Summary
The study of nuclear and atomic shell models involves the calculation of matrix elements of operators between many-body configurations. This paper shows how the occupation number representation of Dirac can be used in such calculations, especially for configurations near closed shells. Methods for the construction of many-body wave functions are given, and the equivalence of holes and particles discussed. Application is made to the calculation of transition matrix elements for holes and particles and to the investigation of two body interactions. In particular the interaction between holes and particles is considered.
Riassunto
Lo studio di modelli nucleari e atomici a gusci richiede il calcolo di elementi di matrice di operatori tra configurazioni di piú corpi. Il presente lavoro mostra come in tali calcoli possa usarsi la rappresentazione per mezzo dei numeri d’occupazione di Dirac, specialmente per configurazioni prossime agli strati chiusi. Si danno metodi per la costruzione di funzioni d’onda di piú corpi e si discute in modo particolare l’equivalenza tra buche e particelle. Si fa un’applicazione al calcolo degli elementi di matrici di transizione fra buche e particelle e all’esame dell’interazione fra due corpi. Si considera in particolare l’interazione fra buche e particelle.
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References
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Brink, D.M., Satchler, G.R. Holes and particles in shell models. Nuovo Cim 4, 549–557 (1956). https://doi.org/10.1007/BF02745378
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DOI: https://doi.org/10.1007/BF02745378