Summary
If the matrix element of a central potential can be approximated by a finite series\(\mathop \sum \limits_{i = 1}^M \mathop \sum \limits_{l = 0}^\infty \mathop \sum \limits_{m = - l}^l a_l^i (k^l )b_l^i (k)Y_{lm} (k^l |P)Y_{lm}^ * (k^l |P)\) where 2P is the center-of-mass momentum, then the K-matrix can be solved in a closed form. The classes of Bose statistics and Fermi statistics are treated. For the Fermi case we have considered both the K-matrix equation without hole-hole inteiaction and with hole-hole interaction.
Riassunto
Se l’elemento di matrice di un potenziale centrale può essere approssimato con una serie flnita\(\mathop \sum \limits_{i = 1}^M \mathop \sum \limits_{l = 0}^\infty \mathop \sum \limits_{m = - l}^l a_l^i (k^l )b_l^i (k)Y_{lm} (k^l |P)Y_{lm}^ * (k^l |P)\) in cui2P è l’impulso del centro di massa, allora la matriceK può essere risolta in forma chiusa. Si trattano i casi della statistica di Bose e della statistica di Fermi. Nel caso di Fermi abbiamo studiato l’equazione della matrice if senza interazione lacuna-lacuna e con interazione lacuna-lacuna.
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This research was supported in part by the National Science Foundation and the Air Force Office of Scientific Research.
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Wong, K.W. A method of solving the many-body K-matrix. Nuovo Cim 34, 591–598 (1964). https://doi.org/10.1007/BF02750001
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DOI: https://doi.org/10.1007/BF02750001