Nuclear charge radii of the Te isotopes from muonic atoms

The muonic atom energies of the 2p-1s and the 3d-2p transitions were measured with a statistical accuracy of better than ±70 and ±40 eV, respectively, for ${}_{}{}^{123,124,125,126,128,130}{}_{}{}^{}\mathrm{Te}$. The values for the Barrett equivalent nuclear radii $R_k$,α and for the root-mean-square radii and their differences were calculated first from muonic data alone and second with the addition of published optical data. The latter data provided the radii of ${}_{}{}^{120}{}_{}{}^{}\mathrm{Te}$ and ${}_{}{}^{122}{}_{}{}^{}\mathrm{Te}$ isotopes, which were not measured by muonic x rays. A combined analysis of the muonic atom and optical isotope shift data yielded high-precision values of the differences in radii Δ$R_k$,α (error <±0.5 am) and Δ〈$r^2$ ${〉}^{1/2}$ (error <±0.9 am) between the neighboring isotopes. The optical constants for the Te line λ=4049 Å were determined (including contributions of higher radial moments) to be F=(509±120) mK/${\mathrm{fm}}^2$ and M=-(104±63)×${10}^3$ mK. Systematic behavior of the radius differences in neighboring isotopes and isotones of Ba, Xe, Te, and Sn, together with odd-even staggering of the Te isotopes, are discussed in this paper. The ΔN=2 Te isotope shifts between even-A nuclei decrease nearly linearly with increasing N, which can be explained by a successive decreasing deformation in accordance with the observed systematics. The experimental data for the Te isotopes proved to be in good agreement with even-A Hartree-Fock calculations and with recent Hartree-Fock calculations for odd-A nuclei in which three-body forces are considered. A linear decrease of the nuclear skin thickness with decreasing deformation was observed and is explained by a simple model.