Algebraic Gorkov solution in finite systems for the separable pairing interaction

TL;DR

This paper develops an algebraic quantum field theory approach to finite spherical systems with separable pairing interactions, deriving a closed-form energy equation and comparing it with exact models.

Contribution

It introduces an algebraic formulation using Green functions for finite systems with separable pairing, providing a new method to compute energies.

Findings

Derived a closed equation for many-body energy

Validated the approach by comparison with exact models

Applied Green function techniques to finite systems

Abstract

An algebraic Quantum Field Theory formulation of separable pairing interaction for spherical finite systems is presented. The Lipkin formulation of the model Hamiltonian and model wave function is used. The Green function technique is applied to obtain the model energy through the spectral function. Closed equation for the many-body energy of the system is given and comparison with exact models are performed.