Generalized levinson theorem: Applications to electron-atom scattering

A recent formulation provides an absolute definition of the zero-energy phase shift delta for multiparticle single-channel scattering of a particle by a neutral compound target in a given partial wave l. This formulation, along with the minimum principle for the scattering length, leads to a determination of delta that represents a generalization of 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 relates delta/pi for scattering in a state of given angular momentum to the number of composite bound states of that angular momentum plus a calculable number that, for a system described in the Hartree-Fock approximation, is the number of states of that angular momentum excluded by the Pauli principle. Thus, for example, for electron scattering by Na, with its (1s)(2)(2s)(2)(2p)(6)3s configuration and with one L=0 singlet 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 been listed first. The method is applicable to a number of e(+/-)-atom and nucleon-nucleus scattering processes, but only applications of the former type are described here. We obtain the absolute zero-energy phase shifts for e(-)-H and e(-)-He scattering and, in the Hartree-Fock approximation for the target, for atoms that include the noble gases, the 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 agreement with expectations.