Abstract
We derive the Casimir-Polder interaction between two polarizable atoms with a method based on electromagnetic normal modes found by generating self-sustained fields. Numerical results are given for the alkali-metal atoms. We give results for both zero temperature and finite temperature. In connection with the finite temperature derivations we discuss classical and quantum contributions. We furthermore derive the equation of state for a Casimir-Polder gas and show that the corrections from going beyond van der Waals interactions are small.
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Notes
- 1.
Also a magnetic field is produced but we neglect magnetic effects here.
- 2.
Here we should point out that we have not been strictly stringent. We have neglected the temperature dependence of the polarizabilities. For the very highest temperatures we have included, these are bound to be important. The atoms might even be ionized at these temperatures.
- 3.
We have here assumed that the gas consists of separate atoms. The treatment is still valid for molecular gases. In that case read molecule instead of atom.
- 4.
Note that an atom can not come closer to another than the atom diameter. This means that a spherical volume of radius \(d_0\) centered around each atom is excluded from the free volume in which other atoms can move.
References
M. Marinescu, L. You, Phys. Rev. A 59, 1936 (1999)
S.S. Batsanov, Van der Waals Radii of Elements. Inorg. Mater. 37(9), 871 (2001)
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Sernelius, B.E. (2018). Casimir Interaction. In: Fundamentals of van der Waals and Casimir Interactions. Springer Series on Atomic, Optical, and Plasma Physics, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-319-99831-2_12
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DOI: https://doi.org/10.1007/978-3-319-99831-2_12
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