HIGH-ENERGY ASYMPTOTICS OF RESONANCES FOR 3-DIMENSIONAL SCHRODINGER OPERATOR WITH SCREENED COULOMB POTENTIAL

Resonances for one-particle three-dimensional Schrodinger operators wi th Coulomb potential perturbed by a spherically symmetric compactly su pported function q(r) are studied. The mth derivative of q(r) has a ju mp on the boundary of the support (m greater-than-or-equal-to 0). Reso nances are defined as poles of an analytical continuation of the quadr atic form of the resolvent to the second Riemann sheet through the bra nch cut along the continuous spectrum. It is shown that there exists a n infinite set of resonance poles which splits into an infinite sequen ce of infinite series corresponding to different values of an angular momentum. Resonances in each series have the only point of accumulatio n at infinity. The main result of the work is an asymptotic formula fo r resonances in each series. It follows from this formula that high-en ergy resonances of the above operator are asymptotically close to thos e of the Schrodinger 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 convergi ng to zero. The result of this work together with the above result sho ws that the Coulomb part of the potential, while dramatically changing the geometry of resonances at low energies, does not destroy their as ymptotic behavior at high energies.