### Deuteron D-state probability from finite size effects in muonic deuterium *[Cross-Listing]*

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Recent analyses of the Lamb shift data in muonic deuterium ($\mu^- d$) have shown that precision atomic spectroscopy determines a more accurate radius of the deuteron than scattering experiments do. This precision can be used to determine the D-state probability, $P_D$, in deuteron accurately. To demonstrate the method, we evaluate the nuclear structure corrections of order $\alpha^4$ within a few body formalism for the $\mu^- p n$ system in muonic deuterium using different values of $P_D$ and find $P_D$ close to 2\% to be most favoured by the $\mu^-d$ data.