Non topological solitons, Q balls can arise in many particle theories with $U(1)$ global symmetries. As was shown byCohen et al. [A.G. Cohen, S.R. Coleman, H. Georgi and A. Manohar,Nucl.Phys.B272 (1986) 301.], if the corresponding scalar field couplesto massless fermions, large Q-balls are unstable and evaporate, producing a fermion flux proportional to the Q ball's surface. In this work we analyse Q-ball instabilities as afunction of Q-ball size and fermion mass. In particular, we construct an exact quantum-mechanical description of the evaporating Q-ball.This new construction provides an alternative method to compute Q-Ball's evaporation rates. We shall also find a new expression forthe upper bound on evaporation as a function of the produced fermion mass and study the effects of the size of the Q ball on particle production.We also analyse what happens if external fermion is scattered on a Q ball anddemonstrate that it can be converted into antiparticle with a probability ofthe order of one. This result has important implications for astrophysicalapplications of dark matter Q balls.
