Photodisintegration of the deuteron

The thesis is divided into three parts. In the first part, a general survey of the two-nucleon problem is given, with particular attention paid to those aspects which impinge directly on the photodisintegration of the deuteron. In the second part, we consider the conventional theory of deuteron photodisintegration, with the radiative interaction being taken as given on the basis of the gauge invariance of the non-relativistic Hamiltonian for the two-nucleon system. Differential cross-section and polarization formulae are presented, and a discussion given of previous calculations in this field. New calculations are carried out using the Gammel-Thaler type Y.L.A.M. phase parameters obtained in the analysis of Breit et al. Wherever possible, phenomenological wave-functions are used, and where this is not feasible, they are calculated from a suitable Gammel-Thaler potential. Differential cross-sections and polarizations are obtained for photon laboratory energies up to 130 MeV, the calculations being carried out both for a 4% and 6% deuteron D-state probability. Finally the results obtained are compared and contrasted with those of previous calculations, and both sets compared with experiments. In the third part of the thesis, the calculation of the matrix element for deuteron photodisintegration by dispersion relations is considered. There are twelve invariant amplitudes. The covariant form of the transition amplitude is related to the non-covariant (Pauli-matrix) form, which is further related to the individual multipole transition amplitudes. The Born terms of the covariant amplitudes are derived, and the dispersion relations written down in energy for a fixed difference in the photon-proton and photon-neutron momentum transfers. It is necessary to use this rather than a fixed momentum transfer, in order to exhibit explicitly all the poles in the dispersion relations. The dispersion relations contain integrals over both positive and negative energies, the latter arising from the crossed diagrams for which the imaginary part of the amplitude is related to processes such as the radiative absorption of an antie.nucleon by a deuteron, and to the structure of the deuteron through the anomalous singularities of the deamp vertex. These complications are ignored, and we retain only the pole terms and the integrals over positive energies. The relations are restricted to dipole and quadrupole transitions, and by considering the relations at two different "momentum transfers", equations are obtained explicitly for the individual electric dipole and magnetic dipole spin flip transition amplitudes. The equations are solved in a low energy approximation in which the final state nsp rescattering cut and single pion exchange cut only are considered, for the two cases of the Y.L.A.M. and Signell-Marshak phase-parameters. The results obtained are compared with those obtained in part two of the thesis