α3Corrections to the Hyperfine Structure of the1Sand2SStates of Hydrogen

Recent precision measurements of the hyperfine splitting in the $1S$ and $2S$ states in hydrogen would make possible the observation of ${\alpha }^3$ corrections. A calculation of these corrections would be difficult because of the many processes that can contribute to this order and because of the uncertainty of the nuclear structure effects that can contribute in this numerical order. For these reasons only the ratio of the hyperfine structure in the $2S$ state to that in the $1S$ state is calculated here. It is shown that the formation of the ratio eliminates the contribution of most of the ${\alpha }^3$ corrections and totally eliminates the nuclear structure effects. The coefficient, $B-A$, of the ${\alpha }^3$ terms in the ratio is calculated as $\mathrm{}(B-A)=5.28\mathrm{}$. This compares with the experimental value, ${\mathrm{}(B-A)\mathrm{}}_{\exp }=3.4\mathrm{}\pm 0.8$.