RESONANCE SELECTION PRINCIPLE AND LOW-ENERGY RESONANCES FOR A RADIAL SCHRODINGER OPERATOR WITH NEARLY COULOMB POTENTIAL

We study resonances for the radial Schrodinger operator with Coulomb p otential perturbed by a compactly supported function. Resonances are d efined as poles of an analytic continuation of the quadratic form of t he resolvent to the second Riemann sheet through the continuous spectr um. We show that, like in the non-Coulomb case, resonances can be desc ribed as roots of the Jost function. Using this result we prove that z ero cannot be a point of accumulation of resonances, i.e., for a given value of an angular momentum l there exists a disk on the second Riem ann sheet centered at the origin which is free of resonances. The radi i of these disks may tend to zero when l --> infinity. In our next pap er we show that these radii do tend to zero for a nonnegative perturba tion with finite positive first moment. This means that the three-dime nsional Schrodinger operator with Coulomb potential perturbed by a com plactly supported spherically symmetric function of the above type has a sequence of resonances accumulating to zero. (C) 1994 Academic Pres s, Inc.