Proton-to-electron mass ratio

The absolute frequency of the fundamental IS — 2S transition in atomic hydrogen has now been measured to 1.8 parts in 1014, an improvement by a factor of 104 in the past twelve years. This improvement was made possible by a revolutionary new approach to optical frequency metrology with the regularly spaced frequency comb of a mode locked femto-second multiple pulsed laser broadened in a non-linear optical fiber. Optical frequency measurement and coherent mixing experiments have now superseded microwave determination of the 2S Lamb shift and have led to improved values of the fundamental constants, tests of the time variation of the fine structure constant, tests of cosmological variability of the electron-to-proton mass ratio and tests of QED by measurement of g — 2 for the electron and muon. 

An important feature of the study of the g factor of a bound electron at Z = 20 — 30 is also the possibility to learn about higher-order two-loop corrections, which are one of the crucial problems of bound state QED theory. Below we discuss in detail the present status of theory and experiment. We consider a new opportunity to precisely test bound state QED and to accurately determine two fundamental constants the electron-to-proton mass ratio and the fine structure constant. 

Carbon experiment and electron-to-proton mass ratio... 

Concluding our consideration we would like to underline, that the study of the g factor of a bound electron [1] offers a new opportunity for us to precisely test bound state QED theory and to determine two important fundamental constants the fine structure constant a and the electron-to-proton mass ratio m/mp. The experiment can be performed at any Z with about the same accuracy [1] and one can expect new data at medium Z which will allow to verify the present ability to estimate unknown higher-order corrections (i. e. theoretical uncertainty) in both low-Z and high-Z calculations. 

Each of the terms in this expression is smaller than the magnetic susceptibility terms by the electron to proton mass ratio, and may therefore be neglected. With this simplification equation (8.114) can be written in the more compact form... 

In atomic and molecular physics, two of these constants are particularly important. They are the fine structure constant a, and the electron-to-proton mass ratio p, = me/mp. The Rydberg energy Ry sets the gross scale of electronic binding energy. Relative to this, the fine structure splittings are characteristically smaller by the factor... 

In this chapter, we describe the application of precision molecular spectroscopy to the study of a possible temporal and spatial variation of the fundamental constants. As we will show below, molecular spectra are mostly sensitive to two such dimensionless constants, namely the fine-structure constant a = e jhc and the electron-to-proton mass ratio p, = m jm (note that some authors define p as an inverse value, i.e., the proton-to-electron mass ratio). At present, NIST lists the following values of these constants [1] a = 137.035999679(94) and p- = 1836.15267247(80). 

Astrophysical observations of the spectra of diatomic and polyatomic molecules can reveal a possible variation of the electron-to-proton mass ratio pi on a timescale from 6 to 12 billion years. However, the astrophysical results obtained so far are inconclusive see Equations 16.15, 16.19, and 16.36. Much of the same can be said about the astrophysical search for an a-variation. In principle, the astrophysical observations can be explained by a complex evolution of p, and a in space and time. Likely, there are also systematic errors in the measurements that have not been fully understood. Therefore, it is imperative to complement the astrophysical studies with laboratory measurements of the present-day variation of these constants. This work is under way in a number of laboratories. Most use atomic frequency standards and atomic clocks. In this chapter we discussed several recent ideas and proposals on how to increase the sensitivity of the laboratory tests by using molecules instead of atoms. 

Erohlich, U., Roth, B., Antonini, P., Lammerzahl, C., Wicht, A., and Schiller, S., Ultracold trapped molecules Novel systems for tests of the time-independence of the electron-to-proton mass ratio, Lect. Notes Phys., 648, 297, 2004. 

Heteronuclear diatomic ions with large vibrational and rotational frequencies are promising systems for high-precision laser spectroscopy and fundamental studies, such as tests of time independence of the electron-to-proton mass ratio. They can also serve as model systems for the implementation of schemes for internal state manipulation [79,80]. Molecular hydrides, such as ArH+ and ArD" ", are interesting examples, with the advantage of a relatively simple hyperfine structure of the rovibrational transitions [79,81]. These hydrides were formed by the ion-neutral reactions [49] (Figure 18.28a through c)... 

It thus appears that the experimental method demonstrated for HD+ provides a new approach for determination of the electron-to-proton mass ratio If... 

FrohUch, U., Roth, B., Antonini, P., Lammerzahl, C., Wicht, A., and SchiUer, S., Ultracold trapped molecules Novel systems for tests of the time-independence of the electron-to-proton mass ratio, Lect. Notes Phys., 648, 297, 2004 Kim, J.K., Theard, L.P., and Huntress W.T., Jr. ions to N2, O2, and CO molecules, Chem. Phys. Lett., 32, 610, 1975 Roche, A.E., Sutton, M.M., Rohme, D.K., and Schiff, H.I., Determination of proton affinity from the kinetics of proton transfer reactions. I. Relative proton affinities, J. Chem. Phys., 55, 5840,1971. 

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