Summary
An exact Gell-Mann-Goldberger (GG) formula for the two-body off-energy-shellt-matrix is derived. It follows that the simple extension of the matrix elements in the usual on-shell GG formula, which has so far been used in the literature, is not exact. It is explicitly shown that in the case of the Coulomb plus Yamaguchi potential such an extension cannot even be considered as an approximation.
Riassunto
Si deduce una formula esatta di Gell-Mann-Goldberger per la matricet di due corpi fuori dallo strato dell'energia. Se ne deduce che la semplice estensione degli elementi di matrice nella formula usuale GG dentro il livello, che è stata finora usata nella produzione corrente, non è esatta. Si mostra esplicitamente che nel caso del potenziale di Coulomb più Yamaguchi una tale estensione non può più essere considerata un'approssimazione valida.
Резюме
Выводится точная формула Гелл-Манна-Гольдбергера для двухчастичнойt матрицы вне энергетической поверхности. Из нее следует, что простое распространение матричных элементов в обычной формуле Гелл-Манна-Гольдбергера на энергетической поверхности, которое до сих по⌕ исполязуется в литературе, оказывается неточным. Показывается, что в случае кулоновского потенциала плюс потенциал Ямагучи такое распространение не может рассматриваться даже как аппроксимация.
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Bajzer, Ž. On the application of the Gell-Mann—Goldberger formula to the off-energy-shell proton-protont-matrix. Nuov Cim A 22, 300–312 (1974). https://doi.org/10.1007/BF02813440
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DOI: https://doi.org/10.1007/BF02813440