The love-hate relationship between the shell model and cluster models

Abstract

We adopt a personal approach here reviewing several calculations over the years in which we have experienced confrontations between cluster models and the shell model. In previous cluster conferences we have noted that cluster models go hand in hand with Skyrme Hartee-Fock calculations in describing states which cannot easily, if at all, be handled by the shell model. These are the highly deformed (many particle -many hole) intruder states, linear chain states e.t.c. In the present work we will consider several topics; the quadrupole moment of 6 Li, the non-existence of low lying intruders in 8 Be, and then jumping to the f 7/2 shell, we discuss the two-faceted nature of the nuclei -sometimes displaying shell model properties, other times cluster properties. I. THE QUADRUPOLE MOMENT OF THE

Overview of neutron–proton pairing

“…They used the interaction "Model I" of Zamick and Robinson [118] with a normalization to zero of the largest matrix element (two-nucleon angular momentum J = 6) so as to make the total interaction attractive. Like Satu la et al [116], they switched off successively the interactions in individual J channels.…”

Symmetries in theg9/2shell

“…It should be added that one of us had previously studied the problem of the effects of varying two-body matrix elements in the f 7/2 region [18] and that one can learn a lot by studying the explicit f 7/2 wave functions in Ref. [6], which are based on previous works in Refs.…”

Schematic interactions with many degeneracies

“…in 44 Ti the half-life of the 12 + state is 2.1 ns (weakly isomeric) whilst for 52 Fe the corresponding value is 45.9 s. All this is discussed in Ref. [8].…”