Electric dipole polarizabilities of hydrogen and helium isotopes

The electric dipole polarizabilities of ${}^3\mathrm{H}$, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ are calculated directly using the Schrödinger equation with the latest generation of two- and three-nucleon interactions. These polarizabilities are necessary to obtain accurate nuclear-polarization corrections for transitions involving $S$ waves in one- and two-electron atoms. Our results are compared to previous results, and it is shown that direct calculations of the electric polarizability of ${}^4\mathrm{He}$ using modern nuclear potentials are smaller than published values calculated using experimental photoabsorption data. The status of this topic is assessed in the context of precise measurements of transitions in one- and two-electron atoms.

Figure 1

The dependence of (the electric polarizability) ${\alpha }_E$ of ${}^3\mathrm{H}$ (in units of ${\mathrm{fm}}^3$) on the model-space truncation parameter, $N_{\max }$. The results have been obtained using (a) $\mathit{NN}$ interactions only, and (b) $\mathit{NN}+\mathit{NNN}$ interactions. Each curve is obtained using a different frequency parameter for the basis states, shown in the legend in MeV. For sufficiently large $N_{\max }$ each result should be independent of that frequency.

Figure 2

Same as in Fig. 1, but for ${}^3\mathrm{He}$.

Figure 3

Same as in Fig. 1, but for ${}^4\mathrm{He}$.