Theory of light hydrogenlike atoms

Abstract

The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion He + , and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium. *

Point-particle effective field theory III: relativistic fermions and the Dirac equation

“…In what follows we specialize for simplicity to parity-preserving interactions and spinless compact central objects, and so strictly speaking the interactions we find suffice in themselves to describe finite-size effects in the He + ion or muonic states in even-even nuclei [24,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. The effects we find also apply to nuclei with spin (such as hydrogen) once the effective theory of the first-quantized source is supplemented by the extra interactions that a nuclear spin allows.…”

Proton polarizability contribution to hydrogen hyperfine splitting

“…The calculation of different corrections to E F has a long history. Modern status in the theory of hydrogenic atoms was presented in details in [3]. δ QED denotes the contribution of higher-order quantumelectrodynamical effects.…”

“…The corresponding amplitudes of virtual Compton scattering on proton can be expressed through nucleon polarized structure functions G 1 (ν, Q 2 ) and G 2 (ν, Q 2 ). Inelastic contribution of the diagrams (a), (b) Figure 1 may be presented in the form [3][4][5][6][7][8]:…”

“…The theoretical bound for the proton polarizability contribution is |δ P | ≤ 4 ppm. As noted in [3], the problem of the proton polarizability contribution requires new investigation, which takes into account more recent experimental data on the spin structure of the nucleon.…”

“…First part of the error in (24) is connected with statistical and systematical errors of the experimental data from [12]. The difference between the experimental value (1) and the theoretical result ∆E th HF S without the proton polarizability contribution can be presented in the form [2,3,37,38]:…”