Extension of continuum time-dependent Hartree-Fock method to proton states

TL;DR

This paper extends the time-dependent Hartree-Fock method to include proton states and introduces an absorbing boundary condition scheme to accurately simulate nuclear resonances in a finite spatial region.

Contribution

The paper develops an absorbing boundary condition scheme for the time-dependent Hartree-Fock method applied to nuclear resonances, improving boundary handling in continuum calculations.

Findings

The absorbing boundary scheme effectively minimizes artificial boundary effects.

The method accurately models nuclear giant monopole resonances.

The scheme is computationally efficient and stable.

Abstract

This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of non-linear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are a effective way of handling the artificial boundary.