Hyperfine structure in hydrogen and helium ion

QED theory of the hyperfine splitting of the 1s and 2s state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8EHFS(2s)−EHFS(1s). We take into account higher-order QED and nuclear structure effects. In particular, we found the vacuum polarization contribution in order α(Zα)3EF and examined the recoil contribution in order (Zα)3m/M and thus completed a calculation of the fourth order QED corrections. The higher-order nuclear structure contributions were also analysed. The theoretical predictions reported here are now of a higher accuracy than the experiment. The study of the difference provides the most accurate test (at a level of a part in 108) of the QED theory of ns HFS up to date. The theory agrees with most of the experimental data.