Watson’s theorem for low-energyp−dradiative capture

Abstract

The use of Watson's theorem in the analysis of $p\ensuremath{-}d$ radiative capture measurements at low energies is discussed. The principle of Watson's theorem is outlined, and a detailed description of how the theorem can be used in a matrix element analysis of radiative capture data is presented. It is shown that with Watson's theorem it is possible to reduce the number of unknown parameters in a matrix element analysis by essentially a factor of 2. This is done by employing a representation in which the capture matrix elements are all real. The phase information needed to construct the reaction amplitudes is then obtained from a separate phase shift analysis of elastic scattering data. Details concerning the extension of Watson's theorem to situations in which there is mixing between angular momentum states are given. The paper presents a consistent formulation which facilitates the simultaneous analysis of the elastic scattering and radiative capture channels.