General Theory of the van der Waals Interaction: A Model-Independent Approach

Gerald Feinberg and Joseph Sucher
Phys. Rev. A 2, 2395 – Published 1 December 1970
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Abstract

We study the van der Waals interaction V2γAB(R) arising from two-photon exchange between neutral spinless systems A and B. By using the analytic properties of the two-photon contribution to the scattering amplitude for A+BA+B and of the full amplitudes for γ+Aγ+A and γ+Bγ+B, we show that it is possible to express V2γAB(R) entirely in terms of measurable quantities, the elastic scattering amplitudes for photons of various frequencies ω. This approach includes relativistic corrections, higher multipoles, and retardation effects from the outset and thus avoids any vc expansion or any direct reference to the detailed structure of the systems involved. We obtain a generalized form of the Casimir-Polder potential, which includes both electric and magnetic effects, and, correspondingly, a generalized asympotic form V2γAB(r)DR7, where D=[23(αEAαEB+αMAαMB)7(αEAαMB+αMAαEB)]4π and the α's denote static polarizabilities. In addition, we show that the potential may be written as a single integral over ω, involving products of the dynamical polarizabilities αX(ω) evaluated at real frequencies, in contrast to the familiar integral over imaginary frequencies; for the case of interacting atoms, the domain of applicability of the various formulas is clarified, and the problem of evaluating V2γAB(R) from present experimental information is discussed. Some simple interpolation formulas are presented, which may accurately describe V2γAB(R) in terms of a few constants.

  • Received 8 June 1970

DOI:https://doi.org/10.1103/PhysRevA.2.2395

©1970 American Physical Society

Authors & Affiliations

Gerald Feinberg

  • Department of Physics, Columbia University, New York, New York 10027

Joseph Sucher

  • Center for Theoretical Physics, Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742

See Also

Addendum to a Formula of Feinberg and Sucher

Elihu Lubkin
Phys. Rev. A 4, 416 (1971)

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Vol. 2, Iss. 6 — December 1970

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