In order to obtain as narrow as possible paramagnetic resonance signals, it is of importance to investigate the conditions under which long relaxation times can be realized. In the present experiment on sodium atoms diffusing in argon gas, relaxation due to sodium-sodium collisions was minimized by employing very low sodium partial vapor pressures (about 10-7 mm Hg). While at lower pressures the argon is serving its function well to slow down relaxation by inhibiting wall diffusion, at about 10 cm Hg relaxation due to sodium-argon collisions becomes the decisive factor. Nevertheless it was possible to realize a relaxation time of 0.21 sec for a 1-liter spherical bulb filled with 3 cm argon. About 0.02 sec was found for a 0.1-liter, 40 cm argon sample. In carrying out the experiments, optical pumping by circularly polarized resonance radiation was used to create an orientation of the sodium atoms which then was monitored by measuring the transmission of the pumping radiation through the sample. By suddenly reversing a small axial magnetic field, the polarization of the atoms could be made to reverse too. From the decay rates of this inverted polarization under the combined effects of relaxation and continuing optical pumping, the experimental relaxation times were deduced. The strong signals obtained are indicative of available signal to noise ratios in future radio-frequency resonance reorientation experiments using the transmission monitoring technique. A theoretical analysis of the optical pumping process, including the dynamic aspects and allowing for collisions with argon that the sodium atoms undergo while in the excited state, was carried out and used to describe the experimental data.