Adiabatic approach to large-amplitude collective motion with the higher-order collective-coordinate operator

TL;DR

This paper introduces an enhanced adiabatic self-consistent collective-coordinate theory incorporating second-order operators, improving the accuracy of collective motion descriptions, especially for highly excited states, demonstrated through the Lipkin model.

Contribution

It develops a new set of equations including second-order collective operators within the ASCC framework, and proposes an alternative fundamental equation set, advancing the theoretical modeling of collective nuclear motions.

Findings

Including second-order operators improves agreement with exact solutions at high excitation energies.

The new equations better reproduce the exact solutions compared to first-order only models.

Discussion on gauge symmetry of the proposed equations.

Abstract

We propose a new set of equations to determine the collective Hamiltonian including the second-order collective-coordinate operator on the basis of the adiabatic self-consistent collective-coordinate (ASCC) theory. We illustrate, with the two-level Lipkin model, that the collective operators including the second-order one are self-consistently determined. We compare the results of the calculations with and without the second-order operator and show that, without the second-order operator, the agreement with the exact solution becomes worse as the excitation energy increases, but that, with the second-order operator included, the exact solution is well reproduced even for highly excited states. We also reconsider which equations one should adopt as the basic equations in the case where only the first-order operator is taken into account, and suggest an alternative set of fundamental equations instead of the conventional ASCC equations. Moreover, we briefly discuss the gauge symmetry of the new basic equations we propose in this paper.