Electromagnetic annihilation into charged leptons and scattering off nucleons of spin-$3/2$ Majorana particles

We compute the cross section for the electromagnetic annihilation into charged leptons, and the electromagnetic scattering off nucleons, of spin-$3/2$ self-conjugate (Majorana) particles using the general form of the electromagnetic vertex function that was obtained previously for such particles. In addition to the restrictions imposed by common principles such as electromagnetic gauge invariance and Hermiticity, the vertex function incorporates the restriction due to the Majorana condition as well as the particular properties related to the spinors in the Rarita–Schwinger representation and is the counterpart of the so-called anapole interaction of spin-$1/2$ Majorana particles. The formulas obtained for the cross sections share certain similarities with the corresponding results in the spin-$1/2$ case, but they also reveal some important differences which are pointed out and discussed. The results given here can be useful for applications involving the electromagnetic interactions of spin-$3/2$ or spin-$1/2$ Majorana particles in several contexts that have been of interest in the recent literature such as nucleosynthesis and dark matter.