Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms

The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry, and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.

Figure 1

Strength functions $S^{\left(\alpha \right)}(q,\omega )$ for the spin-isospin channels $\left(\alpha \right)=(S,M,I)$ in asymmetric nuclear matter at density $\rho =0.16$ fm${}^{-3}$ and momentum transfer $q=0.1$ fm${}^{-1}$, calculated with Skyrme functional T44. (a) and (e) correspond to the asymmetry parameter $Y=1$ (SNM). (b) and (f) to $Y=0.21$. (c) and (g) to $Y=0.5$. (d) and (h) to $Y=1$ (PNM). Only channels $(S,M)$ are relevant in PNM. The dotted lines in (a)–(d) are the $S_{\mathrm{HF}}$ strengths.

Figure 2

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

Figure 3

Same as Fig. 1, for $q=1.34$ fm${}^{-1}$.

Figure 4

Same as Fig. 1 for $\rho =0.08$ fm${}^{-3}$.

Figure 5

Same as Fig. 4, for $q=0.5$ fm${}^{-1}$.

Figure 6

Inverse-energy weighted sum rule $M_{-1}$ for spin-isospin channels $(S,M,I)$ at asymmetry $Y=0.5$, as calculated analytically (solid line) and numerically (dashed line).

Figure 7

Strength function $S^{\left(\alpha \right)}(q,\omega ,T)$ for spin-isospin channels $\left(\alpha \right)=(S,M,I)$ calculated at density $\rho =0.16$ fm${}^{-3}$, temperature $T=16$ MeV, and momentum transfer $q=0.1$ fm${}^{-1}$ (a) and $q=1.34$ fm${}^{-1}$ (b).

Figure 8

We show the spinodal instability ($S=0,M=0,I=0$) for the T44 Skyrme functional for different values of the neutron ${\rho }_n$ and proton ${\rho }_p$ density. (a) at $T=0$ and (b) for $T=10$ MeV.

Figure 9

In each panel we represent the critical density ${\rho }_c$ in the different channels $S=1,M=0,1,I=0,1$ for several values of the asymmetry parameter Y and at zero temperature. The horizontal dashed line corresponds to $\rho =0.16$ fm${}^{-3}$.