Casimir Effects for a Conducting Spherical Shell:

Between C60 and the Lamb Shift

G. Barton

Centre for Theoretical Physics
University of Sussex,
Brighton BN1 9QH, UK

To calculate the total Casimir binding-energy B of a single body (as opposed to couplings between disjoint bodies), one must model at least semi-realistically not just the macroscopic electromagnetic response function of the material, but also certain microscopic correlations inside it. I extend the theory from insulators to conductors in its simplest possible form, using the archetypal example of a very thin spherical shell. For insulators, negative B is now known to follow from reasonable models allowing for the hard cores of interatomic potentials, and entails a negative (inward) pressure  P on the shell. For conducting shells, positive B follows from the standard non-retarded hydrodynamic plasma model, if B is taken to denote the total zero-point energy of the plasmons. The corresponding (positive)  P requires, in addition to Coulomb forces, also purely mechanical stresses due to the kinetic energy of the fluid. (The correction for the quantized nature of the Maxwell field, namely the Lamb shift, is also positive, but smaller than the leading terms of B by many orders of magnitude.) The physically expected negative B and  P must stem from other effects, like the attraction between the ion cores responsible for the cohesion of metals, or the covalent bonds between the carbon atoms of C60.