Light and heavy $Λ$ hyperclusters in nuclear matter with RMF models

In the framework of RMF models, we investigate the properties of light and heavy $Λ$ hyperclusters emersed in nuclear matter at various densities ngas and proton fractions Yₚ. 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 ngas, which eventually become unbound and melt in the presence of nuclear medium, i.e., Mott transition. For light clusters with proton numbers Nₚ < 4, with the addition of $Λ$ hyperons, the binding energies per baryon for $Λ$ hyperclusters become smaller and decrease faster with ngas due to the weaker N-$Λ$ attraction. For heavy clusters with Nₚ ≥ 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 1s1/2 orbital. The isovector effects on (hyper)clusters in nuclear medium are also identified, where the binding energies for (hyper)clusters with Nₚ> Nₙ (Nₚ< Nₙ) increase (decrease) with Yₚ. For those predicted by nonlinear relativistic density functionals, light (hyper)clusters are destabilized drastically as ngas increases, while the binding energies of heavier (hyper)clusters vary smoothly with ngas. By fitting the binding energy shifts to an analytical formula, the corresponding coefficients describing the in-medium properties of various (hyper)clusters are fixed, which should be useful to understand the evolutions of (hyper)clusters in both heavy-ion collisions and neutron stars.