Theory of Fine Structure Pressure Broadening of Spectral Lines

The difference of pressure broadenings and shifts of the doublet components of the principal series lines of alkalis is treated in an approximate manner. Applying the perturbation method and the Franck-Condon principle to the Michels, deBoer, and Bijl model of compressed atoms in the doublet $P$ states, it is shown that the doublet separation becomes smaller with increasing pressure at rather low pressure. Consequently, the shift of the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ must be smaller than that of the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ component of the principal series. The attractive forces are recalculated with the inclusion of the quadrupole moment for the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state. This consideration requires the splitting of the state according to the magnetic quantum numbers so that the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ component will be 1.12 times larger in half-width than ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ in the approximation of the collision theory. This result is in good agreement with experimental values.