Approximate solution of the pairing Hamiltonian in the Berggren basis

TL;DR

This paper develops an approximate method to solve the pairing Hamiltonian within the Berggren basis, which includes bound, resonance, and scattering states, effective especially under weak pairing interactions.

Contribution

It introduces a novel approximate solution for the pairing Hamiltonian in the Berggren basis, encompassing a broad spectrum of single-particle states.

Findings

Solution is reliable for weak pairing interactions

Includes bound, resonance, and scattering states in the Berggren basis

Provides a practical approach for complex nuclear systems

Abstract

We derive the approximate solution for the pairing Hamiltonian in the Berggren ensemble of single particle states including bound, resonance and non-resonant scattering states. We show that this solution is reliable in the limit of a weak pairing interaction.