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March 18, 2005
Note from Shizhong on the Casimir and Casimir-Polder effects
I checked the Casimir Effect. I should apologize for one misleading statement made in class. The first theoretical justification of the van der Waals force is made by F. London in 1930 using QM, who showed that there is a R^{-6} behaviour. In 1940, Overbeek did the experiment and he found that when distance between two particles is small, then we have R^{-6} dependence. However, if distance is large, then one has R^{-7} dependence. The R^{-7} dependence comes actually from the retarded potential. Casimir and Polder did the calculation taking into account the retarded potential and did find the R^{-7} potential.
The Casimir physics in this problem is that the R-dependence of the potential is _INDEPENDENT_ of the atom shell structure. Since it is tempting to argue that the van der Waals force comes from the fluctuation of electric dipoles in each of the atom, it is hard to understand why the shell structure of atom does not matter so much. It is at this time, when Casimir met Bohr(1947), Bohr suggested that this kind of universal R-dependence may have something to do with vacuum energy. Casimir did the calculation and did find the result R^{-7}. The more elabrate calculation can be found in the following paper Spruch L et al PRA _18_ 845(1978).
With best wishes,
Shizhong
Posted by Brian at March 18, 2005 09:35 AM
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