Towards an Extended Microscopic Theory for Upper-Fp Shell Nuclei

Abstract

An extended SU(3) shell model that for the first time explicitly includes unique-parity levels is introduced. Shell-model calculations for the isotopes of 64 Ge and 68 Se are performed where valence nucleons beyond the N=28=Z core occupy levels of the normal parity upper-f p shell (f 5/2 , p 3/2 , p 1/2 ) and the unique parity g 9/2 intruder configuration. The levels of the upper-f p shell are handled within the framework of an m-scheme basis as well as its pseudo-SU(3) counterpart, and respectively, the g 9/2 as a single level and as a member for the complete gds shell. It is demonstrated that the extended SU(3) approach allows one to better probe the effects of deformation and to account for many key properties of the system by using a highly truncated model space.

ON THE SURVIVAL OF THE SD-PAIR SHELL MODEL UNDER PSEUDO-SPIN TRANSFORMATION

“…the pseudo-spin transformed space also scales approximately according to κ 1 . Even though in this article we only reported the case of n = 8 particles (N = 4 pairs), we did a similar study on (g 7/2 ds) 6 , (h 9/2 f p) 6 , and (g 7/2 ds) 8 [equivalent to ( f p) 6 , ( gds) 6 , and ( f p) 8 ] systems and they give the same general conclusion.…”

“…In the context of quasi-exactly solvable models, we have shown that the quasidynamical symmetry plays a role in the quadrupole limit of the SDPM and there is a strong coupling between the truncated collective SD-pair subspace to the remaining subspace. The strong coupling is indicated by a scaling of the rotational structure [κ 2 1 χ in the shell model space versus 4.53χ in the SDPM space for the case of (h 9/2 f p) 8 ], the scaling of effective charge in B(E2) values, and the pseudo-spin symmetry. It remains to be shown how the su(3) algebra works in the SDPM space; that is, to verify whether the quadrupole limit possesses quasi-dynamical symmetry.…”

“…5,6 Recently, this scheme was applied to the lighter nuclei of the upper f p-shell. 7,8 The success of the theory lies in the near degeneracy of single-particle levels that form pseudo-spin doublets; that is, the levels with radial, angular momentum, and total angular momentum quantum numbers (n r , l, j = l + 1 2 ) and (n r − 1, l + 2, j = l + 3 2 ) are approximately degenerate. This near degeneracy can be traced to a specific combination of the scalar and vector potentials of the relativistic nuclear mean field (RMF).…”

“…If the Fermi level is above the intruder level, the participation of active particles in the intruder level is expected to be adiabatic. 8,15 In this subspace of the truncated oscillator shell, the unitary pseudo-spin transformation effectively acts as N σ • b, where b is the oscillator annihilation operator. 16 Consequently, various physical operators, except for the total angular momentum J, are realized differently in the pseudo-spin transformed space.…”