G-Factor of the electron

For proton resonance, the result (268) is adjusted empirically for the different experimentally observed g factors of the electron (2.002) and proton (5.5857). A more complete theory must rest on the internal structure of the proton or other nuclei. The basic theory of RFR is straightforward, however, and a term emerges with three other well-known terms. In principle, RFR can investigate nuclear properties using microwave or RF generators instead of multi-million superconducting magnets. 

We have performed an experiment to measure the g factor of the electron bound to a Carbon nucleus in a Hydrogen-like C5+ ion [9]. As shown below, the result of our measurement represents a significant test of bound state QED contributions and also accounts for the recoil correction from the finite mass of the carbon nucleus. The experiments are performed on single C5+ ions confined in a Penning ion trap at low temperatures, almost completely isolated from the environment. As outlined in the last paragraph the extension of our experiments to other highly charged systems opens a number of possibilities for future measurements of fundamental quantities such as the electrons mass or the fine structure constant. 

Barely had spectroscopists absorbed news of the Lamb shift when another bombshell burst the g-factor of the electron was not exactly 2. You, who (for the most part) have grown up knowing this will find it difficult to realise how shattering it was to see that beautiful symmetry destroyed. The news came also from Columbia in 1947 NAFE, NELSON and RABI [49] discovered that the hfs of the ground state of hydrogen was 1 part in 103 larger than its value evaluated from the Fermi formula using ge = 2. There followed a succession of experiments (also described in [48]) whereby the... 

The precise measurement of the g-factor of the electron bound in a hydrogen-like ion is a sensitive test of bound-state Quantum Electrodynamics (QED) at high fields. Highly charged ions are ideal for such studies, because the electromagnetic... 

These results are among the most precise predictions ever made with QED, which is the most precise theory to date. Thus, the previously most precise predictions of QED can be considered to be the g-factor of the electron, with an uncertainty on the 13th digit (about 4 x 10 relative [3, p. 64]). This is to be compared, for instance, to the precision on 1S-3D transition frequencies in [1, Table III], which reach about 3 x 10 , which is more precise by about an order of magnitude. 

In addition to obtaining the values of the variables in Z that satisfy system (3) the best, it is possible to obtain their covariance matrix G (see, e.g.. Ref. [3, App. E]). This matrix is also available on the web. Thus, many numerical values of Z satisfy system (3) within the imposed uncertainties V. This defines a set of statistically acceptable values that lie within close range of the best values the covariance matrix of the adjusted values essentially describes the typical dimensions (in the 61-dimensional space of Z (Section 2.2.2.1)) of this set of acceptable values. For instance, statistically plausible sets of numerical values for Z are such that the g-factor of the electron (which is a component of Z) varies with a relative standard error of as little as 4 x 10 (this incidentally makes it the most precise value determined in the latest adjustment of the fundamental constants [3]). 

In many organic molecules, the g factor of the electron is about 2. However, unpaired electrons are also present in many metal compounds, especially metal compounds... 

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