Self-consistent collective coordinate for reaction path and inertial mass

TL;DR

This paper introduces a numerical approach to find the optimal collective reaction path in nuclear collisions using the ASCC method, combining iterative imaginary-time evolution and finite amplitude techniques, demonstrated on alpha-alpha scattering.

Contribution

It develops a new iterative numerical method for solving the ASCC equations, enabling accurate determination of reaction paths, potentials, and inertial masses in nuclear collision models.

Findings

Successfully determined the collective path, potential, and inertial mass for alpha-alpha scattering.

Compared results with other methods, showing consistency and improvements.

Validated the method's effectiveness in a simple nuclear collision case.

Abstract

We propose a numerical method to determine the optimal collective reaction path for the nucleus-nucleus collision, based on the adiabatic self-consistent collective coordinate (ASCC) method. We use an iterative method combining the imaginary-time evolution and the finite amplitude method, for the solution of the ASCC coupled equations. It is applied to the simplest case, the $\alpha-\alpha$ scattering. We determine the collective path, the potential, and the inertial mass. The results are compared with other methods, such as the constrained Hartree-Fock method, the Inglis's cranking formula, and the adiabatic time-dependent Hartree-Fock (ATDHF) method.