Casimir force on a solid ball when
\epsilon(\omega) mu(\omega)=1
I. Brevik;,
Luftkrigsskolen, 7004 Trondheim, Norway
G. Einevoll;,
Institutt for Teoretisk Fysikk, NTH,
Universitetet i Trondheim, 7034 Trondheim, Norway
Physical Review D 37, 2977-2989 (1988)
Abstract
The Casimir surface force on a solid ball is calculated, assuming the
material to be dispersive and to be satisfying the condition
\epsilon(\omega)\mu(\omega)=1, \epsilon(\omega) being the spectral
permittivity and \mu(\omega) the spectral permeability. This particular
condition simplifies
the Casimir theory of dielectric media considerably. As a dispersion
relation the authors choose the analogue of Sellmeir's form (with one
absorption frequency), known from ordinary dispersion theory. They follow
a combined numerical and analytic approach: the low values of the angular
momentum variable are treated numerically, whereas the higher values are
treated analytically by means of the Debye expansion. The dispersive
effect is found to yield a strong, attractive contribution to the surface
force. If the cutoff frequency \omega_{0} is large, the
dispersion-induced surface force becomes proportional to \omega_{0}.