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

TL;DR

This work addresses how $\Lambda$ hyperons modify the binding and stability of nuclear clusters in inhomogeneous matter across densities $n_{\mathrm{gas}}$ and proton fractions $Y_p$. It employs a hybrid RMF framework where cluster states are obtained from solving the Dirac equation in a spherical Wigner-Seitz cell with Dirichlet-Neumann boundary conditions, while the surrounding gas is treated via Thomas-Fermi and binding-energy shifts are computed within a generalized relativistic density-functional approach. The study shows that $\Lambda$ hyperons typically strengthen the binding of heavier clusters ( $N_p \ge 4$ ) and raise their Mott transition densities, whereas light clusters ($N_p<4$) can be destabilized, with pronounced isovector effects modulating the results depending on $Y_p$ and the neutron/proton composition; nonlinear functionals can dramatically destabilize light clusters, and all density- and composition-dependent trends are captured by a simple polynomial expansion, providing practical inputs for modeling hypernuclear environments in heavy-ion collisions and neutron-star matter. These findings advance our understanding of in-medium hypernuclear structure and offer quantitative inputs for EOS modeling in astrophysical contexts.

Abstract

In the framework of relativistic-mean-field (RMF) models, we investigate the properties of light and heavy $Λ$ 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 $Λ$ hyperons, the binding energies per baryon for $Λ$ hyperclusters become smaller and decrease faster with $n_{\mathrm{gas}}$ due to the weaker $N$-$Λ$ attraction. For heavy clusters with $N_p \geq 4$, on the contrary, the addition of $Λ$ hyperons increases the stability of (hyper)clusters so that the Mott transition density becomes larger as nucleons occupying higher energy states while $Λ$ 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.

Figures (6)

• Figure 1: Binding energies of $\Lambda$ hyperon $B_\Lambda$ in the $1s_{1/2}$ state of hypernuclei predicted by the relativistic density functionals DD-LZ1 Wei2020_CPC44-074107, TM1 Sugahara1994_NPA579-557, and PK1 Long2004_PRC69-034319. The corresponding experimental values are indicated by the open circles for comparison Hashimoto2006_PPNP57-564Gal2016_RMP88-035004. The binding energy per nucleon $B_\mathrm{core}/(A-1)$ for the nuclear cores are presented as well. The element symbols (proton numbers $N_p$) are indicated for both $\Lambda$ hypernuclei and their core nuclei with $A\rightarrow A-1$, where each nucleus is presented independently.
• Figure 2: Density profiles of $^4$He, ${}^{5}_\Lambda$He, and ${}^{6}_{\Lambda\Lambda}$He in vacuum, where the relativistic density functional DD-LZ1 Wei2020_CPC44-074107 is employed for the effective $N$-$N$ interactions and $g_{\omega\Lambda} = 1.143 g_{\omega N}$ ($g_{\sigma\Lambda} = g_{\sigma N}$) for the $\Lambda$-$N$ interactions.
• Figure 3: Binding energies $B$ (in MeV) of H and He clusters emersed in nuclear medium with density $n_{\mathrm{gas}}=n_{p,\mathrm{gas}}+n_{n,\mathrm{gas}}$ and proton fraction $Y_p = n_{p,\mathrm{gas}}/n_{\mathrm{gas}}$, which are obtained by employing the relativistic density functional DD-LZ1 Wei2020_CPC44-074107.
• Figure 4: Binding energy per nucleon for various (hyper)clusters emersed in SNM and PNM as functions of the density of nuclear medium $n_{\mathrm{gas}}$, which are obtained by employing the relativistic density functional DD-LZ1 Wei2020_CPC44-074107. The thin curves indicate normal clusters and thick curves correspond to those with one additional $\Lambda$ hyperon.
• Figure 5: Similar as Fig. \ref{['Fig:Bind-DDLZ1']} but for charge radii $R_\mathrm{ch}$ of in-medium (hyper)clusters.