Effect of short-range interaction on positions and widths of resonances

The problem in view is the change of widths and positions of resonances due to variations of the interaction potential at small distances. It is shown that in the case of an isolated resonance state variations of the potential at small distances may result in narrowing of the resonance, i. e. GITA<<GITA0, E approximately equal to E0 (here GITA0 and E0 are the initial resonance parameters and CITA and E the parameters resulting from a variation of the potential at small distances). In the case of a set of the resonance levels a rearrangement of the resonance spectrum is possible similar to the rearrangement of the discrete level spectrum. In this case no considerable change in the level width happens (GITA approximately GITA0). Analytical criteria are presented for realization of the first-type and second-type behaviours of the resonance widths and positions. A physical reason for such a behaviour of the resonance levels is elucidated