Resonance scattering on a negative potential

Abstract

One considers the dependence of the complete quantum scattering cross section β′(g) of a finite potential gv(x). on the coupling constant g>0. It is shown that for a spherical symmetric potential with a nontrivial negative part, the quantity β′(g) increases unboundedly relative to some sequence gt∞ and one has the lower estimate 6(ge≧cg e 1/2 , c>0. For a positive repelling potential (without the condition of spherical symmetry) one establishes the boundedness of the complete scattering cross section, uniform with respect to g.