Higher-rank discrete symmetries in the IBM. II Octahedral shapes: Dynamical symmetries

Proxy-SU(4) symmetry in A = 60–90 region

“…Nuclei in A = 60-90 region exhibit shape co-existence, shape phase transitions and other properties such as triple-forking seen in 68 Ge. These clearly show that one has to go beyond proxy-SU(3) and consider proxy-SO (6), SO (5) and SO (10) symmetry limits (it is well known from interacting boson model studies that interpolation of various symmetry limits is essential for understanding exotic features like shape phase transitions, shape co-existence etc [46] and the same is expected with shell model). Motivated by all these, the aim of this paper is to explore proxy-SO (6), proxy-SU (5) and proxy-SO (10) symmetry limits associated with proxy-SU(4) symmetry and their applications to A = 60-90 nuclei (in particular to N ∼Z nuclei in this region) 3 .…”

“…More importantly, the subject of ʼsymmetries in nuclei' is undergoing a second renaissance in the last 5-10 years with several new directions in this subject are being explored. Some of these are (i) point group symmetries in heavy nuclei such as 152 Sm, 156 Gd, 236 U [8][9][10] and in lighter nuclei such as 12 C, 13 C and 16 O [11][12][13], (ii) symmetries for shape coexistence [14], (iii) multiconfiguration or composite symmetries for cluster states [15], (iv) symmetry adopted no-core-shell model based on SU(3) and Sp(6, R) algebras [16][17][18][19], (v) proton-neutron Sp(12, R) model [20][21][22], (vi) multiple algebras in shell model and IBM spaces giving for example multiple pairing and SU(3) algebras [23,24], (vii) pairing algebras with higher order interactions, generalized seniority and seniority isomers [24][25][26][27], (viii) proxy-SU(3) scheme within shell model [28,29], (ix) symmetry restoration methods in mean-field theories [30], (x) new techniques for obtaining Wigner coefficients involving SU(3) ⊃ SO(3), SO(5) ⊃ SO(3) and spin (S)-isospin(T) SU ST (4) ⊃ SU S (2) ⊗ SU T (2) [31][32][33] and (xi) studies involving Bohr Hamiltonian with sextic and other types of potentials for shape phase transitions and shape coexistence pointing out the need for three and higher-body terms in IBM and perhaps also in shell model [34][35][36][37][38][39]. (xii) random matrix ensembles with Lie algebraic ...…”

“…proxy-SU(4) symmetry (often we drop S and T in SU ST (4) when there is no confusion). However, with proxy-SU(4) it is possible to have also other proxy symmetries with G = SO (6), SU (5) and SO (10). Nuclei in A = 60-90 region exhibit shape co-existence, shape phase transitions and other properties such as triple-forking seen in 68 Ge.…”

“…In section 3 of the paper, further evidence for proxy-SU(4) will be discussed using several examples in A = 60-90 region. In sections 4 and 5 we will describe the new SO(6), SU (5) and SO (10) proxy schemes in A = 60-90 region that arise due to good proxy-SU(4) symmetry. In section 4 the group generators and quadratic Casimir invariants are given.…”

“…For this nucleus, if we consider the valence nucleons to be only in 2 p 3/2 , 1 f 5/2 and 2 p 1/2 orbits with 56 Ni core, we have η = 2 shell and then pseudo SU(3) symmetry. Now, using equation (10) gives (λ H , μ H ) = (4, 8) and therefore oblate ground state shape. However, if the proxy-SU(3) model in conjunction with the proxy-SU ST (4) is used, then η = 3 shell results in table 1 will apply.…”