First Order of the Hyperspherical Harmonic Expansion Method

摘要

The hyperspherical harmonic expansion method is studied in this work. The attention is focused on the properties of the Lsub(m)-approximation in which only the hyperspherical harmonics of minimal order are taken into account. Exact solutions of the Schroedinger equation for few simple hyperspherical potentials are given. Recipes for constructing antisymmetric hyperspherical harmonics for fermions are investigated, and various procedures to derive the effective potential in the Lsub(m)-approximation are discussed. The method is applied to the calculation of ground state and hyperradial excited states (which are identified to the breathing modes) of doubly-magic nuclei. Finally, the energy per particle is derived in the Lsub(m)-approximation with Skyrme like forces for an infinitely heavy N=Z nucleus. (Atomindex citation 10:493205)