Nuclear structure studies of neutron-rich
nuclei produced in 252Cf spontaneous fission
A.V. Ramayya
ISCHIA2014
134Sn
0n
0n
1n
118Cd
120Cd
2n
3n
4n
5n
6n
133Sn
132Sn
1n
119Cd
2n
118Cd
3n
131Sn
130Sn
131Sn
130Sn
4n
117Cd
5n
116Cd
6n
115Cd
114Cd
Partner relationship between Cd and Sn
isotopes produced from SF of 252Cf.
Difficulties in Analysis
• Approximately we have 200 nuclei.
• If each nucleus emits ~30 g-rays we will have ~4500
g-rays.
• Most of them will be in the energy range of 100-1000
keV.
• Approximately four g-rays per keV.
• We need triple g-ray coincidences.
• To resolve them we need Gammasphere or such
large detector arrays. Measured ggg and gggg
coincidences
• Coincidences with g-rays from the partner nuclei
• Wherever possible, measured gg(q)data.
151,153Pr
gated Y relative yields (from 252Cf fission data)
152Ce
426.4-487.6-538.5
578.2
487.6-538.5
Spectra of 152Ce showing the purity of a triple gate compared to a double gate
with contaminations from 106Mo(538.7) – 142Ba(487.0), and 102Zr(486.6) –
148Ce(537.2) fission partners.
Theoretical calculations by Napoli Theory group
Aldo Covello
As a two-body interaction between the valence nucleons, a
realistic effective interaction derived from the CD-Bonnnucleon-nucleon(NN) potential were employed.
133Te 137,138Cs:
132Sn
as a closed core and letting the valence protons and neutrons
occupy the five single-particle (sp) orbits of the 50–82 shells.
93Sr:
88Sr
as a closed core and letting the 5, 2, 4, and 6 valence
neutrons, respectively, occupy the five levels of the 50-82 shell.
As a two-body interaction between the valence nucleons, a
realistic effective interaction derived from the Bonn-A
nucleon-nucleon(NN) potential were employed.
Single proton and neutron energies have been taken from
the experimental data of 133Sb and 131Sn.
C
D
B
• Particle-hole states in 133Te
are interpreted as coupling
of a neutron h11/2 hole to
the 134Te core.
• Shell model calculations
yield results for bands A, B,
C and D in good agreement
with the experimental data.
A
Phys. Rev. C 65, 034319 (2002)
As a two-body interaction between the valence nucleons, a realistic
effective interaction derived from the CD-Bonn nucleon-nucleon(NN)
potential were employed. Single proton and neutron energies have been
taken from the experimental data of 133Sb and 131Sn. Shell model
calculations have been performed by using OXBASH computer code.
As a two-body interaction between the valence nucleons, a realistic
effective interaction derived from the CD-Bonn nucleon-nucleon(NN)
potential were employed. Single proton and neutron energies have been
taken from the experimental data of 133Sb and 131Sn. Shell model
calculations have been performed by using OXBASH computer code.
137
55
Cs
138
55
Cs
Shell model calculations indicated the important role
played by the excitation of the valence protons outside
the Z=50 middle shell and f7/2 valence neutrons outside
the N=82 major shell.
Assuming 88Sr as a closed core, performed shell model
calculations.
• If the intermediate state interacts with a
magnetic field of sufficient strength for a
sufficient length of time, then the
experimentally observed correlation will be
attenuated.
• Specifically, for a constant magnetic field,
B, a nucleus with spin I and magnetic
moment m will precess about the direction
of B with the Larmor precession frequency.
L  
m N gB

W(q)  1  A G P (cosq)  A G P (cosq)
theory
2
2 2
exp
k
theory
k
A
Gk 
A
theory
4
4 4
k
1
1

(1  2
)
2 2
2k  1
q0 1  q 
N (qn )  A (1  A P (cosqn )  A P (cosqn ))
exp
0
exp
2 2
exp
4 4
The Larmor Precession frequency, L
L  
m N gB

mean precession angle,

m N gBHF 

f
 L
BHF : nuclear hyperfine field
 : mean life time
Phys. Rev. C 78, 044331 (2008)
(Covello et al.)
(Brown et al.)
Fragment
 (ns)
B (Tesla)
100Zr
0.78(3)
27.4(4)
0.32(5)
102Zr
2.76(36)
27.4(4)
0.25(4)
104Mo
1.040(59)
25.6(1)
0.28(6)
106Mo
1.803(43)
25.6(1)
0.24(3)
108Mo
0.72(43)
25.6(1)
0.3(3)
146Ce
0.36(4)
41(2)
0.30(6)
148Ce
1.46(9)
41(2)
0.37(5)
g
Generic level schemes of odd-A nuclei
J=0,1,2,3 …
(J+5/2)+
(J+9/2)-
(J+5/2)-
(J+3/2)+
(J+7/2)-
(J+5/2)-
(J+3/2)-
(J+1/2)+
(J+1/2)-
Mixing ratios of DI=1 transitions within a rotational band
gR = ½(Z/A), gK : intrinsic g factor
a: Nilsson coefficients, gl=0, gseff=-2.296
Q0  I f K 20|I i K 
5 1 Eg
 ( E 2/ M1) 
3
12 K 12
. 10 ( g K  g R )  I f K10|I i K 
Q0
  917
. 2/3
ZA
g s  gl
2
2
g K  gl 
(al , K 1/ 2 al ,K 1/ 2 )

2K
13/2
-
390.6
11/2
9/2
-
283.2
138.3
7/2
5/2
-
95.3
105Mo
95.3
5/2[532]
-0.15
-0.12(3)
Qo=3.06
138.3
5/2[532]
-0.17
-0.25(4)
1961 Greiner and
Faessler introduced
improved rotation vibration model for
deformed nuclei
S.J. Zhu et al., Int. J. Mod. Phys. E18, 1717 (2009)
Multi-phonon gamma vibrational bands have
been observed in even-even nuclei
104,106,108Mo and
108,110,112,114Ru
For odd A nuclei, the multi-phonon gamma
vibrational bands involve the coupling of the
single particle, collective vibrational and
collective rotational motions.
Comparison of Triaxial Projected Shell Model (TPSM) calculations
for 105Nb with experimental data.
g
2g
PRC88, (2013)
Y.X. Luo et al., J. Phys. G31, 1303 (2005)
Are 116-126Cd levels good multi-phonon
candidates?
Studied decays of 116-126Ag to 116-126Cd
at LeRIBSS, Batchelder et al.
Studied spontaneous fission of 252Cf to levels
in 116-122Cd, Luo et al.
Earlier observations were interpreted as the vibrational spectrum
Cd isotopes for
Vibrational cases!
Levels and B(E2) values expected for
the harmonic quadrupole vibrator
No Good 0+ or 2+ three-phonon candidates
• Level schemes of Cd isotopes are expanded to high spins.
118Cd – 18+ for the ground band.
Observed several side bands.
120Cd- 18+ for the ground band.
Observed several side bands.
122Cd-14+ for the ground band.
Not observed side bands.
• Complimented with decay spectroscopy of 116Ag-126Ag.
• 118-122Cd ground bands are
a) 2 quasi proton holes (g9/2)-2 to 8+
b) 2 quasi neutrons (h11/2)2 above 8+.
• Possible phonon bands are not definitive.
Mass- and Z- gated spectrum on 151Pr
(from 238U+9Be induced fission data)
Our recent attempts.
151Pr
level scheme obtained in the present work
In the paper J. K.
Hwang et al. Phys.
Rev. C 82, 034308
(2010)
band 1 and band 2
were assigned to 151Pr
In the paper S. H. Liu
et al. Phys. Rev. C 84,
044303 (2011)
band 3 and band 4
were assigned to 152Pr
In the paper T.
Malkiewicz et al. Phys.
Rev. C 85, 044314
(2012)
band 1 and band 2
were assigned to 152Pr,
band 3 was assigned to
151Pr, band 4 was
assgined to 153Pr
New results
Thank You, Aldo,
for your contributions to
shell model calculations