  Detailed analysis of spectral line broadening and variations in relative
intensities of hyperfine spectral components due to optical pumping is
presented. Hyperfine levels of sodium $3p_{1/2}$ and $3p_{3/2}$ levels are
selectively excited in a supersonic beam at various laser intensities under the
conditions when optical pumping time is shorter than transit time of atoms
through the laser beam. The excitation spectra exhibit significant line
broadening at laser intensities well below the saturation intensity, and
redistribution of intensities of hyperfine spectral components is observed,
which in some cases is contradicting with intuitive expectations. Theoretical
analysis of the dynamics of optical pumping shows that spectral line broadening
depends sensitively on branching coefficient of the laser-driven transition.
Analytical expressions for branching ratio dependent critical Rabi frequency
and critical laser intensity are derived, which give the threshold for onset of
noticeable line broadening by optical pumping. Transitions with larger and
smaller branching coefficients are relatively less affected. The theoretical
excitation spectra were calculated numerically by solving density matrix
equations of motion using the split propagation technique, and they well
reproduce the observed effects of line broadening and peak intensity
variations. The calculations also show that presence of dark (i.e., not laser-
coupled) Zeeeman sublevels in the lower state results in effective branching
coefficients which vary with laser intensity and differ from those implied by
the sum rules, and this can lead to peculiar changes in peak ratios of
hyperfine components of the spectra.
