# The Casimir effect - Interplays between theory and experiment

The Casimir effect was predicted in 1948 from quantum electrodynamical calculations by the theoretical physicists HBG Casimir and D. Polder[1]. The particular cases studied were the long-range interactions between two walls, between an atom and a perfectly conducting wall, and between two atoms. Their work indicated the interaction forces are weaker than the corresponding results from Coulomb interaction-based theory at ultra-large separations of the constituents of the atom-atom and the atom-wall systems. For example, according to Casimir and Polder the van der Waals ${R}^{-6}$ potential between two atoms goes over to a ${R}^{-7}$ interaction as $R$ goes towards infinity. Indeed, their work was inspired by a suggestion from Verwey and Overbeek that studies of the stability of lyophobic colloids indicated that the interaction at very long range between two atoms must be weaker than the van der Waals result[2].

Since 1948 some notable interplays between experiment and theory related to the Casimir-Polder paper are the detection of the helium dimer[3], measurement of the atom-wall Casimir force[4], and the measurements of the Casimir force between two surfaces[5].

The Casimir effect in Rydberg states of atoms is an example where a theoretical prediction stimulated experiment. Spruch and Kelsey in 1978 predicted[6] for the case of an electron and an ion an interaction analogous to that given by Casimir and Polder for two atoms. In the 1978 paper they suggested that the effect might be detectable in the Rydberg states of the helium atom. Shortly thereafter S.R. Lundeen and collaborators [7] began an experimental program to test this suggestion. The interplay between these two groups had some influence on later theoretical studies of long-range ion-electron interactions[8], relativistic phenomena[8,9], Lamb shifts[10], and high accuracy variational calculations[11]. The experimental and theoretical studies continue with, notably, additional experiments[12] carried out by E.A. Hessels, a former student of Lundeen, and collaborators.

Some of these topics were covered at the ITAMP Topical Group meeting on Casimir Phenomena during the period March 16-27, 1998.

J.F. Babb 2.25.99
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More extensive bibliography
References:
[1] H. B. G. Casimir and D. Polder, Phys. Rev. 73 (1948), 360 (atom-atom and atom-wall); H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 60, (1948) 793 (two walls).
[2] D. H. Napper and R. J. Hunter in Surface Chemistry and Colloids, M. Kerker ed., (University Park, Baltimore, 1972), vol. 7, ch. 8. See also, for example, P. W. Milonni, The quantum vacuum: An introduction to quantum electrodynamics, (Academic Press, Boston, 1994) for more bibliographic info.
[3] Fei Luo, Clayton F. Giese, and W. Ronald Gentry, J. Chem. Phys. 104 (1996) 1151; W. Schoellkopf and J. P. Toennies, J. Chem. Phys. 104, (1996) 1155; W. Schoellkopf and J. P. Toennies, Science 266, Nov. 25, 1994, 1345; T. Korona et al. J. Chem. Phys. 106 (1997) 5109.
[4] C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, (1993) 560.
[5] S. K. Lamoreaux, Phys. Rev. Lett., 78, 5 (1997); Erratum, ibid., 81, 5475 (1998); M. Bordag, B. Geyer, G. L. Klimchitskaya and V. M. Mostepanenko, Phys. Rev. D, 58, in press (1998).
[6] E. J. Kelsey and L. Spruch, Phys. Rev. A 18, 15 (1978); ibid. 18, 1055; see also C. K. Au, G. Feinberg, and J. Sucher, Phys. Rev. Lett. v.53 (1984) 1145.
[7] D. R. Cok and S. R. Lundeen, Phys. Rev. A 23 (1981) 2488; S. L. Palfrey and S. R. Lundeen, Phys. Rev. Lett. 53 (1984) 1141; E. A. Hessels, F. J. Deck, P. W. Arcuni, and S. R. Lundeen, Phys. Rev. A 41 (1990) 3663.
[8] R. J. Drachman, Phys. Rev. A 26 (1982) 1228; R. J. Drachman, ibid. 31 (1985) 1253.
[9] E. A. Hessels, Phys. Rev. A 46 (1992) 5389.
[10] S. P. Goldman and G. W. F. Drake, Phys. Rev. Lett. 68 (1992) 1683.
[11] G. W. F. Drake , Phys. Rev. Lett. 59 (1987) 1549; G. W. F. Drake, in Atomic, molecular, & optical physics handbook, G. W.F. Drake ed., (American Institute of Physics, Woodbury, NY 1996)
[12] C.H. Storry, N. E. Rothery, E. A. Hessels, Phys. Rev. A 55 (1995) 967; G. D. Stevens, C. S. Birdsell, and S. R. Lundeen BAPS 43 (1998) 1262.