Magnetic Dipole Moments ofp12-Shell Nuclei

Abstract

The magnetic dipole moments of Ply&-shell nuclei are calculated by the first-order perturbation theory. It is shown that the tensor force which causes the configuration mixing is important to explain observed data of these moments.The magnetic dipole moments of odd-mass nuclei have been estimated with the j-j-coupling shell model and are known as Schmidt values. The agreement between the shell-model values and the experimental values is not satisfactory. Also, most of the observed data lie within the regions bounded by the Schmidt lines instead of being scattered on both sides. Noya, Arima, and Horie' MAGNETIC DIPOLE MOMENTS OF P / -SHE LL NUCLEI 1221 have shown that mixing a small amount of the seniority-three configurations into the seniority-one configuration is enough to explain the deviations of the experimental values from the shell-model values. Freed and Kisslinger' carried out the calculations using the same method, but within the framework of the pairing model. However, the seniority-three contributions to the P,/, state, where the magnetic dipole moments are approximately the single-particle values, are all zero, since a 6-function force was chosen to be the residual interaction in their calculations. Later on, Kisslinger and Sorensen' carried out calculations of these magnetic dipole moments using wave functions which involve configuration mixing due to phonons. The results are not plausible for the oddneutron nuclei, especially for the isotopes of Ge and Se, where the corrections for the deviations from the single-particle value are of the opposite sign. On the other hand, the tensor force has been emphasized to be important in calculating the lforbidden magnetic dipole transitions, where three-quasiparticle states are admixed to the seniority-one state by first-order perturbation theory. This indicates that the tensor force might be used to explain the magnetic dipole moments of Py/pshell nuclei.The wave function concerned is a linear combination of a one-quasiparticle state and three-quasiparticle states suits display a large deviation from the singleparticle value of 0.64. Because of the fact that these isotopes belong to the deformed nuclei and apparently reflect the effects of collective motions, we have completely disregarded them in this work.In numerical calculations, the single-particle levels used in solving the gap equation of the pairing model were essentially the same as those which are currently used. ' At both ends of the major shells we only included the pairs of relevant spin-orbit partners, whose separations were readjusted; and the strengths of the pairing interaction are G"=19.5/A MeV and GO=21/A MeV throughout the whole mass region. ' In addition, the harmonic-oscillator wave functions were chosen for the radial integrals.The results are shown in Table I with the experimental values given in the literature. ' Also exhibited in the table are the values calculated byKisslinger and Sorensen' with the gyromagnetic ratios g"=0 and g"=Z/A. In evaluating the deviations from the single-p...