Nuclear charge radii of the even sulphur isotopesS32,S34, andS36and ofP31using muonic atoms

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Abstract

Energies of muonic x rays of the Lyman series of the even sulphur isotopes $^{32}\mathrm{S}$, $^{34}\mathrm{S}$, and $^{36}\mathrm{S}$ and of natural phosphorus have been determined with absolute precisions up to 23 parts/${10}^{6}$. Equivalent Barrett charge radii ${R}_{k,\ensuremath{\alpha}}$ have been deduced. Their differences between the sulphur isotopes amount to $\ensuremath{\Delta}{R}_{k,\ensuremath{\alpha}}(^{34}\mathrm{S}\ensuremath{-}^{32}\mathrm{S})=29.7(1.4)$ am and $\ensuremath{\Delta}{R}_{k,\ensuremath{\alpha}}(^{36}\mathrm{S}\ensuremath{-}^{34}\mathrm{S})=18.7(1.5)$ am. Combining these results with recent elastic electron scattering data, we obtain in a model-independent way $\ensuremath{\Delta}{〈{r}^{2}〉}^{\frac{1}{2}}(^{34}\mathrm{S}\ensuremath{-}^{32}\mathrm{S})=23.1(1.2)$ am and $\ensuremath{\Delta}{〈{r}^{2}〉}^{\frac{1}{2}}(^{36}\mathrm{S}\ensuremath{-}^{34}\mathrm{S})=13.0(1.2)$ am.

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