Muonic Atoms. II. Isotope Shifts

Abstract

Isotope shifts in the muonic spectra of ${}_{20}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$; ${}_{24}{}^{50}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}$; ${}_{29}{}^{63}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$; ${}_{42}{}^{92}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}$; ${}_{50}{}^{116}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{117}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$; ${}_{60}{}^{142}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{143}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{145}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{146}{}_{}{}^{}\mathrm{Nd}$, ${}_{}{}^{148}{}_{}{}^{}\mathrm{Nd}$, and ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}$ have been measured using a stable high-resolution Ge(Li) spectrometer system. The results are compared with values calculated for assumed nuclear charge distributions. In the case of the Nd isotopes, the half-density radius and the skin thickness have been determined from the measured $K$ and $L$ x-ray energies. An interesting shell-closing effect has been observed among the Cr isotopes. The muonic isotope shifts have been used to extract specific-mass shifts from optical measurements. We find that, even in Nd, these specific-mass shifts are very large, and not at all negligible in the analysis of optical results. The isotope shifts in Sn follow favorably the theoretically predicted general trend. The great reduction of the isotope shift between ${}_{}{}^{122-124}{}_{}{}^{}\mathrm{Sn}$ as reported in an optical investigation was not found in the muonic case. Lastly, a comparison has been made between the muonic results and recent electronic x-ray measurements. These were found to be in reasonable agreement.