Systematics of nuclear charge distributions in Fe, Co, Ni, Cu, and Zn deduced from muonic x-ray measurements

The results of precise measurements of the energies of the $2p_{\frac{3}{2}}\to 1s_{\frac{1}{2}}$ and $2p_{\frac{1}{2}}\to 1s_{\frac{1}{2}}$ muonic x-ray transitions of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}$, are reported. Using a highly linear digitally stabilized Ge(Li) spectrometer system, the absolute energies and energy shifts between nuclei were measured with total errors of approximately 40-60 eV (110 eV for ${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}$). The data were analyzed in terms of the Barrett moments $〈r^k{e}^{-ar}〉$ of the nuclear charge distributions from which the equivalent nuclear radii $R_k$ and the isotopic and isotonic differences