We clarify the character of the semi-analytic 1/N-expansion method utilised in otherwise clumbersome studies with the sdg-variant of the interacting boson model. We draw attention to the dynamical foundations of the scheme. We argue that, by respecting the conditions under which use of the asymptotic expansions involved is legitimate, we can hope to learn whether the dynamical assumptions made are appropriate or not. To this end, we show that an ad hoc "gaussian" approximation of previous applications can be avoided without any sacrifice of simplicity. The new asymptotic expansion of the fundamental overlap integral differs in every order beyond leading-order. Nevertheless, we confirm that, to the order of practical interest, the all-important variational functional for the groundstate-band coincides with that employed previously; our demonstration makes explicit the cancellation mechanism. To illustrate the practical advantages of the new scheme, we derive an expression for the gyromagnetic factors of the groundstate-band; it is freed of the deficiencies of the former 1/N-expansion method result. In general, claims that strong variations in an observable unaccounted for by the leading term can be described by higher-order terms are necessarily suspect.
ASJC Scopus subject areas
- Physics and Astronomy(all)