Application of Self-Consistent Field Methods to Rotational Motion insdShell Nuclei

A self-consistent field calculation of the single-particle orbitals in the $\mathrm{sd}$ shell is presented. The calculation is based on a standard shell-model Hamiltonian employing a single-particle spin-orbit force and two-body Yukawa interaction with a Rosenfeld exchange mixture. Using these orbitals the low-lying rotational spectra of the $\mathrm{sd}$ shell nuclei are computed. The variational formula of Skyrme and the cranking model yield moments of inertia which compare well with the experimental data. The rotation-particle coupling interaction is diagonalized and good fits to the nuclear rotational spectra are obtained.