Numerical Values for Hydrogen Fine Structure

Bethe's "average excitation potentials" for states 1s through 4p of hydrogen are calculated numerically. These lead to values of the n₀^2S₁₂-n₀^2P₁₂ level shifts in hydrogen for n₀=3 and 4 of S₇ (3) =314. 6900. 047 Mc/sec and S₇ (4) =132. 9980. 020 Mc/sec, which are 1. 44 Mc/sec and 0. 85 Mc/sec larger than previous estimates. For n₀=2, a value of S₇ (2) =1057. 210. 16 Mc/sec is obtained, which is in close agreement with previous calculation. In conjunction with this work, the oscillator strengths f (n₀l₀, nl) are obtained for n₀=1, 2, 3, and 4; n<50; and all values of l₀ and l. A generalization of the Wigner-Kirkwood sum rule is derived.