Remark on the Primakoff effect

Abstract

The coherent-nuclear reaction $a+A\ensuremath{\rightarrow}{a}^{\ensuremath{\star}}+A$ is in the small-angle region dominated by the one-photon-exchange mechanism, often referred to as the Primakoff effect. In this region information about the electromagnetic decay ${a}^{\ensuremath{\star}}\ensuremath{\rightarrow}a+\ensuremath{\gamma}$ can be obtained. Well-known examples are the two-photon decays of the $\ensuremath{\pi}$ and $\ensuremath{\eta}$ mesons. Also, decays of charged hadrons can be studied. For charged hadrons the one-photon-exchange amplitude comes with a Coulomb-phase factor and a Coulomb-form factor, which depend on the ratio between transverse- and longitudinal-momentum transfers, the latter being fixed. At the peak of the cross-section distribution, where the two momentum transfers are equal, the form factor could cut down the cross-section value by as much as $40%$. Consequently, a determination of a radiative-decay rate that relies on the peak value becomes sensitive to a proper treatment of the Coulomb-form factor.