Behavior of the Elastic-Scattering Cross Section σ(E) in the Vicinity of Two Overlapping Levels with Equal Resonance Energies

The elastic-scattering process proceeding through two resonance levels that have the same spin j and equal resonance energies, (E (1) = E (2)), but different widths (I"(1) not equal I"(2)) is considered. It is shown that the energy dependence of the total scattering cross section has two equal maxima at the points E (1) +/- (1/2) , the cross-section value at the maxima being 4 pi (2j + 1)AE >(2), where AE > is the wavelength of the incident particle in the c.m. frame, and that, at the energy E (1), the cross section vanishes, sigma (E (1)) = 0. The cross section is symmetric with respect to the point E (1).