Linear response theory and neutrino mean free path using Brussels-Montreal Skyrme functionals

The Brussels-Montreal Skyrme functionals have been successful in describing properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predictions from the Brussels-Montreal Skyrme functionals are compared with ab initio methods.

Figure 1

EoS in PNM for the the different functionals adopted in the text. The grey area represents the constraint obtained from Ref. [27]. The triangles correspond to the CBF calculations taken from Ref. [28].

Figure 2

Neutron effective mass in PNM as a function of the density, for the different functionals. The triangles are obtained from Ref. [28] using the CBF method.

Figure 3

Strength function $S^{(S,M)}(q,\omega )$ calculated at $\rho =0.16{\text{fm}}^{-3}$ and transferred momentum $q=0.1{\text{fm}}^{-1}$ for the different functionals used in the present study. The strength functions in the channels (1,0) and (1,1) are degenerate.

Figure 4

Same as Fig. 3, but for $q=0.5$ ${\mathrm{fm}}^{-1}$.

Figure 5

Response function for four selected functionals at $T=2$ MeV and $\rho =0.16$ ${\mathrm{fm}}^{-3}$ and transferred momentum $q=0.1$ ${\mathrm{fm}}^{-1}$.

Figure 6

Landau parameters in PNM as a function of the neutron density. The triangles represent the results of CBF taken from Ref. [61].

Figure 7

Critical densities in PNM for different Skyrme functionals as a function of the transferred momentum $q$. The horizontal dashed-dotted line represents $\rho =0.16$ ${\mathrm{fm}}^{-3}$.

Figure 8

NMFP ${\lambda }_{RPA}$ at $\rho =0.16$ ${\mathrm{fm}}^{-3}$ and zero temperature for different BSk functionals. The triangles represent the result obtained in Refs. [23, 61] using the CBF method.

Figure 9

Same as Fig. 8, but for $T=2$ MeV.

Figure 10

Ratio of the NMFP obtained with the full calculation ${\lambda }_{RPA}$ to the one based on the simple Fermi gas ${\lambda }_{FG}$ as a function of the neutrino energy at $T=2$ MeV.

Figure 11

Ratio of the RPA to the FG NMFP as a function of the temperature of the system at different densities, as indicated in the panels, and for a fixed value of incoming neutrino energy $E_{\nu }=60$ MeV.

Figure 12

Ratio of the $T=0$ NMFP ${\lambda }_{RPA}/{\lambda }_{FG}$ for a fixed neutrino energy $E_{\nu }=60$ MeV.