Using Continuum Level Density in the Pairing Hamiltonian: BCS and Exact Solutions

TL;DR

This paper investigates the impact of continuum single particle level density on pairing in nuclear systems, comparing approximate BCS and exact Richardson solutions, revealing the continuum's significant contribution and differences in model space dependence.

Contribution

It introduces the continuum single particle level density into the pairing Hamiltonian and compares BCS and Richardson solutions, highlighting the continuum's role and the independence of the exact solution from model space.

Findings

Continuum significantly influences the pairing parameter.

BCS solution depends on the model space.

Richardson solution is model space independent.

Abstract

Pairing plays a central role in nuclear systems. The simplest model for the pairing is the constant-pairing Hamiltonian. The aim of the present paper is to include the continuum single particle level density in the constant pairing Hamiltonian and to make a comparison between the approximate BCS and the exact Richardson solutions. The continuum is introduced by using the continuum single particle level density. It is shown that the continuum makes an important contribution to the pairing parameter even in those case when the continuum is weakly populated. It is shown that while the approximate BCS solution depends on the model space the exact Richardson solution does not.