield (0 - 1000 nsec)
Z fissions
50 5 .12
51 5 .06
52 110 .79
53 20 .03
54 10 .03
55 42 .06
56 10 .02
57 10 .03
58 6 .03
59 4 .05
-
IV. STUDIES OF K X RAY MULTIPLICITY FROM Cf252
FISSION FRAGMENTS
(a) INTRODUCTION
It is known that the prompt K x-rays emitted in fission result
from the internal conversion process during the / -deexcitation of
fission fragments. Several workers' ^' have carried out experi-
ments to determine the average yield of K x-rays per fragment as a
function of the fragment charge Z, (or mass M) for the case of sponta-
neous fission of Or and also for the case of thermal neutron induced
fission of various nuclei. The results of these experiments contain
information only on the average number of transitions per fragment
which are internally converted. For a proper interpretation of the
data on the K x-ray yields, it is further necessary to inquire about the
shape of the x-ray emission distribution function f^n), where f^(n) re-
presents the fraction of events in which n x-rays are emitted in a
cascade ( £ fz(n)= 1)-In the present experiments we have determined
both the first moment (IT ) and the second moment (n 2) of the x-ray
emission distribution function fz(n) for fragments of specified nuclear
charges to learn about the cascade emission of K x-rays from
nuclear charges.
The experimental arrangement consists of two Independent
x-ray detectors operated in triple coincidence with each other aad
with fission to record the energies of the coincident x-rays. In additioa,
the independent spectrum of x-raye in each detector in coincidence
-
-42-
with fission are also recorded. From the analysis of this data infor-
mation about n(Z), n^(Z) and about the simultaneous x-ray emis-
sion probability from complementary fragments are obtained.
(b) EXPERIMENTAL SET UP
A schematic diagram of the experimental assembly is shown
In Fig. 13. The fission fragments from the Cf source were detected
in 2TT geometry by a parallel plate mini-ionization chamber filled
with pure Argon gas. A Cf " source of strength about 5 x 10' fission
per minute, coated on a nickel backing formed the cathode of the ioni-
cation chamber. The cathode-anode separation was kept about 0.15 cm
and the chamber was operated with a voltage of 100 volts. The walls of
the fission chamber were made of perspex and the perspex windows
through which the x-rays were viewed were reduced to a thickness of
0. 5 mxn to minimize the attenuation of the x-rays. The energies of the
x-rays were measured by two cooled Si(Li) detectors A and B each of
size 1. 0 cm x 0. 3 cm placed on either side of the ionization chamber
assembly at distances cf about 2. 0 cm from the source foil. Each of
the Si(Li) detectors was housed in a cryostat and coupled to a cooled
FET preamplifier. The energy resolutions of X-ray spectrometers
A and B invterms of the full width at half maximum of 26. 25 keV line
of Am2 4 1 were 0. 8 keV and 1.0 keV respectively.
(c) ELECTRONIC ARRANGEMENT
A block diagram of the electronic arrangement is shown in
Fig. 14. The pulses from the ion chamber and the x-ray detectors were
-
DETBIAS.ION CHAMBER OUTPUT
DETBIAS.
' s * ^ J \ / ' y * t* ' f ' '4 J
FET OUTPU1
COLD FINGER Si (Li) Si (Li) COLD FINGER
SCHEMATIC OF THE EXPERIMENTAL ASSEMBLY
FIG. 13
-.s.-iati'.1 diacrr.;n of the experimental r.etuj)the X-ray ruultiplicity experiment.
-
X-RAY DETECTORA
AMP
FISSIONDETECTOR
LAMP
BX-RAY DETECTOR
DISC
DISC
CSINC.
DISC
SCAI+ 128
•0 COlNCc
COINCSCAi£R-M2B
O-
I DELAYED• COMCCENCE
ADC
Q
IADC ADC
2 | 3O I
15MSacDELAY
Ex.
ADC
O
GATINGPULSE
^"•"^• MOfwFfSSJOW
ITORSCALER
BLOCK DIAGRAM OF ELECTRONIC ARRANGEMENT F O R E X A E X B F EXPERIMENT
-
-45-
amplified and fed to discriminators to cut off the natural alpha pulses
and noise pulses respectively. The out-put of the three discriminators
were fed to two double coincidence and a triple coincidence units as
shown in Fig. 14. The double as well as the triple coincidence resolu-
tion time was 1 p.sec. The double coincidence pulses (EXF, EXF )
after being scaled down by a factor of 128, and the triple coincidence
(Ex Ex2
F) P"*868 were fed to an OR gate, the output of which gated the
4 parameter system in the delayed external coincidence mode. The
amplifier outputs from the fission fragment detector and the two x-ray
detectors representing Ff E,,. and Ev were fed to the three ADCs of the
4-parameter system. Thus the triple coincidence events of the type
E x . E F (x-rays detected in both the x-ray detectors A and B and in
coincidence with fission) together with the double coincidence events
of the type Ex F and E F (K x-rays detected in either A or B X-ray
detector in coincidence with fission) were recorded event by event on
to the 4 parameter data acquisition system coupled to a paper punch.
The pulses from the fission chamber,although not containing the infor-
mation about the fragment kinetic energy, were used to discri-
minate against natural alpha pile-up pulses from the Cf̂ source.
During the experiment, the fission events were monitored continuously.
The two x-ray detection systems A and B were previously energy
calibrated using the x-rays from Am241 source and in between the runs
of the experiment this was checked by means of an energy calibrated
precision mercury pulser. For an on-line check on the energy cali-
bration of the x-ray system, the pulser was set at 50 keV which gave
-
-46-
a peak due to chance coincidences with fission. The K x-ray peak
from the Nickel backing of the Cf " source also helped to keep a
check on the stability of '.he system and energy calibration during the
experiment.
(d) DATA ANALYSIS
The recorded data were analysed to obtain the following spectra
for the total number of fission events: (1) Independent energy spectrum
Of K x-vays detected in A and B systems, We will refer to these
independent spectra as NA(E) and N;B(E) respectively. (Z) Energy
spectra of K x-rays detected in system A for the triple coincidence
events of the type Xj X£-F for those cases in which the photons detected
in system B belong to the energy regions of (a) light fragment K x-rays
(10-24 keV), (b) heavy fragment K x-rays (25-50 keV) and (c) compton
scattered gamma rays (50-60 keV). We will refer to these spectra
as NA (E), N̂ ~ (E) and N^ (E) respectively. The observed spectra
NA(E), NA(E) and N^(E) are shown in Figs. 15-17.
These measured K x-ray spectra were converted into K x-
ray yield from specified fragment nuclear charges Z using the least
squares fitting code described earlier in section in e(ii). The code
tock into account the efficiency of detection of detector A and the cor-
rections for the background counts arising from the true coincidences
between the fission and the compton scattered fission gamma-rays.
Using the numbers Ng , Ng and NR of double coincidences per
fission between fission and x-rays detected in system B in the energy
-
:oo
3000
20 00
uoo
10 0Q
i r I I I I
INDEPENDENT SPECTRUM-OF
K X-RAYS DETECTED IN SYSTEM A
NA(E)
putice
I ' ' ' I ' I I 1 1 1 1 1 1 1 1 L 1 L50 100 150
CHANNEL NUMBERFIG.15
Inde pent! e-it spectr.rn of the K X-rpyadetected i.n oysfcem A.
200 250
-
400
300
200
en
CO
UN
1
100
;
•
-
- i*- I- 5
: i•••• •**• ••
•XV•
j 1 •
•
•
•
•
•
• 4
•
• i i t i i
NAL(E)
m
m
*
* * • - .
• •
i . . . • i i i 1 f 1 1 k 1 I 1
03I
50 100 150
CHANNEL NUMBER200 250
FI6-16
Spectravi of K X-rayc detected i n sysSc . A fort : icse GKSotj in which a l i y h t fracrna'it ••' T - r y^.-.K 'aeon detected in s y s t e i "D.
-
ou
300
200
100
• i
ii
i i
i .
KX
RA
Y
- "5
:• i* •
"V
m m
I I
1 |.
1 " 1
t
•t • / *V* •
i I 1
•
#
•
*
i i i
1 1 ' . '
•
•
<
* •
*•
•••
i 1 i i
i i | i i
KlIN
•V.
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 , 1 1
1 1
\ 1
1
•
i i i "
so 100 150CHANNEL NUMBER
200 250FIO.I7
i J p a c t . r u - " , .}i" K X - n ; - t . J o ' . " ! ' " • l e i ' j r . eyat•;••' / . C O J - f i e ; . f
c u o c i n v/hic-i o nonvy frr.;-; i^i-L K " - r n . y h'r..i beo:T -1" tor; tncl
i n s;\ f-i t r M B.
-
-50-
region 10-24 keV, 25-50 keV, and 50-60 keV respectively and the
above spectra, we obtained the distributions YX(Z), Yx and
YX(Z) of K X-ray yields for a specified change Z per fission for those
selected fissions in which another photon falling in the energy region
of light fragment x-rays, heavy fragment x-rays and comptun scattered
i rays respectively has also been detected in system B. The un-
biased K x-ray yields v x ( ^ ) Pe r fission detected in detector A, were
i
also obtained using the number of fission monitors. The triple coin-
cidence spectra YZ'(Z) and YV(Z) this obtained contain two compo-
nents: one representing events in coincidence with the genuine K x-rays
in the energy regions of 10-24 keV and 25 to 50 keV detected in system
B and the second representing events in coincidence with the compton
scattered / -rays detected in system B In these same energy regions.
Corrections to the triple coincidence spectra for the events of the
second type were made as follows: The spectral shape of the component
which Is in coincidence with the compton scattered j -rays was taken
to be the same as that of the experimentally observed Y (Z). Let
fB and fg denote the fraction of the compton background counts
under the light and the heavy fragment K x-ray peaks respectively in
the spectrum NB(E). Then the spectra Y j * (Z) and Y ^ Z ) of the
K x-rays detected in system A in coincidence with the light fragment
group and the heayy fragment group of K x-rays detected in system
B were obtained from the relations:
-
-51-
YXC(Z)]
Thus we get the spectrum of K x-rays detected in system A for the
following three cases; (I) the spectrum of K sprays per fissica, v?ith=
out regard to any x-ray detection by system B (ii) the spectrum
Y^OC(Z) of K x-ray per fission when a light fragment x-ray is detected
in system B and (iii) the spectrum Y X(Z) of K x-rays per fission
when a heavy fragment K x-ray is detected in system B.
Let -H- j and - ^ - ^ be the solid angles of X-ray detections
for systems A And B respectively. The solid angle il_j was deter-
mined from the measured total x-ray yield from the light and heavy
fragments per fission, YX(Z) and the known value of average total
K x-ray yield per fission (viz. 0. *1 per fission). If Y(Z) be the
fragment charge yield per fission .stnd f̂ O*) be the fraction of
fragments of charge Z that emit n number of K x-rays in a cascade,
it follows that
Yx(Z) = Y(Z) ( £ n fz(n)) J L x (1)
W h e " fz(n) = 1
The average yield of x-rays per fragment, n(Z) is given by
^(Z) = £ n fz{n) (2)
(i) Heavy-Heavy or Light-Light X-ray Coincidence Data
The triple coincidence X-ray yields Y^X(ZH) corresponding
-
-52-
to the cases when both systems A and B detect x-rays from the same
fragment charge, say heavy fragment charge ZJJ, is given by
N B
where 7) (ZJJ) is the efficiency of detection in system B of the x-rays
emitted from charge ZJJ and
Y(ZR) T^(ZH) n (ZH) _Q_2 (4)
from eqns. (1), (3) and (4) it follows that
RH* (ZH) = Y " X ( ZH } = ^ n ( n " 1 ) f z H l n ) < r l ( Z H ) ( 5 )
YX(2H)
where2 / - v v/"7 \ ~n l
-
-53-
From the measured values of R and ~5, the second moment n2 of the
distribution function £7(n) can therefore be determined from Eqs. (6 & (7).
Since corresponding to a specified nuclear charge Z we have a
number of fragment masses contributing to x-ray emission, the distri-
bution function. ftnj represents a suitably weighted average of the
responding quantity for the various isotopes
fz(»)= £z,A >A
andOJ(Z.A) = 1
where (JO(Z, A) represents the relative yields of different isotopes of
fragment charge Z. Fig. 18 shows n(Z), the unbiased K x-ray yield
per fragment, and also n*(Zjj). n*(Zj,). In Fig. 19 is shown
n (Z), the second moment of the x-ray emission distribution function fQ.
(ii) Light-Heavy X-ray coincidence Data
Now, n(Z) is the normal (unbiased) average yield of K x-ray
emission per fragment from fragment charge Z. It is of interest to
find out if this yield is altered if one selects only those fission events in
which the complementary fragment charge also emits a K x-ray. If
P (ZJJ, ZL) denotes the probability of simultaneous emission of K x-
rays per complementary fragment (charge) pair (ZH, ZjJ one can
write
-
-54-
The triple coincidence x-ray yield YH x(ZL) or ^ ^ j
corresponding to the case when the detector A detects K x-rays from
a light fragment charge Z^ (heavy fragment charge Zu) and the detec-
tor B detects K x-ray from the complementary heavy fragment
charge Z-_ (light fragment charge ZjJ is given by
PX(ZH, ZL) 7 ] ^ ) Sl2 - O - 7 | / N H (9)
where NB = V^ SL2
also Yx(ZXi) = Y(ZL) ^ ) Si-X (10)
From Eqs. (8), (9) & (10), we get
) = J ^ =L n(ZH) n(ZL) Yx (ZjJ n(ZH).
and similarlyK L ( Z H ) =
Y * ( Z H ) ^ (il)
The value of K (ZL) and K (ZH) thus determined are shown in
Fig. 20.
(e) RESULTS AND DISCUSSION
The normal K x-ray yield per fragment is plotted in Fig, 18
as a function of fragment atomic number Z. It is observed that in the
heavy fragment region (Z = 51 to 57) the yield of K x-ray; from odd Z
fragments is significantly higher than those from even Z nuclei, whereas
a similar dependence was not observed in the light fragment group.
This effect of odd-even nature of fragment charge on the K x-ray emis-
sion probability from heavy fragments was observed earlier by
-
-55-
ft r^ff
OUI
2»
O0
8*2aUiV)
at3-.
J _ JL...J, » I.
-
-56-
(9)Watson et al . Since the x-ray emission is known to be mainly due
to the internal conversion during the V -deexcitation of the fragments,
the yield of K x-ray from a fragment charge Z is dependent on the
relative predominance of low-energy / transitions for which the
internal conversion coefficient is large. Thus the observed large K
x-ray yield per fragment in the region of N = 88 corresponds to the
well known deformed region where a predominance of low energy
transitions is expected. Also shown in Fig. 18 is the K x-ray yield per
fragment from fragment change Z when it is known to have already
emitted one K x-ray. The most striking feature of this plot Is that
for almost all fragment charges the second x-ray emission probability
is significantly large which shows that x-ray emission is in general
a cascade process. Another noteworthy feature of this plot is that
the yield of K x-rays per fragment from a fragment charge (Z) which
is known to have already emitted one K x-ray is, in general, higher
than the average unbiased K x-ray yield per fragment from the same
charge. In view of the fact that the average K x-ray yield per frag-
ment, n(Z), is less than unity and there exists a significantly large
probability for multiple (or cascade) x-ray emission, one can con-
clude that a very sizable fraction of fission events do not emit any x-
rays. Furthermore, the multiple x-ray emission probability is con-
siderably larger for the heavy fragments than for the light fragments.
There is evidence which indicates that multiple K x-ray emission
probability depends on the odd-even nature of the emitting fragment
-
-57-
charge. Further, it is seen that for some fragments (Z = 53, 55, 57,
59, 60, 61), the second x-ray emission probability is greater than
unity indicating a fairly large probability of emission of more than 2 K
x-rays per event in these cases.
The second moment n^ of x-ray emission distribution function
fz(n), defined in Eqn. 6, has been plotted in Fig. 19 as a function of frag-
ment charge. The average second moment n2 of the x-ray emission
distribution function is nearly constant for all lig'it fragment charges
except Z = 43 which has a larger n2 value. This larger value of She
width n^ of the distribution function f(n) for Z = 43 indicates a larger
probability of multiple x-ray emission from this fragment charge com-
pared to its neighbours. In the heavy fragment region the width n^ of
the x-ray emission distribution function shows a strong dependence on
the oddreven nature of the fragment charge and also there is a large
increase in n2 for fragment nuclei in the deformed region (N "%> 88)
indicating an increased cascade x-ray emission in these cases.
Fig. (20} shows a plot of the coefficients K1" (ZR) and K H ( Z L )
as a function of the fragment charge. In general the value of the co-
efficient lies close to unity within the experimental errors but in a few
cases the value is greater than unity. There is a tendency for K
and KH (ZjJ, corresponding to a complementary fragment charge pair,
to be unequal for some charge pairs. Since the coefficient K, defined
in Eqn. (8), represents the degree of enhancement (or decrease) of the
"observed" average K x-ray emission probability from one of the frag-
-
• t i l i i t i
00
45 50FRAGMENT ATOMIC NUMBER
RG.1t
55 60
The second noraori I of the X-ray, emission d ia t r iba t ionfunction versus the fragrne-'Tt atonic 'nu:.ibc;r.
-
K
5
4
3
2
1 -
e KL(ZH)
vOI
3959
4058
4157
4256
4355
4454
45 ZL53-ZH
X X-rny correlat ion coefficientr-; K vernuothe atomic numbers of the pair fragments.
-
-60-
ments when the other fragment has emitted an x-ray, a deviation from
unity of the K coefficient can arise as a result of the following reasons:
(i) There could exist genuine correlations in the x-ray emission from
the complementary fragments due to the common conditions existing at
the scission point. For example, the x-ray emission probability may
sensitively depend on the spins of the fragment pairs which are expected
to be highly correlated.' (ii) the measured correlation could be purely
"instrumental". By "instrumental" we mean the following: When x-ray
emission from a particular fragment charge is being studied, there al-
ways exists, as was pointed out earlier, the unavoidable mixing of the
various isotopes of the same charge contributing to x-ray emission.
If the K x-ray emission probability is independent of the isotopic com-
position of the element under study, the coefficient K will be unity. If
however, the x-ray emission probability is a function of the isotopic
composition of the emitting fragment, the measured value of K will
deviate from unity even in the absence of a physical correlation between
the x-ray emission process of the two fragments. We discuss below
two such possibilities: (a) It is seen from Fig. 18 that the average K
x-ray emission probability is dependent on the odd-even nature of the
fragment charge. If, on this basis, one assumes that for the same frag-
ment charge, nuclei with odd neutron numbers emit more x-rays than
those with even N, then in the study of simultaneous x-ray emission
from fragment pairs, the isotopic distribution of the complementary
fragments under study will be different from the normal case and this
-
-61-
could lead to a value of K different from unity, (b) A similar biasing
will also be introduced if the x-ray emission probability is a function
of the mass of the emitting fragment (either increasing or decreasing).
Let us assume, for illustration, that the x-ray emission probability
increases with increasing mass for the same charge in both the light
and the heavy fragment groups, when x-rays from one of the fragments,
say the light fragments, have been detected in detector B, and the x-
rays from the other fragments being studied using detector A, we are
selectively looking at those events where the light fragments have a
higher mass to charge ratio. Consequently, the heavyfragments will
have a lower mass to charge and hence a lower average K x-ray emiss-
ion probability for the same charge, that is K will be less than unity.
One can show by similar arguments that if the emission probability de-
L H
creases with increasing mass in both fragment groups, K and K will
continue to be less than unity. On the other hand if the emission proba-
bility has an opposite dependence on mass in the light and the heavy
fragment groups, a value of K greater than unity will be obtained.
It is seen from Fig. 20 that the measured values of K for differ-
ent fragment pairs are greater than unity in most cases. On this basis
one can derive the following general conclusions: If the measured
correlation arises as a result of the mass dependence of the x-ray
emission probability, then it follows that the x-ray emission probability
has an opposite dependence on mass for complementary fragment charges.
Such a dependence can be expected as a result or the N = 82 shell.
-
-62-
Looking at the systematics of the energy of the first 2+ states of even-
even nuclei, a general increase in the level spacing of the low lying
levels is expected as one approaches fromceither side the N = 82 shell
for the same Z. Consequently, for fragment pairs of specified nuclear
charges, the interval conversion probability may be decreasing with
increasing neutron number for higher fragments and vice versa for
heavy fragments. The observed values of K different from unity may
also be taken to indicate the presence of an odd-even effect with respect
to neutron number. Alternately, there could also exist a genuine corr-
elation in the x-ray emission from the fragment pairs, due to common
condition existing at scission.
-
-63 -
V. SUMMARY
In this project, detailed investigations of the K x-rays emitted in235
the thermal neutron fission of U and in the spontaneous fission of252
Cf were undertaken by carrying out three different types of experiments
described in Section II, in & IV. Several new and interesting results con-
cerning K x-ray emission from fragment nuclei have been obtained, which
are summarised below:
(i) From a three parameter study of the kinetic energies of pair235
fragments and K x-rays in the thermal fission of U the K x-ray yield
per fragment versus final fragment mass was determined for two kinetic
energy intervals. The broad features of the observed heavy fragment x-
ray yield curve included low x-ray yields in the region of closed shells
Z = 50, N = 82, and increasing yields as one moves away from closed
shells into the region of permanently deformed nuclei It is found that
for the high kinetic energy group as compared to the low kinetic energy
group, the x-ray yields are somewhat larger in the region of deformed
fragment nuclei (N^r88) and are consistently smaller in the region of spher-
ical nuclei (2~50, N-^82). The increase in the yields in the deformed
region for high kinetic energy case can be ascribed to a larger initial angu-
lar momentum in this case leading to a higher population of states undergo-
ing rotational transitions with a larger probability of internal conversions.
For the spherical region, the effect of initial fragment spin is not significant
and the larger initial excitation energy is found to result in larger x-ray
yield. This result implies two different types of cascades in the two regions
of spherical and deformed nuclei. It is found that the total K x-ray yields
from the heavy fragment group increases, while from the light fragment
-
-64-
group remains essentially constant with dec rea se in the fragment total
kinetic energy.
(ii) F r o m the analysis of the data of the experiments to study x-
ray emission t imes it is found that the x - r ay emission t imes a r e of the
order ofO. 1 nsec in the region of N = 50 in the light fragment group. K
x-ray emiss ion from nuclei Tc, Te and Ce is found to have an aver-43 52 58
age longer half life. For the case of ,-7Te, a significantly l a rge r fraction
of K x - r a y intensity is observed in the t ime interval 110-1000 nsec showing
the presence of a predominantly delayed component. The half life for this
delayed component is es t imated to be about 200 nsec. if only a single de-
layed component is assumed. For fragment nuclei Tc, Ce no signifi-43 58
cant yield in the 110-1000 nsec time inverval is observed above the back-
ground implying that the long life component i s either of v e r y small inten-
sity or the average emission t ime is less than 100 nsec. F o r the case ofCs, a noticeable yield above the background is observed in the time range
55
110-1000 nsec . Considering the average emission time of 2 nsec inferred
from the r e su l t s of 0-110 nsec data, the presence of an intense fast com-
ponent and a l e s s intense slow component with emission t imes of the order
of 100 nsec i s concluded in the case of x - r a y emission from Cs. For55
the remaining fragment nuclei, the average x - r a y emission t imes a re found
to be about 1 nsec. The K x - r a y yield per fragment ve r sus fragment atomic
number shows increasing yields as one moves away from the spherical r e -
gion near N = 50, Z = 50 and N = 82 and a significantly lower yield fromXe as compared to the neighbouring odd Z nuclei and an increasing yield
54
-
mve-
-65-
for N >,. 88.
(iii) The experiments described in Section IV are aimed to
8 tig ate an entirely new aspect of the K x-ray emission in fission namely
the K x-ray multiplicity and a possible correlated emission of K x-rays
from fragment pairs. These investigations were carried out for K x-ray252
emission from Cf fragments. We have determined the correlation coe-
fficient K for simultaneous emission of K x-rays from the fragment pairs
and have discussed in Section IV the implications of this coefficient being
different from unity.
The average K x-ray yield per fragment versus Z shows an odd-
even structure, and an increasing yield with the onset of deformed region
(N »̂ 88). The present investigations have shown a new feature that al-
though the average K x-ray yield per fragment is considerably less than
unity ( ~ 0. 2 for fragments in the light group and ~ 0. 4 for those in the
heavy group), those fission events that do lead to x-ray emission give
rise to a cascade of x-rays rather than a single x-ray. This further imp-
lies that a large fraction of events do not lead to x-ray emission. These
result's should be taken into account in any theoretical investigation of K
x-ray emission in fission. In particular the following pointc are worth
emphasizing:
(i) The cascade emission of x-rays from fragments is a general
rule rather than an exception. Only fragment nuclei with charge Z = 40,
42 and 52 show appreciable deviations from this general trend. Such a
-
-66-
behaviour of the Tellurium (Z = 52) fragments is understandable since
this element is known to have a long half life x-ray component (refer
Section III), which most probably arises from a well defined angualr
momentum isomeric state.
(ii) Ambng fragments that do lead to a cascade emission of
x-rays, the multiple x-ray emission is found" to be more striking for
fragments in the heavy group. In particular, for the fragments in the
deformed region, (N ^88) the present results show that in those cases
where one x-ray is already emitted, the average yield of the additional
K x-ray is already emitted, the average yield of the additional K x-rays
is even more than one per fragment implying an appreciable probability
for the emission of three or more x-rays during the cascade deexcitation
of a single fragment nucleus. It may be pointed out that in the region
of deformed heavy fragments a higher second x-ray emission probabi-
lity may be associated with a preferential selection of events with larger
initial spin and in the spherical region with the preferential selection of
particular odd N isotopes for which x-ray yields may be larger.
ACKNOWLEDGEMENTS
The assistance provided by The International Atomic Energy
Agency for the purchase of the four parameter data acquisition system
is gratefully acknowledged. We wish to express our thanks to
Mr. B. R. Balial for assistance in the data acquisition on the four para-
meter unit and also in the maintanance of the electronic instruments.
-
-67-
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