The original three-body term in the Skyrme interaction is replaced by a two-body explicit density dependent term to reproduce simultaneously the excited and ground states of nuclei. Care has been taken to remove the spin instability of the Hartree-Fock ground state in nuclear matter and also the antipairing nature of the interaction inherent in the original Skyrme interaction. The spin-isospin dependent parameter introduced in the density dependent term is determined from the average asymmetry ratio and asymmetry energy. The modified Skyrme force is used to calculate the low-lying states of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. In the light of these calculations the relative importance of the different Skyrme variants is studied.

NUCLEAR STRUCTURE Ground and excited state properties of nuclei with modified Skyrme interaction, spectra of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

• Received 6 March 1981

DOI:https://doi.org/10.1103/PhysRevC.25.1034