GT resonances from generalized Skyrme functionals

Figure 6: Deviation of calculated and experimental GT resonance energies (lower panel) and a fraction of the GT strength in the GT resonance (upper panel) for ¹¹²Sn, ¹²⁴Sn, and ²⁰⁸Pb, calculated with SkO' and a modified residual spin-isospin interaction. C₁^T is kept at the Skyrme-force value and $C_1^{\Delta s}$ is set to zero. C₁^s is chosen to be density-independent and varied to get $0 \leq g_0' \leq 2.4$. g₁' = 0.19 in all cases.

We turn now to generalized energy functionals in which the time-odd coupling constants C_t^s, $C_t^{\Delta s}$, and C_t^T are treated as free parameters; that is, we no longer insist that the interaction correspond to a two-body Hamiltonian with matrix elements that should be antisymmetrized. As we showed in Sect. 4.2, values of the Landau parameter g₀' alone are insufficient to link the properties of the GT resonance to the coupling constants of the energy density functional. In this section, using the time-even functional of SkO', we study the dependence of the GT resonance on several other combinations of the coupling constants as well. Because the isoscalar time-odd terms do not affect the GT transitions, we focus here on the isovector coupling constants C₁^s, $C_1^{\Delta s}$, and C₁^T.