Role of momentum in the generator-coordinate method applied to barrier penetration

TL;DR

This paper demonstrates that incorporating finite momentum states into the Generator Coordinate Method enhances its ability to model nuclear barrier penetration at higher energies, aligning it more closely with traditional Schrödinger equation results.

Contribution

It introduces a novel approach of including momentum states in GCM, extending its applicability for nuclear barrier penetration modeling beyond previous limitations.

Findings

Inclusion of momentum states improves GCM accuracy at higher energies.

Discrete Kohn's variational method effectively calculates transmission probabilities.

GCM with momentum states aligns better with Schrödinger equation predictions.

Abstract

Nuclear fission at barrier-top energies is conventionally modeled by a one-dimensional Schr\"odinger equation applied to internal fission channels, but that treatment is hard to justify in the configuration-interaction approach to nuclear Hamiltonians. Here we show that inclusion of states of finite momentum by the Generator Coordinate Method (GCM) considerably extends the range of energies at which GCM-based Hamiltonians could reproduce the Schr\"odinger treatment. The transmission probabilities for crossing the barrier are calculated by a discrete version of Kohn's variational method, which may also be useful for other systems of interacting fermions.