A comparison between various expressions for effective interactions and operators in nuclei

✍ Scribed by J Richert; T.H Schucan; M.H Simbel; H.A Weidenmüller

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 951 KB
• Volume: 96
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(76)90188-3

✦ Synopsis

Different choices of effective interactions and operators are related to each other and to definitions given in the literature. Perturbation expansions are given, and the degree of complexity in evaluating terms of a given order is exhibited. The application of Pad& approximants to different choices of effective interactions and to effective operators is investigated numerically.

1. INTRODUCTIOK

This paper continues and extends a series of recent investigations on the structure of, perturbation theory for, and improved approximation schemes for effective interactions and operators [l-3]. In particular, our aims are the following: (i) We compare the implications of a Hermitean and a non-Hermitean choice of the effective interactions in a certain shell-model space. We show that all these choices are related by a one-to-one mapping of the model space onto itself and establish the connection with two standard choices. We show that PadC approximants to the Hermitean and to the non-Hermitean choices complement each other in a very desirable fashion. (ii) We extend the analysis to the algebraic structure of effective operators. We show that a normalization problem exists unless a Hermitean effective interaction is chosen and that the complications