Abstract. We calculate the neutrino mean free path in cold neutron matter with some modern Brussels-Montreal functionals. The three typical functionals used in this article produce quite different results implying a possible impact on the cooling mechanism of neutron stars.
IntroductionThe recent Brussels-Montreal functionals [1] have been very successful in describing both ground state properties of finite nuclei and some astrophysical quantities as the equation of state [2]. These functionals fitted to essentially all the 2149 experimentally known masses are similar to the standard non-relativistic Skyrme effective interaction [3] excepting for the presence of two extra density-and momentum-dependent terms [4]. The latter have been introduced to allow for more flexibilities in reproducing at the same time the properties of nuclei and infinite nuclear matter, including the quality of the functionals against ferromagnetic instabilities in neutron matter [4]. In that respect to avoid such instabilities, the functionals BSk19, BSk20, BSk21 have been fitted to satisfy the Landau inequalities up to very high densities. Furthermore, it has been shown [2] that it was possible to use them for both finite nuclei and astrophysical applications [5,6].The neutrino emission is one of the most efficient mechanism to dissipate the energy accumulated during the formation of a neutron star [7]. Since the neutrinos cross different layers of nuclear matter and are scattered by neutrons, they lose energy, making the cooling mechanism less efficient. The neutrino mean free path (NMFP) is a fundamental ingredient for a proper understanding of the cooling process. In the present article, we investigate the NMFP with the 3 above-mentioned functionals.The article is organized as follows: in Sec.2 we present the linear response formalism necessary for the determination of the response function. Then we show explicitly the influence of the response function on the NMFP in Sec.3 and finally draw our conclusions in Sec.4.