Pairing Theory of the Wigner Cusp

TL;DR

This paper investigates the Wigner cusp in nuclear masses, showing that RPA corrections and shell effects are crucial for understanding the mass variation near N=Z, with implications for nuclear superfluidity and symmetry energy modeling.

Contribution

It introduces RPA corrections to BCS pairing in Nilsson-Strutinskij calculations, clarifying their role in the Wigner cusp and linking symmetry energy to nuclear superfluidity.

Findings

RPA correction accounts for mass variation near N=Z

Macroscopic symmetry energy proportional to T(T+1)

Shell effects dominate Wigner cusp shape

Abstract

Conclusions: (1) Calculations with an RPA correction added to the BCS pairing correction conventionally employed in Nilsson-Strutinskij calculations account well for the variation with A of the pattern of masses near N=Z. (2) The RPA correction is insignificant for reproducing the doubly even masses and hence for the shape of the Wigner cusp. (3) It is important, however, that the macroscopic (liquid drop) symmetry energy be proportional to T(T+1). (4) This form of the macroscopic symmetry energy is understood microscopically, in terms of the RPA, to result from the nuclear superfluidity. (5) The variation of the shape of the Wigner cusp is dominated by shell effects. (6) The RPA correction significally reduces the T=0 binding in doubly odd nuclei, thus reducing the required pair coupling constant.