Scattering of PolarizedμMesons from Extended Nuclei

Scattering solutions of the Dirac equation for a muon in the static electric field of an extended nucleus are numerically obtained for various values of the velocity of the incident particle ($\beta =0.4\mathrm{} \mathrm{to} 0.8$) and of the charge of the scattering nucleus ($Z=48\mathrm{} \mathrm{and} 80$). A Stanford Fermi-type shape for the extended nuclear charge distribution is assumed. Angular distributions of the unpolarized cross section and of the left-right scattering asymmetries ($S$) of a transversely polarized beam of ${\mu }^{+}$ and ${\mu }^{-}$ mesons are presented. For ${\mu }^{-}$ the finite nuclear size strongly reduces $S$ in the forward directions. The reduction of the cross section seems to be more sensitive to the detailed shape of the charge distribution than is the reduction of $S$. In the case of ${\mu }^{+}$, $S$ is appreciably altered from the "point" value, and can depend sensitively on the shape of the nuclear charge distribution. The value of $S$ can be larger for the extended nucleus than for the point nucleus.