Nuclear structure calculations with density-dependent effective interactions

An investigation of density-dependent interactions, such as those of Vautherin and Brink, and Moszkowski and Ehlers, is carried out. The interactions are constrained to give the correct binding energies and mean square radii of closed-shell nuclei such as ¹⁶O and ⁴⁰Ca. Such quantities as the single-particle energies, the effective charges for E0 and E2 transitions, the mean energies of electromagnetic collective states, and the low-lying states consisting of either two particles, two holes, or a particle-hole relative to a given closed shell are then considered. Harmonic oscillator wave functions are used, but radial self-consistency is satisfied. The prescription for handling density-dependent or three-body interactions to obtain bulk properties or to do shell model calculations is given. The rearrangement prescription for the interaction of two particles beyond a closed shell is the same as it is for the interaction of a particle and hole of the same closed shell. It is found that the J = 0 breathing mode state and the E0 effective charge are most affected by the density dependence. But this can be simulated by merely adding a monopole-monopole term to a density-independent interaction. The spin dependence of the interactions is also considered. In this respect the Vautherin-Brink interaction (II) has some desirable consequences for particle-hole calculations, i.e. the J = 0, T = 1 "Coulomb mixing state" is very high in energy. However, two identical particles in a J = 0 state have a repulsive interaction energy. This is precisely the opposite of the wellknown pairing property of nuclei. Unfortunately, if one attempts to modify the spin dependence to improve the particle-particle situation one makes the particle-hole situation worse. Evidently, additional components are required if we are to have a universal interaction.