photon point) leads to C\_=1.28(1).

Adopting these ingredients, the QE contribution of the two-photon exchange (TPE) to Lamb shift in deuterium can be calculated. We evaluated this contribution with the nucleon form factors in Kelly’s parametrization [@kelly] and using $S(\nu,Q^2),\,S_\perp(\nu,Q^2)$ from Paris WF [@lacomb], and list the result with the uncertainty in Table \[tab2\].\

Subtraction term
----------------

Following Ref. [@Birse:2012eb], we identify |T\_1(0,Q\^2)&=&T\_1\^B(0,Q\^2)-T\_1\^[pole]{}(0,Q\^2)\
&+&\_M\^d(0)F\_(Q\^2), where $T^B$ represents the Born contribution, and where in the polarizability term we explicitly factored out the $Q^2$-dependence. The polarizability contribution to the $nS$-level is given by E\^\_[n0]{}=2\^2\_[n0]{}(0)\_M\^d(0)\_0\^dQ\^2F\_(Q\^2), with $\beta_M^d(0)=0.072(5)$ fm$^3$. The $Q^2$-dependent form factor $F_\beta(Q^2)$ is generally not known. We estimate it by setting $F_\beta(Q^2)=G_C^d(Q^2)/G_C^d(0)$, and to estimate the uncertainty we also try $F_\beta(Q^2)=G_M^d(Q^2)/G_M^d(0)$. The average result and uncertainty is quoted in Tab. 2.

Finally, the subtraction function Eq.30 contains the difference between the Born and pole contributions, which results from the contact two-photon deuteron interaction (Thomson term). The pointlike part of it, $-1/4\pi M_d$ was already taken into account in atomic calculations, thus we need to account for &&\[T\_1\^B-T\_1\^[pole]{}\](0,Q\^2)-\[T\_1\^[B,point]{}-T\_1\^[pole,point]{}\](0,Q\^2)\
&&=, thus leading to the shift of an $S$-level E\_[n0]{}\^[Th]{}&=&\^2\_[n0]{}(0)\_0\^dQ\^2 \[thomson\] The result of the numerical evaluation is listed in Table \[tab2\].

   $\Delta \bar E^{el}$    