Many-body approach to superfluid nuclei in axial geometry

TL;DR

This paper develops an efficient method to model superfluid nuclei with axial deformation by combining many-body theory, Dyson equations, and the finite-amplitude method to compute phonon characteristics in nuclear structure calculations.

Contribution

It introduces a novel approach linking quasiparticle-phonon vertices to the variation of the Bogoliubov Hamiltonian, enabling efficient calculations in non-spherical nuclei.

Findings

Validated the method with calculations on $^{38}$Si and $^{250}$Cf.

Demonstrated efficiency of FAM-QRPA in axial geometries.

Showed applicability to heavy and medium-mass nuclei.

Abstract

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in non-spherical geometries. In this work, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of $^{38}$Si and $^{250}$Cf are presented and discussed.