Two-loop effects and current status of the ⁴He⁺ Lamb shift

Abstract

We report on recent progress in the treatment of two-loop binding corrections to the Lamb shift, with a special emphasis on S and P states. We use these and other results to infer an updated theoretical value of the Lamb shift in 4 He + .Résumé : Nous examinons le progrès récent concernant le traitement des corrections à l'ordre élevé des diagrammes à deux boucles contribuants aux déplacement de Lamb, spécialement en ce qui concerne les états S et P . Par conséquent, on déduit de nouvelles précises valeurs théoriques pour le déplacement de Lamb en 4 He + .

Two-loop QED corrections in few-electron ions

“…There are no complete results available at present for the coefficient B 60 for single states. However, its non-relativistic part b L (also termed as the two-loop Bethe logarithm) was calculated for 1s and 2s states in [14] and later for higher excited states in [15,16]. This part presumably yields the dominant contribution to B 60 ; the uncertainty due to uncalculated terms was estimated in [14] to be 15% for the 1s and 2s states.…”

Muonic hydrogen spectroscopy: the proton radius puzzle

“…8 As a consequence, the uncertainty of the experimentally determined Lamb shift δL exp 1S originates basically only from the uncertainty of R ∞ which results mainly from the 2S-8S/D and 2S-12S/D transition frequency measurements. 21 The theoretical prediction of the Lamb shift 8,[22][23][24][25][26] (using α −1 = 137.035999084 and B 60 = −95.3 8 )m a yb e expressed as L theo 1S = 8171.636(4) + 1.5645 r 2 p MHz (8) * The Lamb shift is defined as any deviation from the prediction of the Dirac equation which arises from radiative, recoil, nuclear structure, relativistic and binding effects but excludes leading order recoil and hyperfine contributions. 4 However for simplicity in the following equations we consider it as the deviation from the prediction of the Schrödinger equation.…”

Double-Resonance g Factor Measurements by Quantum Jump Spectroscopy

“…In order to lay a theoretical ground for the evaluation of the 4 He + measurement, we present theoretical predictions for the transition frequencies and for the g factor. According to the recent compilations [31,32,33], the ground state 4 He + Lamb shift values are L(1S) = 107692.522(228) MHz for the "old" value [34] of the nuclear charge radius r 2 1/2 = 1.673(1) fm and L(1S) = 107693.112(472) MHz for the "new" value of the charge radius [35], which is r 2 1/2 = 1.680(5) fm. (The uncertainty estimate for the "old" value has given rise to discussions, see Ref.…”