Precision Measurement of X-Ray Fine Structure; Effects of Nuclear Size and Quantum Electrodynamics

Schawlow and Townes have made a theoretical calculation of the perturbing effect of the finite size of the nucleus on the $L_{\mathrm{II}}-L_{\mathrm{III}}$ x-ray doublet splitting in heavy elements. Combined with approximate calculations by Christy and Keller of the unperturbed splitting for the case of a point nucleus, comparison of this theory with such experimental values of the splitting as were then available led to an anomalously large value of nuclear radius, $R=r_0{A}^{\frac{1}{3}}$ with $r_0=2.1\mathrm{}\times {10}^{-13\mathrm{}}$ cm. Schawlow and Townes offered the suggestion to account for this that quantum electrodynamic effects probably modify the fine structure in much the same way as an oversize nucleus. The present investigation was undertaken to improve on the precision of the x-ray measurements yielding the $L_{\mathrm{II}}-L_{\mathrm{III}}$ fine structure splitting and to incorporate into a new comparison between theory and experiment the recent vacuum polarization correction of Wichmann and Kroll. The measurements of the $L_{\mathrm{II}}-L_{\mathrm{III}}$ splitting for W, Pt, Bi, Th, U, and Pu are based on two-crystal spectrometer determinations of the Bragg angles of the $L{\alpha }_2$ and $L{\beta }_1$ x-ray lines of these elements. Techniques of measurement and corrections for vertical divergence and crystal diffraction pattern asymmetry leading to a relative precision (relative standard deviation) in the splitting of about 50 parts per million are described. A comparison is made with the data used by Schawlow and Townes, and a discrepancy is found in several earlier wavelength values which may account partly for the large value of $r_0$ obtained by them. A comparison of the theoretical to the present experimental values of the splitting, assuming no quantum electrodynamic effects, yields a value of $r_0=1.08\mathrm{}\times {10}^{-13\mathrm{}}$ cm. When corrections are made for vacuum polarization and a nuclear radius of $r_0=1.2\mathrm{}\times {10}^{-13\mathrm{}}$ cm, a comparison with experiment shows that a discrepancy remains which is then used to evaluate an empirical correction term. The sign, magnitude, and $Z$ dependence of this term suggest that the remaining discrepancy might arise principally from the Lamb shift effect.