Orientation and alignment relaxation cross sections have been obtained for the
32P21 and
32P23 states of sodium by measuring resonance broadening of Hanle-effect signals at vapor densities up to about
1015 atoms/
cm3. In order to avoid reabsorption of the resonantly scattered light, the Hanle effect is measured in a region close to the wall of a specially constructed vapor cell. The width of the Hanle-effect signals is found to vary linearly with vapor density. The resulting cross sections for orientation and alignment relaxation are compared with theory.