Summary
A generalized single-particle wave equation is derived in the effective mass approximation, starting from a non-local potential matrix for the nucleon-nucleus interaction as required by recent work on the nuclear many-body problem. The effective nucleon mass appearing in the kinetic energy operator of this equation depends on the shape of the local potential which is assumed as the static limit of the non-local interaction. The non-static effects on the motion of individual nucleons in non-spherical nuclei are illustrated using a spheroidal oscillator potential. By a perturbation treatment of the energy eigenvalue problem, it is shown that the non-static problem is approximately equivalent to a static one with a modified deformation parameter.
Riassunto
Un’equazione d’onda generalizzata per particelle singole si deriva nell’approssimazione della massa effettiva partendo da una matrioe potenziale per l’interazione nucleonenucleo come richiesto dai lavori recenti sul problema nuoleare di più corpi. La massa. nucleonica effettiva che compare nell’operatore dell’energia cinetica di questa equazione dipende dalla forma del potenziale locale che si ritiene essere il limite statico dell’interazione non locale. Gli effetti non statici sul moto dei singoli nucleoni nei nuclei non sferici sono illustrati ricorrendo a un potenziale oscillante sferoidale. Con un trattamento perturbativo del problema dell’autovalore dell’energia si dimostra che il problema non statico è approssimativamente equivalente a un problema statico con parametro di deformazione modificato.
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References
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Frahn, W.E., Lemmbe, R.H. Non-static effects on individual nucleons in a spheroidal potential. Nuovo Cim 6, 664–673 (1957). https://doi.org/10.1007/BF02781371
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DOI: https://doi.org/10.1007/BF02781371