Bethe's "average excitation potentials" for states $1s$ through $4p$ of hydrogen are calculated numerically. These lead to values of the n₀²S1/2-n₀²P1/2 level shifts in hydrogen for n₀=3 and 4 of SH(3)=314.690±0.047 Mc/sec and SH(4)=132.998±0.020 Mc/sec, which are 1.44 Mc/sec and 0.85 Mc/sec larger than previous estimates. For n₀=2, a value of SH(2)=1057.21±0.16 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.
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John Martin Harriman (1956) studied this question.
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