Exact Eigenvalues of the Pairing Hamiltonian Using Continuum Level Density

TL;DR

This paper extends the exact solution of the pairing Hamiltonian to include continuum effects via the continuum level density, enabling accurate energy level calculations for nuclei in the continuum spectrum.

Contribution

It generalizes the Richardson solution to incorporate continuum correlations using CSPLD, demonstrating the feasibility of constant pairing calculations in the continuum.

Findings

Energy levels for Carbon isotopes calculated with continuum pairing.

$^{24}$C identified as unbound.

Developed real and complex continuum energy representations.

Abstract

The pairing Hamiltonian constitutes an important approximation in many- body systems, it is exactly soluble and quantum integrable. On the other hand, the continuum single particle level density (CSPLD) contains information about the continuum energy spectrum. The question whether one can use the Hamiltonian with constant pairing strength for correlations in the continuum is still unanswered. In this paper we generalize the Richardson exact solution for the pairing Hamiltonian including correlations in the continuum. The resonant and non-resonant continuum are included through the CSPLD. The resonant correlations are made explicit by using the Cauchy theorem. Low lying states with seniority zero and two are calculated for the even Carbon isotopes. We conclude that energy levels can indeed be calculated with constant pairing in the continuum using the CSPLD. It is found that the nucleus $^{24}$C is unbound. The real and complex energy representation of the continuum is developed and their differences are shown. The trajectory of the pair energies in the continuum for the nucleus $^{28}$C is shown.