The hyperfine frequency shift of atomic hydrogen in the presence of helium buffer gas

A quantum mechanical thermal average is performed to obtain the temperature dependence of the hyperfine frequency shift (HFS) of hydrogen atoms in the presence of He buffer gas. The calculations are based on existing ab initio calculations of the hyperfine frequency shift as a function of internuclear separation and of the interatomic potential. We find that the HFS changes sign at fairly low temperature and has a small negative value at T = 1 K in agreement with recent measurements. The overall temperature dependence is shown to be quite sensitive to the interatomic potential.