Cesium $7d \, ^2 \! D_{3/2}$ hyperfine coupling constants measured using two-photon fluorescence spectroscopy of a thermal beam

The hyperfine intervals of the $^{133}$Cs $7d \, ^2 \! D_{3/2}$ manifold are determined through resonant two-photon, laser-induced-fluorescence spectroscopy. These intervals are used to calculated the magnetic dipole coupling constant, $A$, and the electric quadrupole coupling constant, $B$. Two single-mode, external-cavity diode lasers counter-propagate through a thermal beam of cesium. A servo-feedback circuit locks one laser to the $6s \, ^2 \! S_{1/2} (F) \rightarrow 6p \, ^2 \! P_{1/2} (F')$ transition. The second laser is scanned over the $6p \, ^2 \! P_{1/2} (F') \rightarrow 7d \, ^2 \! D_{3/2} (F'')$ transitions. Its relative frequency is calibrated through a phase modulation technique, and high accuracy is achieved by referencing the modulation frequency in real time to the $^{87}$Rb $5s \, ^2 \! S_{1/2} (F=1) \leftrightarrow 5s \, ^2 \! S_{1/2} (F=2)$ ground state hyperfine transition using an atomic frequency standard. The $7d \, ^2 \! D_{3/2}$ hyperfine intervals are found through non-linear fitting of Voigt profiles to the fluorescence spectra, and give the hyperfine coupling constants $A = 7.38 \pm 0.04 \,$MHz and $B = -0.06 \pm 0.26 \,$MHz. The magnetic dipole constant, $A$, agrees well with a previously measured value of $7.4 \pm 0.2 \,$MHz (G. Belin et al., Phys.\ Scr.\ {\bf 14}, 39 (1976)).