Abstract
In a previous paper a grouptheoretical scheme for the classification of wavefunctions has been developed from a consideration of the group of all transformations, which leave the nuclear hamiltonian invariant thereby taking into account also accidental degeneracies. This scheme is applied here to a translation-invariant hamiltonian with harmonic oscillator forces. The existence of a shell structure for the ground states is proved and the quantum numbers and symmetry properties of the wavefunctions of the ground states and of some excited states are derived. If translation-invariance is neglected, spurious states appear. It is shown how their quantum numbers and symmetry properties can be determined. Some remarks on a translation-invariant formulation of the Elliot-model conclude the paper.
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An diesem Institut wurde die Arbeit zum Abschluß gebracht und das Manuskript fertiggestellt.
Der Verfasser möchte Herrn Professor H.Steinwedel für zahlreiche anregende Diskussionen danken. Der Abschluß der Arbeit und die Fertigstellung des Manuskripts erfolgten am Lawrence Radiation Laboratory der University of California, an dem der Verfasser als Stipendiat der National Academy of Sciences of USA, Washington D.C., zu Gast war. Sein Dank gilt auch Dr.David Judd und der Akademie für ihre Gastfreundschaft und Unterstützung.
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Kretzschmar, M. Gruppentheoretische Untersuchungen zum Schalenmodell. Z. Physik 158, 284–303 (1960). https://doi.org/10.1007/BF01340561
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DOI: https://doi.org/10.1007/BF01340561