Shell model in the complex energy plane and two-particle resonances

Abstract

An implementation of the shell-model to the complex energy plane is presented. The representation used in the method consists of bound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Two-particle resonances are evaluated, and their structure in terms of the single-particle degrees of freedom is analyzed. It is found that two-particle resonances are mainly built upon bound states and Gamow resonances, but the contribution of the scattering states is also important.

Effective interaction techniques for the Gamow shell model

“…The newly developed Gamow shell model offers such a possibility; see, for example, Refs. [1][2][3][4][5][6][7][8][9]. Also, the recently developed shell model embedded in the continuum [10][11][12][13] conveys similar interesting perspectives.…”

“…In our case, the identification problem is solved based on inspection of the unperturbed many-particle energy spectrum, as done in Refs. [4,5]. We show that by choosing a rotated-plus-translated contour in the complex plane, a large portion of the many-particle energy surface is free from complex-continuum states, and the basic pole configurations will never be embedded in the dense continuum.…”

“…Studies [4,5] related this identification problem to the problem of choosing a contour in the complex k plane, which in the case of two valence particles selects the interesting physical states from the dense distribution of continuum states. Investigators [4,5] pointed out that when using the classical triangular Berggren contour (see, e.g., Ref. [14]), the unperturbed two-particle energy spectrum would embed the pole configurations in a dense distribution of pole-continuum and continuum-continuum configurations, and an identification based on inspection of the zeroth-order energy spectrum was difficult.…”

“…In this work, we consider as a test case the light drip-line nuclei 5,6,7 He and the formation of resonances in these nuclei starting from a single-particle picture. These nuclei have also been studied with a number of other methods; see, for example, Refs.…”

“…[4,5], was the problem of identifying the multiparticle resonances on the many-particle energy surface. Studies [4,5] related this identification problem to the problem of choosing a contour in the complex k plane, which in the case of two valence particles selects the interesting physical states from the dense distribution of continuum states. Investigators [4,5] pointed out that when using the classical triangular Berggren contour (see, e.g., Ref.…”