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Il Nuovo Cimento (1955-1965)

, Volume 33, Issue 2, pp 594–627 | Cite as

A covariant theory of the photodisintegration of the deuteron - I

  • M. Le Bellac
  • F. M. Renard
  • J. Tran Van Thanh
Article

Summary

The calculation of the process γ+d → n+p is made in the framework of a covariant theory. There are twelve invariant amplitudes; they are related to helicity amplitudes and then to multipole amplitudes. A general formula is written explicitly for the calculation of any multipole amplitude from the twelve invariant amplitudes. The Born terms are derived and are then modified in order to take account of deuteron structure; this is done by using n-p-d vertex functions depending on the transfer. In I, we calculate the corresponding cross-section as well as the 10 dipole and 12 quadrupole amplitudes. It is shown that the octupole terms are not completely negligible for incident photon energies of about 100 MeV. The theory is equivalent in the low-energy limit to the usual nonrelativistic theory based upon Siegert’s theorem and excluding final-state interactions, but some of the multipole amplitudes seem to be affected by relativistic corrections for energies of order 100 MeV. Comparison with experiment shows very good agreement in view of the approximations made. In II, the final-state interaction for cross-section and polarization will be treated by means of dispersion relations, using the experimental nucleon-nucleon phase shifts.

Riassunto

Si esegue il calcolo del processo γ+d → n+p nell’ambito della teoria covariante. Le ampiezze invarianti sono dodici, esse vengono riferite alle ampiezze dell’elicità e quindi alle ampiezze multipolari. Si scrive esplicitamente una formula generale per il calcolo di qualsiasi ampiezza multipolare delle dodici ampiezze invarianti. Si deducono i termini di Born, che poi si modificano per tenere conto della struttura del deutone; ciò si effettua servendosi delle funzioni del vertice n-p-d dipendenti dal trasferimento. In I si calcolano le corrispondenti sezioni d’urto ed anche le 10 ampiezze dipolari e le 12 quadrupolari. Si dimostra che i termini ottupolari non sono del tutto trascurabili per energie del fotone incidente di circa 100 MeV. Nel limite delle basse energie la teoria è equivalente all’usuale teoria non relativistica basata sul teorema di Siegert con esclusione delle interazioni dello stato finale, ma alcune delle ampiezze multipolari sembrano infiuenzate da correzioni relativistiche ad energia dell’ordine di 100 MeV. Il confronto con gli esperimenti dà un ottimo accordo tenuto conto, delle approssimazioni fatte. In II, si tratta l’infiuenza dell’interazione dello stato finale sulle sezioni d’urto e sulle polarizzazioni per mezzo delle relazioni di dispersione, servendosi degli spostamenti di fase nucleone-nucleone speimentali.

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Copyright information

© Società Italiana di Fisica 1964

Authors and Affiliations

  • M. Le Bellac
    • 1
    • 2
  • F. M. Renard
    • 1
    • 2
  • J. Tran Van Thanh
    • 1
    • 2
  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesOrsay
  2. 2.Laboratoire de Physique Théorique et Hautes EnergiesFaculté des SciencesOrsay (S.-et-O.)

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