Spin-exchange pulling of the $\ensuremath{\Delta}{m}_{F}=0$ ground-state hyperfine transition in atomic hydrogen is investigated for the case of self-excited oscillation on this transition in the hydrogen maser. Frequency shifts due to mistuning the maser cavity are found to compensate spin-exchange shifts so that both can be effectively eliminated. The result bears importantly on the use of the hydrogen maser as a spectroscopic tool and frequency standard and suggests a method for determining the spin-exchange shift parameter.
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