Theory of the lamb shift in muonic deuterium
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ELEMENTARY PARTICLES AND FIELDS Theory
Theory of the Lamb Shift in Muonic Deuterium∗ A. P. Martynenko1), 2)** , A. A. Krutov1), and R. N. Shamsutdinov2) Received April 3, 2013
Abstract—We present new calculation of the Lamb shift (2P1/2 − 2S1/2 ), fine splitting of the 2P state and hyperfine splitting of the 2S state in muonic deuterium (μd) using the quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure, and recoil effects are calculated with the account of contributions of orders α3 , α4 , α5 , and α6 . The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data. DOI: 10.1134/S1063778814060106
1. INTRODUCTION Muonic atoms represent a unique laboratory for the determination of the nuclear properties [1–5]. The experimental investigation of the (2P − 2S) Lamb shift in light muonic atoms (muonic hydrogen, muonic deuterium, muonic helium ions) can give more precise values of the nuclear charge radii. The first successful measurement of the (μp) F =2 − 2S F =1 ) at Lamb shift transition energy (2P3/2 1/2 PSI (Paul Scherrer Institute) produced the result 49 881.88(76) GHz (206.2949(32) meV) [6]. It leads to new value of the proton charge radius rp = 0.841 84(36)(56) fm which improves the CODATA value [7] by an order of magnitude. Another important project which exists now at PSI in the CREMA (Charge Radius Experiment with Muonic Atoms) collaboration proposes to measure several transition frequencies between 2S and 2P states in muonic helium ions with 50-ppm precision. As a result, new values of the charge radii of a helion and α particle with the accuracy 0.0005 fm will be determined. Theoretical calculations of fine and hyperfine structure of 2S and 2P states should be performed with high accuracy. Theoretical investigations of the Lamb shift (2P − 2S), fine and hyperfine structure of light muonic atoms was performed many years ago in [1, 8] on the basis of the Dirac equation and nonrelativistic three-dimensional method (see other references in review articles [1, 5]). Their calculation took into account different QED corrections with the accuracy ∗
The text was submitted by the authors in English. Samara State University, Russia. 2) Samara State Aerospace University, Russia. ** E-mail: [email protected] 1)
0.01 meV. Recently an approach of [1] was extended to the case of muonic deuterium in [2] where fine and hyperfine structure was analyzed with high accuracy. Different corrections to fine and hyperfine structure of muonic hydrogen are calculated on the basis of threedimensional method in quantum electrodynamics (QED) in [3, 9, 10]. The vacuum polarization effects of order α5 were considered in [11, 12]. In this work we aim to present new independent calculation of the Lamb shift (2P − 2S) in muonic deuterium (μd) with the account of contributions of orders α3 , α4 , α5 , and α6 on the basis of quasipotential method in quantum electrodynamics [9, 10]. We consider such effects of the electron vacu
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