标题： 轻和重$Λ$亚核簇在核物质中的RMF模型 显示英文标题

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

摘要： 在RMF模型的框架下，我们研究了轻量和重量的$\Lambda$超簇在不同密度$n_{\mathrm{gas}}$和质子分数$Y_p$的核物质中的性质。特别地，(超)簇通过求解施加狄利克雷-诺伊曼边界条件的狄拉克方程来固定，而核物质则保持恒定密度，并采用托马斯-费米近似处理。(超)簇的结合能随着核物质密度$n_{\mathrm{gas}}$的增加而减少，最终在核介质存在的情况下变得不稳定并熔化，即发生莫特转变。 对于质子数为$N_p < 4$的轻质量簇，加入$\Lambda$重子后，$\Lambda$重子簇的每个重子结合能变小，并且由于$N$-$\Lambda$引力较弱，结合能随$n_{\mathrm{gas}}$的增加而更快地减少。 对于具有$N_p \geq 4$的重团簇，相反地，添加$\Lambda$超子会增加 (超)团簇的稳定性，使得 Mott 转变密度随着核子占据更高能态而增大，而$\Lambda$超子仍处于$1s_{1/2}$轨道中。 (超)团簇在核介质中的矢量同位旋效应也得到了确认，其中具有$N_p> N_n$($N_p< N_n$) 的 (超)团簇的结合能随着$Y_p$的增加（减少）而增加（减少）。 对于由非线性相对论密度泛函预测的轻 (超) 聚集物，当$n_{\mathrm{gas}}$增加时，它们会显著不稳定，而较重 (超) 聚集物的结合能则随着$n_{\mathrm{gas}}$的变化而平滑变化。 通过将结合能偏移拟合到一个解析公式，可以确定描述各种 (超) 聚集物介质性质的相应系数，这应该有助于理解 (超) 聚集物在重离子碰撞和中子星中的演化。 显示英文摘要

摘要： In the framework of 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 $n_{\mathrm{gas}}$. 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.