The first order of the hyperspherical harmonic expansion method |
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Authors: | M Fabre de la Ripelle J Navarro |
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Institution: | Departmento de Fisica Teorica, Facultad de Ciencias Fisicas, Valencia, Spain |
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Abstract: | The hyperspherical harmonic expansion method is studied in this work. Our attention is focused on the properties of the Lm-approximation in which only the hyperspherical harmonics of minimal order are taken into account. Exact solutions of the Schrödinger equation for a 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 Lm-approximation are discussed. The method is applied to the calculation of ground state and hyperradial excited states (which are identified as the breathing modes) of doubly-magic nuclei. Finally, the energy per particle is derived in the Lm-approximation with Skyrme like forces for an infinitely heavy self-conjugate nucleus. |
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