Transition radiation from a Dirac particle wave packet traversing a mirror

The explicit expression for the inclusive probability to record a photon created in transition radiation from a one Dirac particle wave packet traversing an ideally conducting plate is derived in the leading order of perturbation theory. The anomalous magnetic moment of the Dirac particle is taken into account. It is shown that the quantum corrections to transition radiation from an electrically charged particle give rise to production of photons with polarization vector orthogonal to the reaction plane ($E$-plane). These corrections result from both the quantum recoil and the finite size of a wave packet. As for transition radiation produced by a neutron falling normally onto the conducting plate, the probability to detect a photon with polarization vector lying in the reaction plane does not depend on the observation angle and the energy of the incident particle. The peculiarities of transition radiation stemming from different shapes of the particle wave packet are investigated. In particular, the transition radiation produced by the wave packet of one twisted Dirac particle is described. The comparison with classical approach to transition radiation is given and the quantum formula for the inclusive probability to detect a photon radiated by the $N$-particle wave packet is derived.