μ-Mesonic X-Ray Energies and Nuclear Radii for Fourteen Elements fromZ=12 to 50

Abstract

Precise measurements of $\mu$-mesonic x rays have been made using a NaI scintillation crystal spectrometer. The $2p-1s$ transition energies were determined for fourteen elements ranging from $Z=12\mathrm{}$ (Mg) to $Z=50\mathrm{}$ (Sn). The $3d-2p$ transition energies were also measured for seven of these elements. The results have been interpreted to give a measure of the radial extent of the nuclear charge based on a Dirac theory of the $\mu$-mesonic atom, correcting for the vacuum polarization but taking other possible perturbing effects (e.g., nuclear polarization) to be small. The $2p-1s$ transition energy depends essentially on the second moment of the charge distribution, somewhat independently of the detail of the shape. It is convenient, therefore, to use the equivalent radius $R_{\mathrm{eq}}={\left(\frac{5〈r^2〉}{3}\right)}^{\frac{1}{2}}$ which refers to a sphere of uniform charge distribution having a mean square radius $〈r^2〉$. Our values of $r_0=\frac{R_{\mathrm{eq}}}{A^{\frac{1}{3}}}$ are within (1.23±0.02)×${10}^{-13\mathrm{}}$ cm for all nine of our elements between $A=35\mathrm{}$ (Cl) and $A=119\mathrm{}$ (Sn). There is general, but not detailed agreement with the radii that have been deduced from the Stanford electron scattering experiments.