Nuclear Moments and Configuration Mixing

Abstract

The nuclear static moments are calculated from configuration mixing in the jj-coupling shell model. The residual interactions between particles in different orbits are taken as the cause of the configuration mixing. The singleparticle energy differences in the energy denominators are estimated from a shell model Hamiltonian which gives fairly good agreement with observed single- particle levels, and the denominators contain the pairing effects ih the zeroth order states. Various features of the deviations of magnetic dipole moments from the Schmidt lines are well interpreted by the configuration mixing for almost the whole region of nuclei. The quadrupole moment of an odd-neutron nucleus can be accounted for from the mixing of excited states of the ground configuration and of higher configurations of even numbers of protons. For those of odd-proton nuclei, the corrections by the similar mixing are almost as large as the single- proton values so that the quadrupole moments of the medium-weight nuclei which are two to three times as large as the single-proton values can be explained. However, the large quadrupole moments of the heavy nuclei cannot be interpreted by the perturbational treatment of configuration mixing. The corrections to the magnetic dipole moments of odd-odd nuclei are alsomore » calculated and good agreement with observed values is obtained. The magnetic octupole moments of odd-A nuclei are also considered on the same basis. The numerical results are not sensitive to the choice of the single-particle wave functions, as far as the harmonic oscillator and the square well wave functions are employed. The second order effects are estimated by calculating the mixing probabilities of excited configurations into the ground state for S33, and the treatment by the first order perturbation theory appears justified at least for the medium- weight nuclei. Interactions with finite ranges are also considered and it is shown that, if a suitable exchange character is adopted for the interactions, the results are not much different from those by the delta-function interactions.« less