Perturbative Casimir shifts of nondispersive spheres at finite temperature- art. no. 032103

The quantum-electrodynamic Helmholtz free energy of binding, at temperature T, is determined perturbatively to order (n alpha)(2) for atomic solid sph eres of radius a, having dielectric constant epsilon similar or equal to 1 + 4 pin alpha and magnetic susceptibility either mu = 1 or mu = 1/epsilon s imilar or equal to 1 - 4 pin alpha. Here n is the number density, and the a tomic polarizabilty alpha is taken as independent of frequency. The perturb ative shifts are regularized by disallowing atomic separations below some m inimum lambda; they are renormalized by dropping components proportional to the volume and surface area, and the renormalized shifts DeltaB/(n alpha)( 2) are expressed in terms of moments of the interatomic potential IV at giv en T, quoted from the preceding paper. Such shifts are always dominated by (nominally) divergent components of order -(h) over barc/lambda, independen t of T and a. For kTa/(h) over barc>> 1, the convergent terms are of order -kT ln(kTa/(h) over barc); for kTa/(h) over barc<<1, they are of order -(kT a/(h) over barc)(3)((h) over barc/a) when mu = 1 and of order - (kTa/(h) ov er barc)(4)((h) over barc/a) when mu = 1/epsilon. There is no compelling re ason why these convergent terms should be exactly the same as the shifts de termined by recent normal-mode summations, nevertheless, agreement is compl ete for mu = 1/epsilon and almost complete for mu = 1.