We study the properties of dense matter at finite temperature with various proton fractions for use in supernova simulations. The relativistic mean-field theory is used to describe homogeneous nuclear matter, while the Thomas-Fermi approximation is adopted to describe inhomogeneous matter. We also discuss the equation of state of neutron star matter at zero temperature in a wide density range. The equation of state at high densities can be significantly softened by the inclusion of hyperons.
For the detection of direct dark matter, in order to extract useful information about the funda- mental interactions from the data, it is crucial to properly determine the nuclear form factor. The form factor for the spin-independent cross section of collisions between dark matter particles and the nucleus has been thoroughly studied by many authors. When the analysis was carried out, the nuclei were always supposed to be spherically symmetric. In this work, we investigate the effects of the deformation of nuclei from a spherical shape to an ellipticM one on the form factor. Our results indicate that as long as the ellipticity is not too large, such deformation will not cause any substantial effects. In particular, when the nuclei are randomly orientated in room-temperature circumstances, one can completely neglect them.
