Double-Lambda hypernuclei within a Skyrme-Hartree-Fock approach

TL;DR

This paper extends the Skyrme-Hartree-Fock method to study double-Lambda hypernuclei, analyzing how different force parameters affect binding energies and comparing results with existing data.

Contribution

The study applies and tests a Skyrme-Hartree-Fock approach for double-Lambda hypernuclei, exploring the sensitivity to force parameters and assessing the ability to distinguish between different models.

Findings

Existing data cannot differentiate between various Lambda-Lambda force models.

Lambda-N force parameters show some selectivity based on hypernuclear data.

The approach successfully describes Lambda hypernuclei and provides insights into force sensitivities.

Abstract

We extend our Skyrme-Hartree-Fock (SHF) approach, which was used earlier to describe successfully the single-$\Lambda$ hypernuclei, to investigate the binding and the $\Lambda \Lambda$ bond energies of the double-$\Lambda$ hypernuclei. The nucleon-nucleon ($NN$) and $\Lambda$-nucleon ($\Lambda N$) interactions are taken from our previous study. For the $\Lambda \Lambda$ force several Skyrme-like potentials available in the literature have been used. We discuss the sensitivity of the calculated $\Lambda \Lambda$ binding and bond energies to the $\Lambda \Lambda$ and $\Lambda N$ force parameters. It is found that the existing $\Lambda \Lambda$ hypernuclear data do not allow to distinguish between various $\Lambda \Lambda$ force parameter sets used by us. However, they show some selectivity for a particular set of the $\Lambda N$ potential determined in our previous work.