Nuclear recoil effects on the polarization of spin-1/2 particles

Abstract

In this paper the effects of nuclear scattering on the polarization of a beam of spin-\textonehalf{} particles are calculated. These first-order results include the effects of nuclear recoil and apply to elastic scattering by light, spin-0 nuclei at moderate energies. The net effect of the scattering is that the polarization vector is rotated through an angle $\ensuremath{\beta}$ about the normal to the scattering plane, in the same direction in which the momentum is rotated. The rotation of the polarization vector is less than that of the momentum by an angle given by $cos (\ensuremath{\theta}\ensuremath{-}\ensuremath{\beta})=\frac{[1\ensuremath{-}{(\frac{m}{\ensuremath{\epsilon}})}^{2}{tan}^{2}(\frac{\ensuremath{\theta}}{2})]}{[1+{(\frac{m}{\ensuremath{\epsilon}})}^{2}{tan}^{2}(\frac{\ensuremath{\theta}}{2})]}$, where $\ensuremath{\theta}$ is the scattering angle and $\ensuremath{\epsilon}=E+\frac{({E}^{2}\ensuremath{-}{m}^{2})}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}}$, with $m$ and $E$ denoting the mass and energy of the scattered particle and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}$ the energy of the recoiling nucleus. The magnitude of this effect is illustrated for the scattering of muons from helium at several incident energies.