The Oppenheimer-Phillips Process

Abstract

A critical study of the previous theoretical treatments of the process of neutron capture by heavy nuclei bombarded with deuterons shows that while the dependence of the transmutation function on the incident deuteron energy, $W$, has been given correctly, the energy distribution of the outgoing protons has not been satisfactorily estimated. In I, the application to the Oppenheimer-Phillips process of the usual formula for the cross section is shown to be justified for restricted values of the atomic number $Z$ and of the deuteron energy. Bethe's method is used to express the partial cross section as a product of three factors: the penetrability of the potential barrier, the sticking probability of the neutron, and the energy transfer factor. In II, methods of obtaining the deuteron wave-function are discussed. Calculations of the transmutation function are extended to higher values of $Z$ and $W$, and results obtained by using the O-P-Bethe and the Kapur methods are compared. In III, the proton energy distribution is discussed. A re-evaluation of the dependence of the transfer factor on the proton energy, $K$, leads to a result differing from Bethe's. The transfer factor is found to have a fairly sharp maximum, and to determine essentially the proton energy distribution. For high $Z$ and low $W$ the position and half-breadth of this maximum is given roughly by ${K}_{0}\ensuremath{\sim}W$ and $\ensuremath{\Delta}{K}_{0}\ensuremath{\sim}3.3$ $W{Z}^{\ensuremath{-}\frac{1}{2}}$. Lifshitz' and Kapur's treatments of proton energies are examined, and found to be unsatisfactory.