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Transcript of Study Of Nuclei at High Angular Momentum – Day 3 Michael P. Carpenter Nuclear Physics School, Goa,...
Study Of Nuclei at High Angular Momentum – Day 3
Michael P. CarpenterNuclear Physics School, Goa, India
Nov. 9-17, 2011
Some Current Topics In High-Spin Studies
1)Re-emergence of Collectivity at High Spin 2)A New “Spin” on Octopole Collectivity
3)High Spinners can study Neutron Rich Nuclei too!
Re-Emergence of Collectivity at High Spin
159
Triaxial strongly Deformed (TSD)
Superdeformed (SD)
Nuclei at the highest spins: Beyond band termination
J. Simpson et al., Phys. Lett. B 327, 187 (1994)
?
Mid-90’s: From collective rotation to band termination
87/2-
89/2-93/2+
The very weak feeding transitions originate from the levels of weakly-deformed, core-breaking configurations.
Evans et. al., Phys. Rev. Lett. 92, 252502 (2004)
157Er
Mid-2000’s: Feeding of the terminating states
158Er
157Er
2007: Evidence for return to collectivity
E.S. Paul et al., PRL 98, 012501(2007)
E.S. Paul et al., PRL 98, 012501 (2007)
2007: Return to collectivity
TRIAXIAL(negative-gamma)
TSD
NEAR-AXIAL(Enhanced Deformation)
TRIAXIAL(positive-gamma)
TSD
2011: What deformation?
90O
FW
BW
2011: Doppler Shift (DSAM) Measurement
X. Wang et al., PLB 702, 127
TSD3
ED
TSD1
TSD2
MEASURED
ZONE
MEASURED
ZONE
MEASURED (band 1s)
CALCULATED
TSD1 TSD2 TSD3 ED
Qt
(eb)
158Er: 11.7 (+0.7, -0.6)
157Er: 10.9 (+0.6, -0.5)
6.0 – 7.2
10 – 11.2
8 – 9.2
6.7 –
7.9
Qt = Q0 * cos(+30O)/cos(30O);Q0 = [2*(1+ 2/2)+25/33* 4
2- 2* 4]*[4/5*(1.2)2*Z*A(2/3)]/100;
Qt is transitional quadrupole moment; Q0 is intrinsic quadrupole moment;4 is set to be 0 here; Z is proton number; A is mass number.
Theory vs Experiment
THEORY NEEDS WORK STAY TUNED
X. Wang et al., PLB 702, 127
A New “Spin” On Octupole Collectivity
Octupole Collectivity
I. Ahmad & P. A. Butler, Annu. Rev. Nucl. Part. Sci. 43, 71 (1993).
P. A. Butler and W. Nazarewicz, Rev. Mod. Phy. 68, 349 (1996).
Where to find enhanced octupole collectivity
126
82
50
28
}
}
}
}g9/2
p3/2
h11/2
d5/2
i13/2
f7/2
j15/2
g9/2~134
~88
~56
~34
A~222 (Rn-Th)
A~146 (Xe-Sm)
Long-range interactions between single particle states with Δj = Δl = 3;
Difficult regions to study experimentally
Multi-Nucleon Transfer: 136Xe + 232Th (Gammasphere)
In addition, 226,228,230,232,234ThJ.F.C. Cocks et at., Nuc. Phys. A 645 (1999) 61
A~146 Region (Ba, Ce, Nd, Sm)
144Ba
• Neutron rich region, excited states populated by spontaneous fission.
• CARIBU at ANL will provide reaccelerated beams of neutron-rich Ba isotopes for Coulomb excitation studies.
16
Rotation appears to stabilize static octupole shape
J. Smith et al., Phys. Rev. Lett. 75 (1995) 1050.
12
)1()( 11
I
EIEIEIS III
Large Dipole Moments
D0 ~ [B(E1)/<Ii010|If0>]1/2
where
D0 > 0.2 eb-fm
Octupole Rotation: signatures
Signature 1: 1- energy & hindrance in decay
Odd-A Nuclei Exhibit Evidence of Octupole Collectivity
S. Zhu et al., Phys. Lett. B618, 51 (2005)
Octupole phonon coupled to quasiparticle
Signature of Octupole Collectivity in Odd-A Systems
Parity Doublets (Octupole deformed)
S. Frauendorf, Phys Rev. C 77 (2008) 021304(R).
Alternative Explanation of static Octupole Deformation
)()(:
/
1
3
nnc
c
EE
i
23 2
1)
2
1( nEn
23
'
2
1)
2
1()( ninEn
Energy = Vibrational + Rotational
Lowest excitation when phonon’s align with rotational axis.
At critical frequency, c, all phonon Routhians converge resulting in phonon condensation.
3/3c
What is the Resultant Shape at Condensations
S. Frauendorf, Phys. Rev. C 77 021304(R).
Consequence of Anharmocities.
• Due to anharmocities, phonons bands will cross at different frequencies
• Phonon’s of same parity will interact.
• Resulting yrast line will have states on average which appear to be interweaved as expected for static octupole shape.
Comparison of the energy staggering S(I) in the Pu isotopes [6] and in 220Ra and 222Th. S(I) is defined as:
12
)1()( 11
I
EIEIEIS III
Octupole Correlations around 239,240Pu: Rotation, Vibration or something else?
Evidence for strong correlations at high spin: I+ & I – form 1 band at high spin, parity doublets in 239Pu alignments, E(1-), hindrance factors
I. Wiedenhöever et al., Phys. Rev. Lett. 83, 2143 (1999).S. Zhu et al., Phys. Lett. B618, 51 (2005).R. K. Sheline & M. A. Riley, Phys. Rev. C 61, 057301 (2000).
240Pu
• Interleaving E1 transitions now observed between yrast (1) and octupole (2) bands.
• Positive parity band built on 0+ state at 861 keV is observed to high-spin.- Competes in excitation energy with yrast
band.- Decays exclusively to octupole band- Large B(E1)/B(E2) ratios: ~110-8 fm-2
- Band with these characteristics not seen before
Can One Distinguish Between the Two Pictures?
New Results on 240Pu
X. Wang et al., Phys. Rev. Lett. 102, 122501 (2009)
Dipole Moment at High-Spin is Large
21
25
240Pu
D0 > 0.2 e fm (assuming Q0 ~ 11eb)
, X. Wang et al., Phys. Rev. Lett. 102 122501 (2009)
Evidence for Octupole Condensation?S. Frauendorf, PR C77, 021304(R) (2008) Octupole Condensation concept:
Rotation of a prolate deformed nucleus with a super-imposedoctupole vibration with phonon spin aligned with rotational axis
Band 1 0 phonon, Band 2 1 phonon, Band 3 2 phonons
Accounts for observations, i.e., bands, energies, alignments,branching ratios etc.
X. Wang et al., PRL 102, 122501 (2009)
secondnegative-parity,odd-spin band
B(E1)/B(E2):2 – 3 10-6 fm-2
(staggering)
Vibrational nucleus220Th
W. Reviol et al., PRC 74, 044305 (2006)
S=-1
Octupole Correlations: Generalization of Picture Tidal Waves
N=130 vs. N=132Less “rotational-like”(weakly deformed), butOctupole features persist.
N=130 N=132
hωc = 0.21 MeV(constant ω)
Octupole Correlations: Generalization of Picture Tidal Waves
Superposition of two surface waves with ω2=1/2 Eγ and ω3=1/3ΔEΔI=3
W. Reviol et al., PRC 74, 044305 (2006)
n=0
n=1
n=2
220Th130
High Spinners Can Study Neutron Rich Nuclei Too!
30
Modification or Disappearance of Shell Gaps Stability
Neutron Drip Line
known predicted
Weak BindingJ.Dobaczewski et al., PRL.72, (1994) 981,
T. Otsuka et al., Phys. Rev. Lett. 87
(2001), 082502.
d5/2
d3/2
Explains why 24O16 is heaviest bound oxygen isotope and not 28O20
Explains why 32Mg20 is deformed and not spherical.
31
Do New Shell Gaps Develop in the f-p Shell?
Removal of protons from f7/2 shell
weakens the f7/2-f5/2 monopole interaction
strength, resulting in the f5/2 orbital pushing up in
energy.
Opens possibility for shell gaps at N = 32, 34.
Shell Model Predictions using GXPF1 Interaction
2+
4+
6+
0+
7+
9+
10+
11+
50Ti 56Ti
0+
2+
4+
6+
8+
9+
10+
0+
2+
4+
6+
8+
7+
8+
10+
9+
11+
12+
52Ti 54Ti
0+
2+
4+
6+
7+
8+8+
10+
9+
11+
12+N=28 N=30 N=32 N=34
p3/2
p1/2
f7/2
p3/2
p1/2
f5/2
g9/2
M. Honma et al., Phys. Rev. C65 (2002) 061301(R)
33
Studies of Ca-Ni Neutron Rich Isotopes:
• Collaboration began 2001 between ANL, NSCL, Krakow, Manchester, Maryland
• Data obtained at several different facilities (NSCL and ATLAS) utilizing different techniques to excite the nucleus and measure the decay:
What is the evidence of new shell gaps at N=32 and 34 for Z<28.
How robust is the N=40 gap for Z<28?
Experiment Evidence for N=32 Gap (circa 2001)
J.I. Prisciandaro et al., PLB 501, 17 (2001)
(?)
35
First Results on neutron rich 54Ti (N=32):
Before this investigation, very little known about 54Ti.
Two experiments undertaken to study properties of 54Ti.
Beta decay of 54Sc at NSCL (production of 54Sc from fragmentation of a 86Kr beam).
In-beam spectroscopy with Gammasphere utilizing the reaction 48Ca + 208Pb (production of 54Ti via a deep inelastic reaction instead of fusion-evaporation)
R.V.F. Janssens et al., PLB 546, 22 (2002)
R.V.F. Janssens et al., Phys. Lett. B 546, 22 (2002)
54Sc b-Decay Results (NSCL)
decay
H.L. Crawford et al.,
Phys. Rev. C 82 (2010) 014311
Production rate: 0.5 54Sc/s
37
Deep-inelastic data: Quest for 54Ti
38
Identified Products from 208Pb + 64Ni @ 350 MeV
W. Królas, R. Broda, B. Fornal , T. Pawłat, H. Grawe, K.H. Maier M. Schramm, R. Schubart, Nucl. Phys. A724 (2003) 289.
64Ni
208Pb
39
54Ti results from 48Ca + 208Pb deep inelastic reaction measured with Gammasphere
2+
4+
6+
7+
8+(8+)(9+)
(10+)
R.V.F. Janssens et al., PLB 546, 22 (2002)
40
Similar set of experiments on 56Ti
B. Fornal et al., PR.C 70, 064304 (2004)
48Ca + 238U @ ATLAS with Gammasphere56Sc decay at NSCL with SeGa
S. Liddick et al., PRC 70, 064303 (2004)
41
The Ti story: N=32 shell gap, N=34 no gap.
00+
15542+
1554
26754+
1121
31996+
524
61357+
2936
65398+
3340
404
6769(9+ )
230
7570(10 + )
8790(11+
)
50Ti
00+
17562+
27044+
33886+
58977+
64008+ 66299+
751610 +
879011+
GXPF1
00 +
10502+
1050
23184 +
1268
30296 +
711
4288(8 + )
1259
6693(10 + )
2405
8857
2164
9088
2395
231
52Ti
00 +
12132 +
24184 +
31036 +
45398+ 4750
7 +
61818 +
679010+
75109 +
953811+
1067212+
GXPF1
00 +
1495(2 +)
1495
2497(4 +)
1002
2936(6 +)
439
5111
2175
(7 + )
5459(8 + )
2523
348
5904(8 + )
2967
6187(9 + )
728284
6432(10+ )
245
54Ti
00 +
15092 +
26334+
31526 +
53847+
57708+
62088+
65639 + 679310
+
907511+
1048712+
GXPF1
00 +
1128(2 + )
1128
2289(4 + )
1161
2979(6 + )
690
((8 + ))
1230
56Ti
00+
15162+
25294+
30446+
8 + 5352
9+ 5387
693710 +
GXPF1
3228 34
1129
f7/2
p3/2
p3/2
p1/2
p1/2
f5/2
42
32 34
(6+)
(4+)
Theory Development: GXPF1A
GXPF1A vs GXPF1:
T=1 matrix elements
involving p1/2 and f5/2
modified
p1/2 - f5/2) gap
reduced by ~0.5 MeV
M. Honma et al., Proc. ENAM (2004)
43
Is there a N = 34 gap for 54Ca between f5/2 and p3/2?
• No evidence of shell gap at N=34 for Cr or Ti isotopes.
• Shell model calculations using GXPF1A predict sizeable shell gap for 54Ca (N=34).
• Shell model calculations using KB3G interaction predict no neutron shell gap for 54Ca.
• No experimental data available on 54Ca excited states.
44
Is there a N = 34 gap for 54Ca between f5/2 and p3/2
f7/2p3/2)2f5/2(8+)
(6+) f7/2p3/2)2p1/2
51Ca
(9/2-)
(5/2-)
(p3/2)2f5/2
(p3/2)2 p1/2
B. Fornal et al., Phys. Rev. C 77, 014304 (2008)
See also M. Rejmund et al., Phys. Rev. C 76 (2007) 021304(R)
45
Is there a N = 34 gap for 54Ca between f5/2 and p3/2?
M. Rejmund et al., Phys. Rev. C 76 (2007) 021304(R)
K = KB3GM G=GXPF1A GM=modified GXPF1A
Thank You For Your Attention
andGood Luck With You Thesis
Work