Effective charges and their relation to collectivity and shell structure.

Abstract

Effective boson charges, {ital e}{sub {pi}} and {ital e}{sub {nu}}, are extracted for isotopic chains of most elements from {ital Z}=42 to the actinides from analytic expressions derived in the interacting boson approximation. It is shown that, in {ital valence} space models, such effective charges carry an additional, physically intuitive interpretation, beyond the normal one of ensuring agreement of calculated electromagnetic transition rates with experiment. In valence models {ital e}{sub {pi}} and {ital e}{sub {nu}} are approximately proportional to the derivatives of {ital M}({ital E}2:0{sub 1}{sup +}{r arrow}2{sub 1}{sup +}) with {ital N}{sub {pi}} and {ital N}{sub {nu}}, respectively; that is, they are measures of the rate of change of collectivity. This feature allows one to disentangle the separate roles of protons and neutrons in the development of collectivity and exposes subtle effects originating in the valence {ital p}-{ital n} interaction. The results are striking. While for most elements, {ital e}{sub {pi}}{gt}{ital e}{sub {nu}} as expected, certain regions display anomalously large {ital e}{sub {nu}}, and, sometimes {ital e}{sub {nu}}/{ital e}{sub {pi}}{gt}1. These effects are interpreted in terms of the {ital p}-{ital n} interaction and, in particular, in terms of its monopole component which acts to shift single particle energies and,more » thereby, can alter shell gaps and the effective size of the valence space of one kind of particle as a function of the number of the other. Very small values of {ital e}{sub {nu}} near midshell are also interpreted in terms of the saturation of collectivity in such regions.« less