On the use of Skyrme forces in self-consistent RPA calculations

Self-consistent random-phase (RPA) calculations including the continuum are presented using Skyrme forces. The density-dependent interpretation of the interaction is favoured as it does not violate the spin stability. A possible density dependence of the momentum-dependent S- and P-interaction is taken into account, which allows one to vary the incompressibility K and the effective mass $\text{m}{}^1\text{/m}$ independently. It is shown by analytic relations that these two quantities are the only degrees of freedom left in the parameterization of this Skyrme force,if the ground-state properties shall be reproduced, except for a still open degree of freedom in the spin exchange parameterization. The Landau parameters are discussed as a function of these degrees of freedom in order to find the best possible particle-hole interaction. Continuum calculations of the 1^?, 2 ⁺ and 3^? states in ¹⁶O are presented and compared with-discretized continuum calculations. It is found that the existing Skyrme forces do not show enough attraction and in addition cause relatively large isospin impurities, in ¹⁶O as well as in ²⁰⁸Pb. The influence of large configuration spaces is discussed. A systematic search for an interaction with a stronger particle-hole interaction is presented which seems to favour interactions with a high effective mass, but a low compression modulus.