Spin-isospin excitations as quantitative constraints for the tensor force

Abstract

Gamow-Teller (GT) and charge-exchange spin-dipole (SD) excitation energies in $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$ are systematically studied to determine the appropriate magnitude of the tensor terms of the Skyrme interactions. We have found that the centroid energies of GT and SD excitations are sensitive to the adopted strengths of the triplet-even and triplet-odd tensor interactions. Especially, the ${1}^{\ensuremath{-}}$ SD state plays a crucial role in constraining the triplet-even part while the triplet-odd part is related rather to the GT peaks. Among the 36 $\mathrm{T}\mathit{IJ}$ parameter sets that include nonperturbatively the tensor terms, the four sets, T21, T32, T43, and T54, give reasonable results for the centroid energies in comparison with the experimental data. The sign and magnitude of the tensor terms are also discussed when these terms are added to the existing Skyrme interactions SGII and SLy5. The triplet-even strength can be constrained in a narrow range by using the available experimental data while further empirical data are needed to set a constraint on the triplet-odd term.