Self-consistency and collective effects in semiclassical pairing theory

TL;DR

This paper investigates how self-consistent pairing interactions influence nuclear responses in a simplified model, revealing effects like particle-number symmetry restoration and collective eigenfrequencies, with specific impact on low-energy giant octupole resonances.

Contribution

It introduces an improved semiclassical approach allowing pairing field oscillations, aligning well with quantum results and highlighting the role of pairing in nuclear collective excitations.

Findings

Enhanced low-energy octupole resonance strength due to pairing fluctuations

Restoration of particle-number symmetry in the model

No significant effect on high-energy resonances and other modes

Abstract

A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The pairing-field fluctuations have two main effects: they restore the particle-number symmetry which is broken in the constant-$\Delta$ approximation and introduce the possibility of collective eigenfrequencies of the system due to the pairing interaction. A numerical study with values of parameters appropriate for nuclei, shows an enhancement of the density-density strength function in the region of the low-energy giant octupole resonance, while no similar effect is present in the region of the high-energy octupole resonance and for the giant monopole and quadrupole resonances.