Progress in helium fine-structure calculations and the fine-structure constant

Abstract

The long-term goal of this work is to determine the fine-structure constant α from a comparison between theory and experiment for the fine-structure splittings of the helium 1s2p 3PJ states. All known terms of order α5 a.u. (α7 mc2) arising from the electron–electron interaction, and recoil corrections of order α4 µ / M a.u. are evaluated and added to previous tabulation. The predicted energy splittings are ν0,1 = 29 616.946 42(18) MHz and ν1,2 = 2291.154 62(31) MHz. Although the computational uncertainty is much less than ±1 kHz, there is an unexplained discrepancy between theory and experiment of 19.4(1.4) kHz for ν1,2. PACS Nos.: 31.30Jv, 32.10Fn