Nuclear response for the Skyrme effective interaction with zero-range tensor terms. III. Neutron matter and neutrino propagation

Abstract

The formalism of the linear response for the Skyrme energy density functional including tensor terms derived in articles [1, 2] for nuclear matter is applied here to the case of pure neutron matter. As in article [2] we present analytical results for the response function in all channels, the Landau parameters and the odd-power sum rules. Special emphasis is given to the inverse energy weighted sum rule because it can be used to detect non physical instabilities. Typical examples are discussed and numerical results shown. Moreover, as a direct application, neutrino propagation in neutron matter is investigated through its neutrino mean free path at zero temperature. This quantity turns out to be very sensitive to the tensor terms of the Skyrme energy density functional.

Superfluid properties of the inner crust of neutron stars. II. Wigner-Seitz cells at finite temperature

“…Such kind of calculations are still not available for WS cells, mainly because of the computational time requested. According to our findings, a possible alternative could be represented by performing calculations in the infinite systems of both collective excitations [45][46][47] and pairing gaps [48]. Such results could be then used to fit an effective zero range pairing interactions.…”

Tools for incorporating a D-wave contribution in Skyrme energy density functionals

“…In a recent series of articles, we have presented the Linear Response formalism [35,36,37,38] for a standard Skyrme functional in both symmetric nuclear matter (SNM) and pure neutron matter (PNM). In particular, using the LR formalism we have studied the presence of finite-size instabilities in the infinite medium.…”

“…[36,37,38,35], we have decided to express the system of coupled equations in matrix form as done in Ref. [48] and to solve them numerically to obtain the response function of the system χ (α) (q, ω).…”

Nuclear matter response function with a central plus tensor Landau interaction

“…This simple case illustrates our method for solving the Bethe-Salpeter equation. It has been already employed in the case of a general ph interaction derived from a standard Skyrme effective interaction including tensor components [10] and then generalized in [33,34] to the case of a second order Skyrme functional [35]. The complete ph interaction has a complicated momentum dependence, but due to its zero-range nature it is possible to obtain practical analytical expressions for the response function in that case.…”