Effects of the Skyrme tensor force on 0+ , 2+ , and 3− states in O16 and Ca40 nuclei within the second random-phase approximation

Abstract

The effects of the Skyrme tensor force on the natural-parity ${0}^{+}$, ${2}^{+}$, and ${3}^{\ensuremath{-}}$ states in $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ are studied with the subtracted second random-phase approximation (SSRPA) adopting the Skyrme energy density functional. The strength distribution of these normal parity states are calculated with and without tensor interactions. The tensor force produces a small effect on ${0}^{+}$ and ${2}^{+}$ states in the random-phase approximation (RPA). However, our study shows that the tensor force has a significant effect on these states due to the coupling between one particle-one hole (1p-1h) and two particle-twp hole (2p-2h) model space in SSRPA; i.e., it increases strength for the low-lying ${0}^{+}$ and ${2}^{+}$ states below 10 MeV and shifts the main peak of ${2}^{+}$ transition downwards by about 1 to 2 MeV. For the negative-parity ${3}^{\ensuremath{-}}$ state, the tensor force shifts the lowest state downwards obviously, which helps the prediction of experimental data. The effect of the tensor force on the ${3}^{\ensuremath{-}}$ state is even visible in the 1p-1h RPA model space. We introduce two different parameter sets of tensor forces to clarify the role of the triplet-odd tensor term on the low-lying states. The microscopic structures of the lowest ${0}^{+}$, ${2}^{+}$, and ${3}^{\ensuremath{-}}$ states are examined looking at their 1p-1h and 2p-2h mixing amplitudes.