GENERALIZED LEVINSON THEOREM - APPLICATIONS TO ELECTRON-ATOM SCATTERING

A recent formulation provides an absolute definition of the zero-energ y phase shift delta for multiparticle single-channel scattering of a p article by a neutral compound target in a given partial wave l. This f ormulation, along with the minimum principle for the scattering length , leads to a determination of delta that represents a generalization o f Levinson's theorem. In its original form that theorem is applicable only to potential scattering of a particle and relates delta/pi to the number of bound states of that l. The generalized Levinson theorem re lates delta/pi for scattering in a state of given angular momentum to the number of composite bound states of that angular momentum plus a c alculable number that, for a system described in the Hartree-Fock appr oximation, is the number of states of that angular momentum excluded b y the Pauli principle. Thus, for example, for electron scattering by N a, with its (1s)(2)(2s)(2)(2p)(6)3s configuration and with one L=0 sin glet composite bound state, delta would be pi+2 pi for s-wave singlet scattering, Of 0+3 pi for s-wave triplet scattering, and 0+pi for both triplet and singlet p-wave scattering; the Pauli contribution has bee n listed first. The method is applicable to a number of e(+/-)-atom an d nucleon-nucleus scattering processes, but only applications of the f ormer type are described here. We obtain the absolute zero-energy phas e shifts for e(-)-H and e(-)-He scattering and, in the Hartree-Fock ap proximation for the target, for atoms that include the noble gases, th e alkali-metal atoms, and, as examples, B, C, N, O, and F, which have one, two, three, four, and five p electrons, respectively, outside of closed shells. In all cases, the applications provide results in agree ment with expectations.