Collisional effect with optically pumped atomic clock

It is shown that an atomic clock based on an atomic beam passing through two widely separated small holes can be significantly affected by a collisional frequency shift caused by the broadening of the wave packet in the two directions perpendicular to the atomic beam. This effect cannot be derived from previous formulas of collisional cross-sections, so a new collisional cross-section formula that takes the actual form of incident wave packet into account was developed. With optically pumped atomic clock, this effect is much more serious than with primary atomic clock