### Casimir Effects for a Conducting Spherical Shell:

### Between C_{60}
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 C_{60}.