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 ψNathan.t.brewer@vanderbilt.edu

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.

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 = -0.071/ 0.00 145Ba 13/2+ → 11/2- → 7/2-

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.

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.

Experimental Level Schemes Gate on 199.5 and 331 with 431.5 and 509 feeding transitions subtracted 1351.5 c 1238.5 Gate on 199.5 and Mo partner with 331 and 639 feeding transitions subtracted 1569.5

Experimental Level Schemes prev. known 566.3 Gate on 541.6 and 456.8 New 539.7,546.7,551.6

Experimental Level Schemes

Experimental Level Schemes

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

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.

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, 349-421, (1996) [3] M. Ismail et. al., Nucl. Phys. A, 828, 333-47, (2009) [4] J. Engel et.al., Phys. Rev. C, 61, 035502, (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, 420-44, (1985) [8] L.M. Robledo et. al., Phys, Rev. C, 81, 034315, (2010) [9] D.R. Hamilton, Phys. Rev., 58, 122, (1940) [10] J.H. Hamilton et. al., Prog. Part. Nucl. Phys., 35,635-704, (1995) [11] D.C. Radford, Nucl. Instr. Meth. A, 361, 295-305, (1995) [12] A.V. Daniel et. al., Nucl. Instr. Meth. B, 262, 2, 399-406, (2007) [13] http:/root.cern.ch [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) 273-280 [16] M.A. Jones et. al., Nucl. Phys. A, 605, (1996), 133-159 [17] S.J. Zhu et. al., Phys. Rev. C, 051304, (1999) [18] R.L. Gill et. al., Phys. Rev. C, 27, 1732-44, (1983) [19] H.W. Taylor et. al., Nuclear Data Tables, A9, 1-83, (1971) [20] P. Haustein et. al., Nuclear Data Tables, 10, 321-467, (1972) [21] G.A. Leander, W. Nazarewicz, P. Olanders, J. Ragnarsson, J. Dudek, Phys. Lett., 152B, 5,6 (1985)

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

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

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) 1198.4 / 431.5 (D,Q- Q) - 0.27(3) / - 0.10(5) Assigns I=5,7. Considering transition to 8+ is only consistent with I=7. 1351.5 / 331.0 (D.Q –Q) - 0.27 (2) / -0.03 (3) Assigns I=3,5, with the above I=5. 1030.7 / 431.5 (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) / -0.002(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) / -0.02(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) / -0.24(8) 10(6) Consistent only with I=3 969.9/295.4 (D,Q – Q) -0.06(1) / -0.09(2) 9.6(14) Consistent only with I=5 363.7/969.5 (Q – D,Q) 0.03(2) / -0.02(3) -0.07(9) 2.8(8) Consistent with I= 6,7, δ shown for I=7 167.1/363.5 (D,Q – Q) -0.04(2) / -0.036(35) 0.04(4) Consistent only with 1786.7 level with I=7, and gives I=6, 8, or 9 for the 1953.8 level. δ is shown for I=8 353.0/167.0 (Q- D,Q) -0.07(3) / -0.01(4) Rules out 1953.8 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 295.2/770.9 (Q - D,Q) -0.02(2) / 0.16(4) 3.8(9) Consistent only with I=4 386.3/745.1 (Q – D,Q) -0.07(2) / 0.13(4) 4.5(18) Consistent only with I=6 450.7/463.3 (Q – D,Q) -0.06(2) / -0.01(2) 0.01(3) consistent only with I=9 Table of Angular Correlations

RMF Calculations for Ba

RMF Calculations for Ba

DFT Calculations for Ba