In this Letter, we present a one-dimensional model that includes a hard core at the origin, a
Dirac delta barrier at a point in the positive semiaxis and a mass jump at the same point. We
study the effect of this mass jump in the behavior of the resonances of the model. We obtain
an infinite number of resonances for this situation, showing that for the case of a mass jump
the imaginary part of the resonance poles tend to a fixed value depending on the quotient of
masses, and demonstrate that none of these resonances is degenerated.