Effective interaction techniques for the Gamow shell model

Abstract

We apply a contour deformation technique in momentum space to the newly developed Gamow shell model, using the drip-line nuclei 5 He, 6 He, and 7 He as test cases. A major problem in Gamow shell-model studies of nuclear many-body systems is the increasing number of many-body configurations due to the large number of resonant and complex-continuum single-particle orbits necessary to reproduce multiparticle bound and resonant states. We address this problem using two different effective operator approaches generalized to the complex momentum plane. These are the Lee-Suzuki similarity transformation method for complex interactions and the multireference perturbation theory method. We show that a combination of these two approaches results in a drastic truncation of the number of relevant configurations compared with direct diagonalization. This offers interesting perspectives for studies of weakly bound systems.

Study of resonant structures in a deformed mean field by the contour deformation method in momentum space

“…The method is based on deforming the integration contour and is known as the contour deformation (distortion) method (CDM). As shown in Refs [9,10], CDM allows for accurate calculation of a complete set of single-particle states, involving all kinds of poles of the scattering matrix. However, in Refs.…”

“…The index n represents a bound or resonant state. The eigenfunctions constitute a complete bi-orthogonal set, normalized according to the Berggren metric [9,10,11,12,13,14,15]. In solving Eq.…”

“…However, in Refs. [9,10] only spherically symmetric fields were considered. Here we wish to generalize the method to deformed fields, and therefore we write down the relevant equations for the most general case.…”

“…The results reported in this work, used the same number of integration points for each coupled equation, so the total rank of the matrix to be diagonalized is N × N l , where N is the total number of integration points and N l the total number of angular momentum coupled integral equations given in Eq. (10). Diagonalizing the complex symmetric matrix (36), we obtain a complete set of states within the chosen discretization space.…”

“…The newly developed Gamow Shell Model [1,2,3,4,5,6,7,8,9,10] starts with the Berggren completeness [11,12,13,14,15]. The Gamow Shell Model has proven to be a promising tool in assessing the structure of weakly bound and unbound nuclei.…”