Skyrme-Landau particle-particle interaction and application to ¹⁸O and ¹⁸F

Patterned after Landau's Fermi-liquid theory of nuclear matter, we develop an extension of the theory for finite nuclei. Since the particle-hole interaction V_ph derived from the Skyrme-Landau HF ground state is antisymmetric and the exchange term of the phonon-induced interaction is added to V_ph when the renormalization of the HF single-particles due to the particle-phonon coupling is included, the total effective particle-particle interaction is anti-symmetric. We use the newly developed Skyrme-Landau interaction SL1 to evaluate the particle-particle matrix elements in the s-, d-shells. Except for a few cases, the results agree well with those calculated from the G-matrix and those from the empirical study. The spectra of ¹⁸O and ¹⁸F are predicted which indicate that except for the 5⁺ state of ¹⁸F, the results are similar to those obtained from the Kuo-Brown G-matrix. These results represent great improvement from predictions of the other Skyrme-type interactions which are plagued with either the anti-pairing effect or the lack of anti-symmetry in the particle-particle matrix elements.