Generalized Levinson theorem: Applications to electron-atom scattering
- Department of Physics, New York University, New York, New York 10003 (United States)
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 {ital 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 {ital 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 {ital +} 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 (1{ital s}){sup 2}(2{ital s}){sup 2}(2{ital p}){sup 6}3{ital s} configuration and with one {ital L}=0 singlet composite bound state, {delta} would be {pi}+2{pi} for {ital s}-wave singlet scattering, 0+3{pi} for {ital s}-wave triplet scattering, and 0+{pi} for both triplet and singlet {ital p}-wave scattering; the Pauli contribution has been listed first. The method is applicable to a number of {ital e}{sup {+-}}-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 {ital e}{sup {minus}}-H and {ital e}{sup {minus}}-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 {ital p} electrons, respectively, outside of closed shells. In all cases, the applications provide results in agreement with expectations. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 401700
- Journal Information:
- Physical Review A, Vol. 54, Issue 6; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
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