Spin-exchange frequency shifts in cryogenic and room-temperature hydrogen masers

We have calculated the spin-exchange shifts of the ground-state {Δ}mF=0 transition of a gas of hydrogen atoms in zero magnetic field from zero temperature up to temperatures of 1000 K. Taking into account the hyperfine interaction during spin-exchange collisions we find shifts nonlinear in the atomic linewidth and not compensated for by the usual methods of tuning the microwave cavities of oscillating hydrogen-maser frequency standards. At room temperatures these shifts affect the H-maser stability at the level of {δ}{ω}/{ω}{}10^-15. At cryogenic temperatures these shifts are large compared to the potential thermal instabilities of liquid-helium-lined hydrogen masers. A detailed study of these nonlinear shifts reveals several ways to reduce these new sources of frequency instability.