Nilsson-SU3 selfconsistency in heavy N=Z nuclei

Abstract

It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott' SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a {\em remarkable stability of the quadruplole moments}---which remain close to their quasi and pseudo SU3 values---as the single particle splittings increase. A detailed study of the $N=Z$ even nuclei from ${}^{56}$Ni to ${}^{96}$Cd reveals that the region of prolate deformation is bounded by a pair of transitional nuclei ${}^{72}$Kr and ${}^{84}$Mo in which prolate ground state bands are predicted to dominate, though coexisting with oblate ones,

Replacement I) Title simplified. II) Major revision: structure of paper kept but two thirds totally rewritten (same number of pages); 20 references added

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• Proxy-SU(3) symmetry in heavy deformed nuclei
• Shape coexistence in even-even nuclei: A theoretical overview
• The proxy-SU(3) symmetry in atomic nuclei
• Proxy-SU(3) symmetry in the shell model basis
• Pairing-quadrupole interplay in the neutron-deficient tin nuclei: first lifetime measurements of low-lying states in ${}^{106,108}$Sn
• Parameter-free predictions for the collective deformation variables beta and gamma within the pseudo-SU(3) scheme
• Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
• Quadrupole dominance in the light Sn and in the Cd isotopes
• Symmetries and deformations in the spherical shell model
• Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods
• Ab initio computations of strongly deformed nuclei around ${}^{80}$Zr
• Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions
• Shape evolutions of ${}^{72,74}$Kr with temperature in the covariant density functional theory
• Shell model analysis of the $B(E2,2^{+}\to 0^{+})$'s in the A=70 T=1 triplet
• Single-particle and collective structures in neutron-rich Sr isotopes
• Deformed shell model study of event rates for WIMP- ${}^{73}$Ge scattering
• Generic features of the neutron-proton interaction
• Multiple $SU(3)$ algebras in interacting boson model and shell model: Results for $(\beta ,\gamma$) bands and scissors $1^{+}$ band
• Proxy-$SU(4)$ symmetry in A=60-90 region
• Shell model results for $T=1$ and $T=0$ bands in ${}^{66}$As
• Understanding Xe isotopes near $A=130$ through the prolate-oblate shape phase transition
• Puzzling $B(E2;0^{+}\to 2^{+})$ strength in the proton dripline nucleus ${}^{36}$Ca
• Yrast band in the heavy $N=Z$ nucleus ${}^{88}$Ru: $\alpha$-cluster approach
• Effective field theories for collective excitations of atomic nuclei
• Partial conservation of seniority in semi-magic nuclei
• Quadrupole dominance in light Cd and Sn isotopes
• Large scale shell model calculation for collectivity in nuclei beyond 78Ni
• Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
• Inter-band B(E1) Strengths in Heavy Nuclei based on the Proxy-SU(3) Scheme