High multipole moments in nuclei

Deformed Hartree-Fock calculations with the Skyrme interactions are carried out for various nuclei in the $s-d$ and $f-p$ shell regions to obtain $E2\mathrm{}$, $E4\mathrm{}$, and $E6\mathrm{}$ intrinsic multiple moments. It is found that the higher moments have an increasing sensitivity to the size of the basis used in the calculation and that the basis must span at least nine major shells to produce reliable results for $E6\mathrm{}$ moments in this mass region. The results are sometimes not monotonic in the number of shells that are included. The results differ greatly for the Skyrme SI and SII interactions used here. More insight into these moments and a better understanding of the Hartree-Fock results is gained by using deformed harmonic oscillator wave functions. The results are compared with shell model calculations. It is found that the collective model approach, when used sensibly, can be very useful in understanding the experimental results. Much of the data can be explained, although some discrepancies still remain. It is found that in open shell nuclei, the simple use of an effective charge calculated for a closed shell plus one nucleon is inadequate. A necessary (but not sufficient) condition for obtaining sensible results for higher moments is that the lower moments come out correctly.