Collision frequency shift of hyperfine transitions in atomic hydrogen at a low temperature

The experimental results on the collision frequency shift of ESR in diluted two-and three-dimensional atomic hydrogen at ultralow temperature have been analyzed. The apparent contradiction between experiment and theory is resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin $S$. For example, transitions between symmetric and antisymmetric states of a pair of atoms induced by a symmetric perturbation are forbidden. If symmetric and antisymmetric states are, respectively, pure electronic triplets ($S=1$) and singlets ($S=0$), this results in the cancellation of the singlet-triplet transitions. Thus, the collision frequency shift of $b\to c$ and $b\to a$ transitions vanishes in a completely electron and nuclear spin-polarized gas (hyperfine state $b$). The comparison is performed with experiments in ultracold alkali vapors.