Nuclear charge radii of the tin isotopes from muonic atoms

Abstract

The muonic atom 2${\mathit{p}}_{1/2}$-1${\mathit{s}}_{1/2}$ and 2${\mathit{p}}_{3/2}$-1${\mathit{s}}_{1/2}$ transition energies were measured with an experimental accuracy of better than 20 ppm for the isotope chain $^{112,114,116,117,118,119,120,122,124}\mathrm{Sn}$. Precise values for the Barrett equivalent nuclear radii ${\mathit{R}}_{\mathit{k}\mathrm{\ensuremath{\alpha}}}$ and their differences as well as root-mean-square radii were deduced. The \ensuremath{\Delta}N=2 isotope shifts between the even Sn isotopes show a subshell effect at the neutron number N=64. Otherwise, there is a nearly linear decrease with increasing N, in accordance with the general systematics of nuclear charge radii. Our muonic atom results are in a good agreement with recent optical data, including odd-even staggering. Hartree-Fock calculations reproduce the general trend but not the subshell effect. Regarding the nuclear polarization corrections, the problem in the 2p splitting found earlier in ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$-Zr and ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$-Pb seems also to persist in ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$-Sn.