Precise $2p-1s$ muonic x-ray transition energies and energy shifts were measured for the $1f_{\frac{7}{2}}$-shell nuclei ${}_{}{}^{39,41}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{40,42,43,44,46,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{46,47,48,49,50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{50,52,53,54}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$. The data were analyzed in terms of the Barrett moments $〈r^k{e}^{-ar}〉$ of the nuclear charge distribution, from which equivalent nuclear radii $R_k$ and isotopic and isotonic differences $\Delta R_k$ were computed. For those nuclei for which electron-scattering data were available, model-independent rms radii and radius differences were deduced from a combined analysis of the present data and elastic electron-scattering data. The $\Delta N=2\mathrm{}$ isotope shifts between even-$A$ nuclei decrease nearly linearly with increasing $N$ and become negative in the second half $24\le N\le 28$ of the $1f_{\frac{7}{2}}$ shell; a strong shell-closure effect is evident at $N=28\mathrm{}$. The isotope shifts are independent of $Z$, suggesting that the added neutrons interact with the entire proton core rather than with the valence protons. The $\Delta Z=2\mathrm{}$ isotone shifts between even-$A$ nuclei decrease smoothly and uniformly with increasing $Z$ for $20\le Z\le 28$ and are essentially independent of $N$. Like the isotope shifts, the isotone shifts display a sudden increase at $Z=28\mathrm{}$. Both the $\Delta N=1\mathrm{}$ isotope shifts and the $\Delta Z=1\mathrm{}$ isotone shifts show pronounced odd-even staggering. A strong correlation is found between nuclear deformation, as revealed by experimental $B\left(E2\mathrm{}\right)\mathrm{}$ values, and the measured isotope and isotone shifts. The measured isotope and isotone shifts, including those for odd-$A$ nuclei, are satisfactorily described by a simple empirical formula. The experimental results were compared with Hartree-Fock calculations; some recent calculations that include ground-state correlations display improved agreement with experiment through the inclusion of these deformation-related effects.

NUCLEAR STRUCTURE ${}_{}{}^{39,41}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{40,42,43,44,46,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{46,47,48,49,50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{50,52,53,54}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$; measured muonic x-ray spectra; deduced nuclear charge radii, isotope and isotone shifts; performed model-independent combined analysis of muonic x-ray data and elastic electron scattering data; compared charge parameters with Hartree-Fock and other calculations.

• Received 14 July 1980

DOI:https://doi.org/10.1103/PhysRevC.23.533