Microwave spectroscopy of heliumlike Rydberg states of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2:$ Determinations of the dipole polarizabilities of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ ground states

The fine-structure intervals separating the highest-L, $n=9\mathrm{}$ and 10 Rydberg states of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ bound to the $\nu =0,$ $R=0\mathrm{}$ ground states of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ have been measured precisely with microwave spectroscopy and used to deduce the isotropic dipole polarizabilities of the ground states of both these ions. The results, ${\alpha }_S{(\mathrm{H}}_2^{+})=3.167\mathrm{}{96\left(15\right)a}_0^3$ and ${\alpha }_S{(\mathrm{D}}_2^{+})=3.071\mathrm{}{87\left(54\right)a}_0^3,$ agree with a priori theory to within about 0.02%, but the ${\mathrm{H}}_2^{+}$ result indicates that the theory is incomplete at this level.