Effect of an Inelastic Channel on the Position and Width of a Resonance

Abstract

The effect of an inelastic channel on the position and width of a resonance is investigated for the case of a two-channel problem using effective-range theory and the uncoupled-phase method. Some estimates are obtained for the shift in the position and reduction in the width of the resonance due to the introduction of the inelastic channel. It is shown that an inelastic channel has, in general, the effect of shifting the resonance maxima towards the first threshold and reducing the asymmetry in width on the high-energy side and the low-energy side of the single-channel resonance. An estimate for the reduction in the asymmetry is also obtained. A two-channel computer experiment is performed to test the quantitative validity of the estimates. Good quantitative agreement of the estimates is obtained with the exact two-channel results.