We study the nuclear (or $A)$ dependence of the coherent $\eta$ 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 $\eta$-nucleus optical potential that is computed in a simple “$t\rho$” approximation.

• Received 2 October 1997

DOI:https://doi.org/10.1103/PhysRevC.57.2053