We measure the magnetization quantum beats of spin-polarized hydrogen (SPH) and spin-polarized deuterium (SPD) with a pickup coil, from the UV photodissociation of HCI, HBr, and DI, in the 5-5000 mbar pressure range. The pressure-dependent depolarization rate is linear at low pressures and reaches a plateau at higher pressures. The high-pressure depolarization rate is observed to be proportional to the halogen nuclear electric quadrupole coupling constant. We also investigate how the presence of an inert gas, SF6 or N-2, affects the depolarization rate. The results are explained using a model in which depolarization occurs predominantly through an HY-H intermediate species (Y = Cl, Br, I).