Title: Supernova equations of state including full nuclear ensemble with in-medium effects Show Chinese title

Title: 包括全核集合体及介质效应的超新星状态方程

Abstract: We construct new equations of state for baryons at sub-nuclear densities for the use in core-collapse supernova simulations. The abundance of various nuclei is obtained together with thermodynamic quantities. The formulation is an extension of the previous model, in which we adopted the relativistic mean field theory with the TM1 parameter set for nucleons, the quantum approach for $d$, $t$, $h$ and $\alpha$ as well as the liquid drop model for the other nuclei under the nuclear statistical equilibrium. We reformulate the model of the light nuclei other than $d$, $t$, $h$ and $\alpha$ based on the quasi-particle description. Furthermore, we modify the model so that the temperature dependences of surface and shell energies of heavy nuclei could be taken into account. The pasta phases for heavy nuclei and the Pauli- and self-energy shifts for $d$, $t$, $h$ and $\alpha$ are taken into account in the same way as in the previous model. We find that nuclear composition is considerably affected by the modifications in this work, whereas thermodynamical quantities are not changed much. In particular, the washout of shell effect has a great impact on the mass distribution above $T \sim 1$ MeV. This improvement may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. Show Chinese abstract

Abstract: 我们构建了用于核子在亚核密度下的新的状态方程，以供核心坍缩超新星模拟使用。各种原子核的丰度与热力学量一起被确定。该公式是对先前模型的扩展，在其中我们采用了带有TM1参数集的核子相对论平均场理论，以及量子方法来处理$d$、$t$、$h$和$\alpha$，同时还采用了核统计平衡下的液滴模型来处理其它原子核。 我们基于准粒子描述重新制定了除$d$、$t$、$h$和$\alpha$以外的轻核模型。此外，我们修改了该模型，以便可以考虑重核表面能和壳层能对温度的依赖性。 重核的糊状相以及对$d$、$t$、$h$和$\alpha$的泡利位移和自能位移，在本模型中以与前一模型相同的方式加以考虑。 我们发现核组成受到本工作中修改的显著影响，而热力学量的变化不大。 特别是，壳效应的消失对高于$T \sim 1$MeV 的质量分布有重大影响。 这一改进可能会对超新星核心中的电子俘获率以及相干中微子与原子核的散射率产生重要影响。