Comparative study of the requantization of the time-dependent mean field for the dynamics of nuclear pairing

TL;DR

This paper compares various requantization methods of time-dependent mean-field theory for nuclear pairing dynamics, finding that the microscopic wave function approach with EBK quantization is most accurate, especially for systems with few levels.

Contribution

It evaluates and compares different requantization techniques for TDHFB, highlighting the effectiveness of the EBK-based microscopic wave function method.

Findings

EBK quantization yields the most accurate results

Collective model's applicability is limited for small systems

Microscopic wave function approach outperforms other methods

Abstract

To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.