Spin and spin-isospin instabilities and Landau parameters of Skyrme interactions with tensor correlations

The Landau parameters of Skyrme interactions in the spin and spin-isospin channels are studied using various Skyrme effective interactions with and without tensor correlations. We focus on the role of the tensor terms on the spin and spin-isospin instabilities that can occur in nuclear matter above saturation density. We point out that these instabilities are realized in nuclear matter at the critical density of about two times the saturation density for all the adopted parameter sets. The critical density is shown to be very much dependent not only on the choice of the Skyrme parameter set, but also on the inclusion of the tensor terms.

Figure 1

Landau parameters $G_0$ and $G_0^{\prime }$ for different Skyrme parameter sets. See the text for details.

Figure 2

Landau parameters as a function of nuclear-matter density $\rho$ in spin and spin-isospin channels. The Skyrme parameter sets SLy5 and T44 are adopted in the top and bottom panels, respectively.

Figure 3

Various instabilities of nuclear matter given by Skyrme forces with the tensor terms. Panels (a) and (b) are for the instabilities of the isoscalar $0^{-}$ [Eq. (14)] and $1^{+}$ [Eq. (17)] modes, respectively, and panels (c), (d), and (e) are for those of the isovector $0^{-}$ [Eq. (18)], $1^{-}$ [Eq. (19)], and $1^{+}$ [Eq. (21)] modes, respectively. The color classifies the magnitude of the critical density ${\rho }_c$ for the instability. See Table and the text for details.

Figure 4

The same as Fig. 3 without the tensor terms. Panel (a) is the instability for the isoscalar spin mode [Eq. (22)], and panel (b) is that for the isovector spin mode [Eq. (24)]. See Table , the caption to Fig. 3, and the text for details.