Empirical physical formula for potential energy curves of 38-66Ti isotopes by using neural networks

TL;DR

This paper employs neural networks to develop empirical physical formulas for potential energy curves of titanium isotopes, aligning well with Hartree-Fock-Bogoliubov calculations, aiding understanding of nuclear shape transitions.

Contribution

It introduces a neural network-based approach to derive empirical formulas for nuclear potential energy curves, providing a new tool for nuclear structure analysis.

Findings

Neural network-derived PECs match HFB calculations.

The method effectively models shape phase transitions.

Empirical formulas simplify complex nuclear calculations.

Abstract

Nuclear shape transition has been actively studied in the past decade. In particular, the understanding of this phenomenon from a microscopic point of view is of great importance. Because of this reason, many works have been employed to investigate shape phase transition in nuclei within the relativistic and non-relativistic mean field models by examining potential energy curves (PECs). In this paper, by using layered feed-forward neural networks (LFNNs), we have constructed consistent empirical physical formulas (EPFs) for the PECs of 38-66Ti calculated in Hartree-Fock-Bogoliubov (HFB) method with SLy4 Skyrme forces. It has been seen that the PECs obtained by neural network method are compatible with those of HFB calculations.