= Hydrogen fine-structure correction
{title2=$\Delta E_{nj}=-m_ec^2\alpha_{\rm fs}^4[1/(j+1/2)-3/(4n)]/(2n^3)$}
For a point, fixed proton, the sum of the <relativistic kinetic-energy correction>, <spin-orbit interaction> including the <Thomas precession> factor, and <Darwin term> has the displayed leading correction. It depends on n and total <angular momentum> j, but not separately on l. Thus $2S_{1/2}$ and $2P_{1/2}$ remain degenerate while $2P_{3/2}$ lies above them. Radiative corrections, recoil, nuclear size and <hyperfine structure> require additional terms. The fine-structure constant is $\alpha_{\rm fs}=e^2/(4\pi\epsilon_0\hbar c)$.
Back to article page
