Quantum electrodynamics between conducting plates II. Spin-dependent effects in neutral atoms

Abstract

We consider the spin-dependent changes in the electromagnetic energy of a system when the system is inserted between infinite perfectly conducting parallel plates, separated by a distance L . For practicable values of the magnetic field and of L , the change δμ in the magnetic moment μ of an electron bound in a neutral atom is of the order δμ/μ ~ (μ/ L ) 2 , where h = 1 = c . The change A v in the hyperfine splitting v is of the order A v/v ≈ ( a/L ) 3 , with a the Bohr radius; this falls many orders of magnitude short of the experimental upper limit of Guttrich & Billman. We show that, surprisingly, a non-relativistic calculation yields correct results for a bound electron, though for a free electron one needs a fully relativistic calculation, to be reported separately.