Family of relativistic deuteron wave functions

Abstract

We present a family of realistic relativistic deuteron wave functions obtained by numerically solving an integral equation with a $\ensuremath{\pi}\ensuremath{-}NN$ coupling which is a mixture of ${\ensuremath{\gamma}}^{5}$ and ${\ensuremath{\gamma}}^{5}{\ensuremath{\gamma}}^{\ensuremath{\mu}}$ forms. We present six solutions for different values of the mixing parameter $\ensuremath{\lambda}$, varying smoothly from 0 (pure ${\ensuremath{\gamma}}^{5}{\ensuremath{\gamma}}^{\ensuremath{\mu}}$) to 1 (pure ${\ensuremath{\gamma}}^{5}$). We find that the small relativistic components of the wave function increase rapidly with $\ensuremath{\lambda}$, and we give a simple explanation for this result. In addition to $\ensuremath{\pi}$ exchange, our model includes $\ensuremath{\sigma}$, $\ensuremath{\rho}$, and $\ensuremath{\omega}$ exchanges. Analytic forms are given for the wave functions which can be used in either position or momentum space. We discuss the validity of various nonrelativistic approximations and the convergence of the equation.