Fitting Single Particle Energies in $sdgh$ Major Shell

TL;DR

This paper improves shell model predictions for Sn isotopes by fitting single-particle energies using nonlinear methods, resulting in spectra that better match experimental data.

Contribution

It introduces two nonlinear fitting procedures to optimize single-particle energies in the $sdgh$ shell, enhancing shell model accuracy for Sn isotopes.

Findings

Fitted single-particle energies yield spectra closer to experimental data.

Nonlinear fitting methods outperform traditional approaches.

Improved energy eigenvalues for $^{104-110}$Sn isotopes.

Abstract

We have performed two kinds of non-linear fitting procedures to the single-particle energies in the $sdgh$ major shell to obtain better shell model results. The low-lying energy eigenvalues of the light Sn isotopes with $A=103-110$ in the $sdgh$-shell are calculated in the framework of the nuclear shell model by using CD-Bonn two-body effective nucleon-nucleon interaction. The obtained energy eigenvalues are fitted to the corresponding experimental values by using two different non-linear fitting procedures, i.e., downhill simplex method and clonal selection method. The unknown single-particle energies of the states $2s_{1/2}$, $1d_{3/2}$, and $0h_{11/2}$ are used in the fitting methods to obtain better spectra of the $^{104,106,108,110}$Sn isotopes. We compare the energy spectra of the $^{104,106,108,110}$Sn and $^{103,105,107,109}$Sn isotopes with/without a nonlinear fit to the experimental results.