Light and heavy $\Lambda$ hyperclusters in nuclear matter with relativistic-mean-field models

TL;DR

This study uses relativistic-mean-field models to analyze how light and heavy $ ext{Lambda}$ hyperclusters behave in nuclear matter, revealing their stability, binding energies, and medium effects relevant for nuclear physics and astrophysics.

Contribution

It provides a detailed analysis of hypercluster properties in nuclear matter, including the effects of $ ext{Lambda}$ hyperons and medium density, with new analytical formulas for energy shifts.

Findings

Binding energies decrease with nuclear matter density, leading to Mott transition.

Addition of $ ext{Lambda}$ hyperons stabilizes heavy clusters but destabilizes light ones.

Binding energy shifts are fitted to an analytical formula for practical applications.

Abstract

In the framework of relativistic-mean-field (RMF) models, we investigate the properties of light and heavy $\Lambda$ hyperclusters emersed in nuclear matter at various densities $n_{\mathrm{gas}}$ and proton fractions $Y_p$. In particular, the (hyper)clusters are fixed by solving the Dirac equations imposing the Dirichlet-Neumann boundary condition, while the nuclear matter take constant densities and is treated with Thomas-Fermi approximation. The binding energies of (hyper)clusters decrease with the density of nuclear matter $n_{\mathrm{gas}}$, which eventually become unbound and melt in the presence of nuclear medium, i.e., Mott transition. For light clusters with proton numbers $N_p < 4$, with the addition of $\Lambda$ hyperons, the binding energies per baryon for $\Lambda$ hyperclusters become smaller and decrease faster with $n_{\mathrm{gas}}$ due to the weaker $N$-$\Lambda$ attraction. For heavy clusters with $N_p \geq 4$, on the contrary, the addition of $\Lambda$ hyperons increases the stability of (hyper)clusters so that the Mott transition density becomes larger as nucleons occupying higher energy states while $\Lambda$ hyperons remain in the $1s_{1/2}$ orbital. The isovector effects on (hyper)clusters in nuclear medium are also identified, where the binding energies for (hyper)clusters with $N_p> N_n$ ($N_p< N_n$) increase (decrease) with $Y_p$. For those predicted by nonlinear relativistic density functionals, light (hyper)clusters are destabilized drastically as $n_{\mathrm{gas}}$ increases, while the binding energies of heavier (hyper)clusters vary smoothly with $n_{\mathrm{gas}}$. The binding energy shifts of various (hyper)clusters due to the impact of nuclear medium are fitted to an analytical formula, which could be employed to examine the evolutions of (hyper)clusters in both heavy-ion collisions and neutron stars.