Experimental Determination of Relative Transition Probabilities in the Sodium Atom

Determination of the relative transition probabilities for lines 2 to 16 in the principal series of sodium.—Direct measurement of line absorption intensities was made by a precise method of photographic photometry previously described. On each plate 11 spectra were photographed, 5 absorption spectra of light from an aluminum underwater spark which had passed through 10 cm of vapor, and 6 calibrating spectra of a constant cadmium spark. Corrections were applied for densitometer slit width, plate characteristics, band absorption, and sensitometer slit width and dispersion curve. The doublets were unresolvable at the vapor pressures used and were treated as single lines. Line shapes were measured at 18 different vapor densities, covering a four-fold variation, and from these were determined the constants $C_1$ and $C_2$ in Slater's formula for transition probabilities as given by his theory of virtual oscillators, $\mathrm{Nxh}{\lambda }_0{B}_{\mathrm{ij}}=c\pi {log}_{e}10\times \sqrt{\frac{C_1}{C_2}}$, and the relative transition probabilities $B_{\mathrm{ij}}$ for the various lines 2 to 16. No decrease in relative probability of the higher numbers with increasing vapor pressure was found, the curves for ${log}_{10}N{B}_{\mathrm{ij}}$ as a function of term number for different pressures being practically parallel. From the smoothed curves average relative values of $B_{\mathrm{ij}}$ were obtained with a variation of 2 to 4 percent, and from these the corresponding relative values of $A_{\mathrm{ij}}$ were calculated from Einstein's relation $c^3{A}_{\mathrm{ij}}=8\mathrm{}\pi hv_0^{}{}_{}{}^3{B}_{\mathrm{ij}}$. Hoyt's preliminary theoretical calculation of the ratio of the first two terms was found to agree closely with these results.