Method to circumvent the neutron gas problem in the BCS treatment for nuclei far from stability

TL;DR

This paper presents a modified BCS approach that effectively addresses the neutron gas problem in nuclei far from stability, ensuring convergence of spatial observables and mimicking more complex methods.

Contribution

The authors extend Kruppa's prescription and demonstrate a simple, convergent BCS method that accurately accounts for continuum effects in finite-depth potentials.

Findings

Convergence of nuclear radius with increasing basis size.

The method reproduces results similar to Hartree-Fock-Bogoliubov calculations.

It effectively circumvents the neutron gas problem in BCS treatment.

Abstract

Extending the Kruppa's prescription for the continuum level density, we have recently improved the BCS method with seniority-type pairing force in such a way that the effects of discretized unbound states are properly taken into account for finite depth single-particle potentials. In this paper, it is further shown, by employing the Woods-Saxon potential, that the calculation of spatial observables like nuclear radius converges as increasing the basis size in the harmonic oscillator expansion. Namely the disastrous problem of a "particle gas" surrounding nucleus in the BCS treatment can be circumvented. In spite of its simplicity, the new treatment gives similar results to those by more elaborate Hartree-Fock-Bogoliubov calculations; e.g., it even mimics the pairing anti-halo effect. The obtained results as well as the reason of convergence in the new method are investigated by a variant of the Thomas-Fermi approximation within the limited phase space which corresponds to the harmonic oscillator basis truncation.