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Physical Review Letters

New Method for Treating Systems Containing Elementary Composite Particles (Nonrelativistic Theory)

Robert H. Stolt, Wesley E. Brittin

Published Aug 30, 1971• 20 citations
Publisher

Abstract

Systems containing bound and free particles are described by simple Bose or Fermi fields, one representing bound particles and others representing free particles. The lack of proper symmetry for states corresponding to given numbers of bound and free particles is corrected by drawing a correspondence (partial isometry) between proper physical states and these. When transformed to the new basis, the Hamiltonian is found to contain non-particle-conserving terms and exchange terms.

DOI
10.1103/physrevlett.27.616

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Systems containing bound and free particles are described by simple Bose or Fermi fields, one representing bound particles and others representing free particles. The lack of proper symmetry for states corresponding to given numbers of bound and free particles is corrected by drawing a correspondence (partial isometry) between proper physical states and these. When transformed to the new basis, the Hamiltonian is found to contain non-particle-conserving terms and exchange terms.
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A method of constructing ’’atomic second quantization’’ representations is described, based on the introduction of redundant modes (’’ideal atom variables’’) which are then given physical content by carrying out a suitable unitary transformation, the ’’generalized Tani transformation.’’ In such a representation bound atoms or molecules are described by elementary Bose or Fermi operators, the field operators for nuclei and electrons referring only to unbound particles. The Hamiltonian thus obtained contains not only nucleus–nucleus, electron–electron, and nucleus–electron Coulomb interactions, but also atom–atom, atom–nucleus, and atom–electron Coulomb and exchange interactions, including breakup and recombination terms. All possible scattering and reaction channels are exhibited simultaneously in this transformed Hamiltonian. The method is applicable to any species or mixture of species of composite particles, but for simplicity the derivation is restricted here to the case of atomic hydrogen.