Self-broadening of the sodium resonance lines and excitation transfer between the $3P_{\frac{3}{2}}$ and $3P_{\frac{1}{2}}$ levels

Sodium vapor, in the density range ${10}^{13}$ to 5 × ${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$, was excited by a cw dye laser, tuned 20-150 GHz from either the $D_1$ or $D_2$ resonance line. We observed a three-peak scattered spectrum, consisting of the Rayleigh component at the laser frequency, and the two fluorescence components (direct and sensitized) at the atomic resonance-line frequencies. Corrections to the Rayleigh signals for anisotropy and polarization effects, and to the fluorescence signals for radiation trapping, were made in order to obtain the ratio of the sum of the total intensities of the two fluorescence components to that of the Rayleigh component. This ratio combined with a measurement of the line-wing absorption coefficient yields the sodium density and the $D$-line self-broadening rate coefficients [$k_{\mathrm{br}}=4.67\mathrm{}\times {10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{-1\mathrm{}}$ (±15%) for the $D_2$ line and $k_{\mathrm{br}}=3.07\mathrm{}\times {10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{-1\mathrm{}}$ (±15%) for the $D_1$ line]. Asymmetry in the self-broadened line wings due to fine-structure recoupling was observed. The measured intensity ratio of the $D$ lines, combined with pulsed measurements of the effective radiative decay rates in the presence of radiation trapping, yields the fine-structure collisional-mixing cross section [$\sigma (3\mathrm{}{P}_{\frac{3}{2}}\to 3P_{\frac{1}{2}})=172\mathrm{}$ ${\mathrm{\AA }}^2$(±18%)] at $T\cong 300°$ C. Our results are compared to other experiments and to theory.