A method for estimating the singular part of the effective shell-model interaction and its influence on perturbation theory

Abstract

A method for estimating the part of the effective shell-model interaction that results from intruder-state singularities within the unit circle is presented. The method is applied to an exactly solvable test problem which involves several such intruder-state singularities and it is found to be accurate to roughly 5–10 %. It is then applied to a realistic description of the ¹⁸O J^π= 0⁺ system, in which a 4p–2h intruder state is known to occur. Using the Nilsson model to describe the intruder state, we estimate the contributions of the associated branch-cut singularities to a perturbation theory (PT) expansion of the effective interaction. Estimates of the errors associated with the use of nth order PT in the presence of these branch-cut singularities are also obtained. The possibility of eventually combining this method and diagrammatic PT into a useful theory of the effective interaction is discussed.