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Physica A Statistical Mechanics and its Applications

A generalized Fock-Tani representation of non-relativistic systems containing composite particles

J. Gilbert

Published Mar 1, 1988• 1 citation
Publisher
DOI
10.1016/0378-4371(88)90223-3

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The transformation from the usual Fock representation to the Fock–Tani representation for composite particles is carried out for a simplified model of the composite which allows closed-form expressions for the transformed quantities. A ’’statistical renormalization’’, in which single particle energies and interactions become dependent on the composite particle occupation number, plays an essential rôle in the solution, allowing absorption of unlinked terms into the definition of the renormalized energies.
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.