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 $\delta R_k$ were computed. Particular attention was given to higher-order corrections of the energies of the muonic states. Appropriate quantum-electrodynamical corrections were calculated to all significant orders. Nuclear polarization corrections for multipole interactions up to and including $L=4\mathrm{}$ were computed for each isotope. The $\Delta A=2\mathrm{}$ isotone shifts $\delta R_k$ for even $A$ isotopes show a strong shell closure effect at $Z=28\mathrm{}$, which is quite independent of the neutron number. The $\Delta N=2\mathrm{}$ isotope shifts between even nuclei decrease smoothly and uniformly with increasing $N$ from $N=28\mathrm{}$ to $N=40\mathrm{}$ and are essentially independent of $Z$. This unexpected behavior suggests that the added neutrons interact with the entire proton core rather than with the valence protons. The $\Delta N=1\mathrm{}$ isotope shift results show a pronounced odd-even staggering effect, which, however, is somewhat smaller than theoretical predictions. The isotone series ${}_{}{}^{58}{}_{}{}^{}\mathrm{Fe}$-${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$- ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, which is just below the $Z=28\mathrm{}$ shell closure, shows strong odd-even staggering, whereas the series ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$- ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$-${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$-${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$- ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ just above $Z=28\mathrm{}$ exhibit only a very small staggering effect. A comparison of the experimental data of the rms radii ${〈r^2〉}^{\frac{1}{2}}$ with the results of spherically constrained Hartree-Fock calculations shows good agreement for all four Zn isotopes and the heavier Ni isotopes (${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$), but poor agreement for the Fe isotopes and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$.

NUCLEAR STRUCTURE, MOMENTS ${}_{}{}^{54,56,57,58}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{58,60,61,62,64}{}_{}{}^{}\mathrm{Ni}$ ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}$; measured muonic x-ray spectra; deduced nuclear charge parameters, isotope and isotone shifts. Calculated quantum-electrodynamic and nuclear-polarization corrections. Compared charge parameters with Hartree-Fock calculations.

• Received 12 April 1976

DOI:https://doi.org/10.1103/PhysRevC.14.731