We have used two-photon absorption from counterpropagating laser beams of different frequencies to measure Stark shifts and splittings of the
62S,
72S,
82S,
52D, and
62D states in sodium. Beams from a fixed-frequency, single-mode
Ar+ laser and a tunable, single-frequency cw dye laser were focussed into a coarse sodium atomic beam and the fluorescence was monitored. The collimation of the atomic beam reduced the residual Doppler width inherent in using two different frequencies. Using the two lasers allowed two-photon transitions to be observed at frequencies unattainable with the dye laser alone, and enhanced the transition rates due to the near resonance of the dye laser with the strong Na $3^{2}S\ensuremath{\rightarrow}3^{2}P$ transition. Our experimental results for the scalar and tensor polarizabilities, ${\ensuremath{\alpha}}_{0}$ and ${\ensuremath{\alpha}}_{2}$, agree with calculations in the Bates and Damgaard Coulomb approximation within 2% for ${\ensuremath{\alpha}}_{0}$ and 9% for ${\ensuremath{\alpha}}_{2}$. As a by-product the hyperfine-interaction constants
a for the
S states and the fine-structure intervals $\ensuremath{\delta}\ensuremath{\nu}=\frac{({E}_{\frac{3}{2}}\ensuremath{-}{E}_{\frac{5}{2}})}{h}$ for the
D states were obtained.
We have measured the fine-structure splitting of the
4d2D state of neutral sodium using high-resolution, cw, simultaneous two-photon excitation from the
3s2S ground state. Sodium atoms in an atomic beam were excited by a single-mode, cw, tunable dye laser, and the resonance was detected by monitoring the decay fluorescence from the excited state. The fine structure of the
4d2D state was well resolved and measured to be ${\ensuremath{\Delta}}_{\mathrm{fs}}=1025\ifmmode\pm\else\textpm\fi{}6$ MHz.