Landau parameters

The time-odd coupling constants of the Skyrme energy functional, see I, are poorly known, because of the lack of experimental data that would be sufficiently sensitive to this channel of energy density. Recently, such sensitivity has been analyzed for the effects related to the Gamow-Teller strength in nuclei [19]. In this analysis, it turned out that one can make a useful unique link between some time-odd coupling constants and the Landau parameters $g_0$, $g'_0$, $g_1$, and $g'_1$. In view of that, it is more practical, and physically more intuitive, to use the Landau parameters at saturation density as input data for the code HFODD. This is done by employing Eq. (15) of Ref. [19], together with ratios of density-dependent coupling constants, $C_0^{s}[\rho]$ and $C_1^{s}[\rho]$, i.e.,

where $\beta = ( 3 \pi^2 / 2 )^{2/3}$ and

$$N_0 = \pi^{-2}\left(\frac{\hbar^2}{2m}\right)^{-1} \left(\f... ...\frac{3\pi^2\rho_{\mbox{\scriptsize {sat}}}}{2}\right)^{1/3} .$$ (18)

Altogether, six parameters appearing at the left-hand-sides of Eqs. (21) uniquely determine six coupling constants $C_0^{s}[0]$, $C_0^{s}[\rho_{\mbox{\scriptsize {sat}}}]$, $C_1^{s}[0]$, $C_1^{s}[\rho_{\mbox{\scriptsize {sat}}}]$, $C_0^{T}$, and $C_1^{T}$, provided the constant $\hbar^2/2m$, effective mass ${m^*}/{m}$, and saturation density $\rho_{\mbox{\scriptsize {sat}}}$ are given.