Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell

We study analytically the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the Klein-Gordon wave equation for the composed charged-shell-charged-massive-scalar-field system. Interestingly, it is proved that the resonant oscillation frequencies of this composed physical system are determined by the characteristic zeroes of the confluent hypergeometric function. Following this observation, we derive a remarkably compact analytical formula for the resonant oscillation frequencies which characterize the marginally-bound charged massive scalar field configurations. The analytically derived resonance spectrum is confirmed by numerical computations.