Numerical Test of a Mapping Theory for the IBM3

Abstract

A mapping theory for the IBM3 presented in a previous paper is numerically investigated. The calculations in the (/712)n systems confirm that the IBM3 qualitatively reproduces the shell model results. The renormalization of the contributions from non·SD subspace to the boson interactions is necessary for obtaining enough number of energy levels at low energy. Numerical analysis also indicates the important effects of the Pauli principle between nucleon pairs on the E2 matrix elements. Some of the effects are roughly reproduced by the present mapping method. 6 ) (referred to as I), the author proposed a mapping theory for the IBM3, which makes it clear how the sand d bosons with T=l are extracted from the original shell model. The theory aims at taking account of the important effects of the Pauli principle between the nucleon pairs with J=O, T=l and J=2, T=1. It should be stressed that the boson operators st and d t do not directly correspond to the nucleon pairs but are the building blocks representing leading excitation modes. The purpose of this paper is to discuss numerically the microscopic foundation of the IBM3 presented in I and to test its applicability in the (f7/2Y systems. The effects depending on the s- (d-) boson number pen) and isospin ret) treated in I can be roughly expressed in terms of two-body boson interactions when we consider a boson image of the shell model hamiltonian. We do not consider higher order terms because they are complicated. As shown in § 2, the hamiltonian of Thompson, Elliott and Evans (TEE)4) is equivalent to our boson hamiltqnian with two-body interactions at most if we fit the parameters to the four mucleon system. Although TEE have investigated the energy levels of some (f7/2)n systems, their calculations are not complete. In this paperwe perform complementary calculations about the energy levels in order to confirm the usefulness of the IBM3. Our mapping theory has a different feature from that of TEE based on the Otsuka-Arima-Iachello (OAl) method.7) An important difference appears in evaluat­ ing the matrix elements of (c t C )2M between many nucleon pairs. We show that the difference cannot be ignored, by comparing with shell model calculations. Our first-order approximation is not sufficient to correct the quantitative discrepancies but we can get a guiding principle to modify the boson image of (c t C)2M. In § 2 we derive the boson expressions of hamiltonian and (c t C)zM and discuss the relation of our boson expressions to those of TEE. We discuss numerical results in § 3 and concluding remarks are given in § 4.