Summary
The single particle wave equation describing the motion of nucleons in nuclei, as derived from the nuclear many-body problem, is of a non-local form in coordinate space. It is shown, that in the effective mass approximation, this equation reduces to a velocity-dependent Schrödinger equation, which contains a spatially variable effective nucleon mass in a properly symmetrized kinetic energy operator. The eigenvalue problem is treated for the special case of the infinite harmonic oscillator potential as the local part of the interaction.
Riassunto
L’equazione d’onda di una singola particella che descrive il moto di nucleoni nei nuclei, come si deriva dal problema nucleare di più corpi, è di forma non locale nello spazio delle coordinate. Si dimostra che nell’approssimazione della massa effettiva quest’equazione si riduce a un’equazione di Schrödinger dipendente dalla velocità che contiene una massa nucleonica spazialmente variabile in un operatore di energia cinetica opportunamente simmetrizzato. Il problema degli autovalori è trattato per il caso speciale del potenziale di oscillatore armonico infinito come parte locale della interazione.
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References
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Frahn, W.E., Lemmer, R.H. Velocity-dependent nuclear interaction. Nuovo Cim 5, 1564–1572 (1957). https://doi.org/10.1007/BF02856046
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DOI: https://doi.org/10.1007/BF02856046