Nuclear dependence of the coherentηphotoproduction reaction in a relativistic approach

Abstract

We study the nuclear (or $A)$ dependence of the coherent $\ensuremath{\eta}$ photoproduction reaction in a relativistic impulse approximation approach. We use a standard relativistic parametrization of the elementary amplitude, based on a set of four Lorentz- and gauge-invariant amplitudes, to calculate the coherent production cross section from ${}^{4}\mathrm{He}$, ${}^{12}\mathrm{C}$, and ${}^{40}\mathrm{Ca}$. In contrast to nonrelativistic treatments, our approach maintains the full relativistic structure of the process. The nuclear structure affects the process through the ground-state tensor density. This density is sensitive to relativistic effects and depends on $A$ in a different manner than the vector density used in nonrelativistic approaches. This peculiar dependence results in ${}^{4}\mathrm{He}$ having a cross section significantly smaller than that of ${}^{12}\mathrm{C}$---in contrast to existent nonrelativistic calculations. Distortion effects are incorporated through an $\ensuremath{\eta}$-nucleus optical potential that is computed in a simple ``$t\ensuremath{\rho}$'' approximation.