Langevin approach to magnetic-field-gradient-induced spin relaxation in a coated cell

Magnetic-field-gradient-induced spin polarization transverse relaxation is re-examined in an alkali-metal atomic cell with antirelaxation coating. The experimentally observed motional-narrowing effect in a paraffin-coated vapor cell, a phenomenon for depicting the suppression of spin polarization transverse relaxation caused by the magnetic-field gradient, is more than an order of magnitude weaker than theoretical predictions. Such a discrepancy is due to the existence of background gas. By taking the background gas into consideration, Redfield theory combined with the Langevin approach is proposed to depict the magnetic-field-gradient-induced spin relaxation in a coated cell, and the model is verified to be consistent with the previous results derived under two limits in which the mean free path is either much smaller (diffusion regime) or much larger than (ballistic regime)the cell size. Our work provides a potentially feasible method to evaluate the background gas pressure inside the coated cell, and it can help to foster better comprehension of the performance of an antirelaxation coated cell.