We consider different options for the search for possible variations of the fundamental constants. We give a brief overview of the results obtained with several methods. We discuss their advantages and disadvantages with respect to simultaneous variations of all constants in both time and space in the range 1081010 years. We also suggest a few possibilities for the laboratory search. Particularly, we propose some experiments with the hyperfine structure of hydrogen, deuterium, and ytterbium171 and of some atoms with a small magnetic moment. Other suggestions are for some measurements of the fine structure associated with the ground state. Special attention is paid to the interpretation of the hfs measurements in terms of variations of the fundamental constants. PACS No.: 31.30G

Some possibilities for laboratory searches for variations of fundamental constants

A critical compilation of experimental data on spectral lines and energy levels of hydrogen, deuterium, and tritium

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA least-squares adjustment (LSA) of the fundamental physical constants. We give a deuteron charge radius from D spectroscopy alone of 2.1415(45) fm. This value is independent of the measurements that lead to the proton charge radius, and five times more accurate than the value found in the CODATA Adjustment 10. The improvement is due to the use of a value for the transition in atomic deuterium which can be inferred from published data or found in a PhD thesis.

http://iopscience.iop.org/article/10.1088/1681-7575/aa4e59/pdf

Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium

https://cyberleninka.org/article/n/914511.pdf

Hyperfine structure in hydrogen and helium ion

We obtain a model-independent prediction for the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen. We use the relation of the Wilson coefficients of the spin-dependent dimension-six four-fermion operator of NRQED applied to the electron-proton and to the muon-proton sectors. Their difference can be reliably computed using chiral perturbation theory, whereas the Wilson coefficient of the electron-proton sector can be determined from the hyperfine splitting in hydrogen. This allows us to give a precise model-independent determination of the Wilson coefficient for the muon-proton sector, and consequently of the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen, which reads $$ \delta {\overline{E}}_{p\mu, \mathrm{H}\mathrm{F}}^{\mathrm{TPE}}(nS)=-\frac{1}{n^3}1.161(20) $$
 meV. Together with the associated QED analysis, we obtain a prediction for the hyperfine splitting in muonic hydrogen that reads E
 ,HF
 th
 (1S) = 182.623(27) meV and E
 ,HF
 th
 (2S) = 22.8123(33) meV. The error is dominated by the two-photon exchange contribution.

/pdf/model-independent-determination-of-the-two-photon-exchange-1qvg1jnqj8.pdf

Model-independent determination of the two-photon exchange contribution to hyperfine splitting in muonic hydrogen

The principal accuracy limitation of a hydrogen maser is the uncertainty in the determination of the hydrogen maser wail shift. In this paper, we describe in detail the experiments on hydrogen maser wall shift and introduce briefly works on hydrogen masers in the Shanghai Bureau of Metrology. In experiments, we changed five different size storage bulbs by. turns. These bulbs were all coated in the same way with a locally made F4 coating. Results of the experiments are K(40°C) = -293 ± 17 mHzcm and a(40°C) = (-17 ± 2) × 10-30C-1. The unperturbed hyperfine frequency of the ground state of the hydrogen atomf0-0 was obtained by comparing five hydrogen masers to Loran C navigation system signals for one month. The average value in respect to TAI isf0-0 = 1420 405 751.768 ± 0.002 Hz. This value is closely in agreement with values of f0-0, which have been published by other authors since 1970.

Wei Shen

Papers

Hydrogen Maser Wall Shift Experiments and Determination of the Unperturbed Hyperfine Frequency of the Ground State of the Hydrogen Atom