High-energy asymptotics of resonances for three-dimensional Schrödinger operator with screened Coulomb potential.

Resonances for one-particle three-dimensional Schrödinger operators with Coulomb potential perturbed by a spherically symmetric compactly supported function q(r) are studied. The mth derivative of q(r) has a jump on the boundary of the support (m≥0). Resonances are defined as poles of an analytical continuation of the quadratic form of the resolvent to the second Riemann sheet through the branch cut along the continuous spectrum. It is shown that there exists an infinite set of resonance poles which splits into an infinite sequence of infinite series corresponding to different values of an angular momentum. Resonances in each series have the only point of accumulation at infinity. The main result of the work is an asymptotic formula for resonances in each series. It follows from this formula that high-energy resonances of the above operator are asymptotically close to those of the Schrödinger operator with the same potential q(r) but without Coulomb term. It was shown in one of the previous works of the author that, in contrast with the non-Coulomb case, some perturbations q(r) of the Coulomb potential can produce a sequence of resonances converging to zero. The result of this work together with the above result shows that the Coulomb part of the potential, while dramatically changing the geometry of resonances at low energies, does not destroy their asymptotic behavior at high energies. [ABSTRACT FROM AUTHOR]