1. Observation of Octupole Correlations in Ba and Ce Nuclei
N. T. Brewerψ, W.A. Yzaguirre, J.H. Hamilton, S.H. Liu, A.V. Ramayya, J.K. Hwang, Y.X. Luo,
J.O. Rasmussen, S.J. Zhu, C. Goodin, G.M. Ter-Akopian, A.V. Daniel

2. Experimental Details
Gamma-rays emitted in the Spontaneous Fission of 252Cf were measured with Gammasphere at LBNL and have given great insight into the structure of neutron rich nuclei.
Using our high statistics data (5.7 *1011 triple and higher γ-ray coincidences), we have reexamined high-spin states and the gamma-transitions associated with octupole correlations in 143−146 Ba and 148 Ce.
Both the high statistics of our data and the angular coverage afforded to us by Gammasphere also allow us to do angular correlation measurements.

3. Experimental Details
21/2+ → 17/2+ → 13/2+
145Ba
Examples from 145Ba are shown here for the angular correlation for a Quadrupole-Quadrupole cascade and for a Dipole-Quadrupole cascade.
Ideally Q-Q has A2/A4 = 0.102/ 0.009
And D-Q has A2/A4 = / 0.00
145Ba
13/2+ → 11/2- → 7/2-

4. We therefore expect to see two rotational bands For even A
Observables associated with Reflection Asymmetry
W. Nazarewicz and P. Olanders Nucl. Phys. A441 (1985)
For a simplectic rotational band, parity (p) alternates with spin (I ) for simplex characterized states as
p = s e-i πI s2= (-1)A
We therefore expect to see two rotational bands
For even A
s= +1, Ip= 0+,1-,2+,3-,4+…
s= - 1, Ip= 0-,1+,2-,3+,4-…
And for odd A
s= +i, Ip= 1/2+, 3/2-, 5/2+, 7/2-…
s= - i, Ip= 1/2-, 3/2+, 5/2-, 7/2+…
Until now, in even-even isotopes, spins and parities have not been established for both types of rotational bands s= +1 and s= -1.

5. new angular correlations are shown in blue.
Experimental Level Schemes : New levels and gammas are shown in red and
new angular correlations are shown in blue.

6. Experimental Level Schemes
Gate on and 331 with and 509 feeding transitions subtracted
1351.5 c
1238.5
Gate on and Mo partner with 331 and 639 feeding transitions subtracted
1569.5

7. Experimental Level Schemes
prev. known 566.3
Gate on and 456.8
New 539.7,546.7,551.6

8. Experimental Level Schemes

9. Experimental Level Schemes

10. s = -1 144Ba 144Ba s = -1 s = -1 s = -1 148Ce 148Ce gamma band 148Ce
Angular Correlation curves from 144Ba and 148Ce including first time measurement of 3+, 5+, 6- and 7+ states.
6- → 6+ → 4+
7+ → 6+ → 4+
s = -1
144Ba
144Ba
s = -1
3+ → 4+ → 2+
5+ → 4+ → 2+
s = -1
s = -1
148Ce
148Ce
gamma band
9- → 8+ → 6+
4+ → 4+ → 2+
148Ce
148Ce
s = +1

11. Conclusion
Extended to very high spins the level schemes of 5 neutron rich nuclei near Z= 56 , N = 88.
Firmly assigned spin and parity to s = -1 type bands in 144Ba and 148Ce.
Observed the 3+ state in 144Ba and the 3- state in 148Ce.
Proposed a gamma vibrational band in 148Ce.
Proposed an s = -1 band in 146Ba .
Observed the angular momentum stabilization of octupole deformation at high spin as well as trends in and further measurement of the dipole moment.
All of this paints a consistent picture of octupole deformation in these nuclei.

12. References
[1] F. Yang and J. H. Hamilton, Modern Atomic and Nuclear Physics, Rev. Ed,(2010)
[2] P.A. Butler, W. Nazarewicz, Rev. Mod. Phys.,68, 2, , (1996)
[3] M. Ismail et. al., Nucl. Phys. A, 828, , (2009)
[4] J. Engel et.al., Phys. Rev. C, 61, , (2000)
[5] K.E.G. Löbner, Gamma-Ray Transition Probabilities in Deformed Nuclei, (1975)
[6] P. Ring and P. Schuck, The Nuclear Many Body Problem, 1 ed., (2004)
[7] W. Nazarewicz, P. Olanders, Nucl. Phys. A,441, , (1985)
[8] L.M. Robledo et. al., Phys, Rev. C, 81, , (2010)
[9] D.R. Hamilton, Phys. Rev., 58, 122, (1940)
[10] J.H. Hamilton et. al., Prog. Part. Nucl. Phys., 35, , (1995)
[11] D.C. Radford, Nucl. Instr. Meth. A, 361, , (1995)
[12] A.V. Daniel et. al., Nucl. Instr. Meth. B, 262, 2, , (2007)
[13]
[14] W. Zhang, Z.P. Li, S.Q. Zhang, Chinese Physics C 34, 8, (2010) and private communication
[15] S.J. Zhu et. al. Phys. Lett. B, 357, (1995)
[16] M.A. Jones et. al., Nucl. Phys. A, 605, (1996),
[17] S.J. Zhu et. al., Phys. Rev. C, , (1999)
[18] R.L. Gill et. al., Phys. Rev. C, 27, , (1983)
[19] H.W. Taylor et. al., Nuclear Data Tables, A9, 1-83, (1971)
[20] P. Haustein et. al., Nuclear Data Tables, 10, , (1972)
[21] G.A. Leander, W. Nazarewicz, P. Olanders, J. Ragnarsson, J. Dudek, Phys. Lett., 152B, 5,6 (1985)

13. Observables associated with Reflection Asymmetry
W. Nazarewicz and P. Olanders Nucl. Phys. A441 (1985)
In addition, We use three formulae to quantitatively analyze our data δE(I) , ω(I)-/ω(I)+, and D0.
δE(I) = E(I-) -1/2 (E((I+1)+) + E((I – 1)-))
ω(I)-/ω(I)+ = 2[E(I+1)- - E(I-1)-]/[E(I+2)+-E(I-2)+]
B(E1)/B(E2)= 0.771[Eγ(E2)5Iγ(E1)]/[Eγ(E1)3 Iγ(E2)] (10-6 fm-2)
D0 = [5B(E1)/16B(E2)]1/2 Q0
δE(I)= 0, ω(I)-/ω(I)+ =1 , and D0 <<1 are indicative of stable octupole deformation

14. Analysis including δE(I), ω(I)-/ω(I)+, D0 and Angular correlation
Stable
Octupole
Deformation
Stable
Octupole
Deformation

15. Table of Angular Correlations
Coincident γ’s
(mixing considered
D- Dipole
Q-Quadrupole
O-Octupole)
A2/A4 δ
Comments
144Ba
655.5/584.7 (Q,O - Q)
0.11(1) / 0.04(2)
0.02(3)
0.102/0.009 (Q-Q)
/ (D,Q- Q)
- 0.27(3) / (5)
Assigns I=5,7. Considering transition to 8+ is only consistent with I=7.
/ (D.Q –Q)
(2) / (3)
Assigns I=3,5, with the above I=5.
/ (D,Q – Q)
0.15 (6) / 0.08 (7)
.13 (16)
Consistent only with 6 and likely 6-
145Ba
(Iπ previously known)
350.0/112.9 (Q – D,Q)
-0.11(1) / 0.01(2)
0.11(4)
112.9 is M1/E2 previously δ=0.13(7)
185.7/277.0 (D,Q - Q)
-0.21(2) / (24)
0.20(4)
185.7 is M1/E2 previously δ=0.2(+1,-1), 3(+1,-1)
364.0/165.0 (Q – D,Q)
-0.15(2) / (2)
-0.18(4)
165.0 is M1/E2 previously δ = -0.31(+24,-27)
148Ce
New Spin Assignments
295.4/663.0 (Q – D,Q)
0.05(5) / (8)
10(6)
Consistent only with I=3
969.9/295.4 (D,Q – Q)
-0.06(1) / (2)
9.6(14)
Consistent only with I=5
363.7/ (Q – D,Q)
0.03(2) / (3)
-0.07(9)
2.8(8)
Consistent with I= 6,7, δ shown for I=7
167.1/ (D,Q – Q)
-0.04(2) / (35)
0.04(4)
Consistent only with level with I=7, and gives I=6, 8, or 9 for the level. δ is shown for I=8
353.0/167.0 (Q- D,Q)
-0.07(3) / (4)
Rules out as I=6, most consistent with D-Q value but cannot assign spin to the level at 2307.
353.5/444.6 (Q – Q,O)
0.16(3) / 0.03(5)
.14(8)
is consistent with Q-Q
295.2/ (Q - D,Q)
-0.02(2) / 0.16(4)
3.8(9)
Consistent only with I=4
386.3/ (Q – D,Q)
-0.07(2) / 0.13(4)
4.5(18)
Consistent only with I=6
450.7/ (Q – D,Q)
-0.06(2) / (2)
0.01(3)
consistent only with I=9
Table of Angular Correlations

16. RMF Calculations for Ba

17. RMF Calculations for Ba

18. DFT Calculations for Ba