Perturbative Casimir shifts of nondispersive spheres at finite temperature

The quantum-electrodynamic Helmholtz free energy of binding, at temperature T, is determined perturbatively to order (n alpha)(2) for atomic solid spheres 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 similar or equal to 1 - 4 pin alpha. Here n is the number density, and the atomic polarizabilty alpha is taken as independent of frequency. The perturbative shifts are regularized by disallowing atomic separations below some minimum 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 given T, quoted from the preceding paper. Such shifts are always dominated by (nominally) divergent components of order -(h) over barc/lambda, independent 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 -(kTa/(h) over barc)(3)((h) over barc/a) when mu = 1 and of order - (kTa/(h) over barc)(4)((h) over barc/a) when mu = 1/epsilon. There is no compelling reason why these convergent terms should be exactly the same as the shifts determined by recent normal-mode summations, nevertheless, agreement is complete for mu = 1/epsilon and almost complete for mu = 1.