High Energy Photo-Disintegration of the Deuteron

Abstract

The disintegration of the deuteron by $\ensuremath{\gamma}$-rays in the range 50-250 Mev is investigated. The lower energy limit is imposed by the neglect of nuclear forces between the neutron and proton after absorption of the photon. Moreover, the effects of retardation and of multipole radiation higher than dipole, the investigation of which constitutes one of the primary purposes of the present work, become apparent only above 50 Mev. The upper limit is imposed by the assumption that the nuclear particles can be treated non-relativistically. It is shown that at the high radiation energies considered it is essential to take into account the range of the nuclear forces in the ground state and that this is the case because of the importance of interference effects (short de Broglie wave-length of the nucleons) which depend very strongly on the "size" of the deuteron. The cross section at 50 Mev is 37\ensuremath{\mu}b(37\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}30}$ ${\mathrm{cm}}^{2}$) and decreases with $\ensuremath{\gamma}$-ray energy up to 150 Mev as ${(\ensuremath{\hbar}\ensuremath{\omega})}^{\ensuremath{-}n}$ where $n$ lies between 4 and 5. Beyond 150 Mev the cross section decreases less rapidly because of a more favorable phase relation between outgoing waves from different parts of the deuteron. The general features of the cross section and of the angular distribution of the particles can be understood in terms of interference; the most important effect of the interference is to favor strongly small momentum for the recoil particle (proton in the case of charge coupling and both proton and neutron in the case of spin coupling). The error caused by neglect of nuclear forces in the final state is estimated, by a consideration of electric dipole transitions, to be less than 30 percent in the worst case (low energy photons). The effects of retardation and higher multipoles are calculated explicitly, and it is shown that these effects are small at 50 Mev and important at 100 Mev. It is also shown that the effect of non-central forces between the nucleons in the ground state introduces negligible error.