3) the corrected values for the transition energies in keV. The uncertainties in the values of E th in Table II range from 5 to 10 eV, and are the same as in Dixit et al. We see now by a comparison of the theoretical and experimental values that the discrepancy is reduced considerably, the only transitions having any significant discrepancy being the 4f-3d transition in Ba and the 5^-4/transition in Pb.We have also considered the effect of the finite size of the nucleus on the vacuum-polarization corrections: The rather complicated convolution integral required to do this in configuration space becomes a trivial multiplicative factor in the momentum-space integral. Taking the uniform model for the nuclear shape, we find that the individual shifts are increased by rather less than 1%, giving less than 10 eV from the Uehling term itself, and correspondingly smaller corrections from the higher-order terms. A more realistic model for the nuclear shape can hardly be expected to give rise to any significant difference.An effect of the same magnitude arises if the vacuum-polarization potential is included in the Dirac equation itself, rather than treating it perturbatively as we have done. The E th in Table II is, in fact, calculated by the former method; the difference between this value and the perturbative value is of the order of 10 eV.A number of authors 5 * 6 have suggested a possible anamolous interaction of the muon via a scalar field. The model suggested by Bar shay, 5 with a scalar meson of mass around 750 MeV, turns out to give shifts of less than 1 eV for the states in which our interest lies; this is because the large mass implies a very short-range forceThe electron paramagnetic resonance (EPR) spectrum of Ce 3+ (4/ 1 configuration) in cubic single crystals has previously been the subject of numerous investigations. 1 " 6 Until the present which dominantly affects only the 5-wave states. We note that the 4/-3d transition in Ba and the 5^-4/transition in Pb have almost equal discrepancies of about 70 eV. This enables us to put a rather good upper limit on the mass m s of the scalar meson of about 8 MeV. Assuming this mass, the required coupling constant is G s = g silll X £SNN = 6 x 10 " 7 . The final column in Table II shows the theoretical value, including the effects of this particle, once again incorporating the effects of the finite nuclear size. It is remarkable that the remaining discrepancy is eliminated:The reader is at liberty to regard this as evidence for a physical particle of mass 8 MeV, coupling mainly to M"V". It is amusing to speculate that if this particle is very weakly coupled to e *e", it would escape experimentally detection, as well as provide a mechanism for the breaking of \ie universality. . work, however, no EPR spectra have been reported which could be attributed unequivocally to Ce 3+ in a cubic symmetry site. 7 The observation of the EPR spectrum of Ce 3+ in a site of local cu-The EPR of Ce 3+ has been observed in sites of cubic symmetry for the first time. The unusually large...