On the description of collective motion by th use of superfluous co-ordinates
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Summary
By introducing superfluous co-ordinates a method is demonstrated for treating the problem of combined collective and individual particle aspects of nuclear structure. The application to the case of the center of mass gives a simple exposition of the method and rigorously defines conditions for the validity of the usual shell-model assumptions regarding the center of mass. The application to rotation gives results similar to those obtained by A. Bohr using a hydrodynamical model and by Inglis using a classical rotating shell model. The present treatment is rigorous except for the fundamental shell-model assumption, the replacement of the inter-particle potential by a single-particle potential which may not be spherically symmetric.
Riassunto
Si espone un metodo, basato sull’introduzione di coordinate superflue, atto a trattare il problema della struttura nucleare considerata contemporaneamente nei suoi aspetti a particelle singole o collettivo. L’applicazione al caso del centro di massa permette una esposizione semplice del metodo e definisce rigorosamente le condizioni per la validità delle ipotesi riguardanti il centro di massa prese a base del consueto modello a shell. L’applicazione al caso rotativo dà risultati simili a quelli ottenuti daA. Bohr servendosi di un modello idrodinamico e daInglis servendosi di un classico modello a shell. Il trattamento che presentiamo è rigoroso eccetto che per l’ipotesi fondamentale del modello a shell, la sostituzione al potenziale fra particelle di un potenziale monoparticellare che può non esser dotato di simmetria sferica.
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References
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