Non-Hermitian quantum mechanics allows one to calculate a physical observable, e.g., scattering cross section, as a sum over a finite number of discrete resonance states. The coefficients in the sum can get complex and negative values even in cases where conventional scattering theory predicts real positive coefficients only. Consequently, structure (or absence of structure) in scattering cross section can be obtained as a result of interference between a small number of discrete resonance states; whereas, conventional scattering theory would require integration over the continuum of scattering states and therefore it is a heavy numerical task. We show here that in electron scattering experiments the interference between overlapping broad resonances leads to oscillations in the phase of transition probability amplitude and to enhancement of the transition state lifetime due to nuclear motion.