Shift, muonic

Theoretically, light muonic atoms have two main special features as compared with the ordinary electronic hydrogenlike atoms, both of which are connected with the fact that the muon is about 200 times heavier than the electron First, the role of the radiative corrections generated by the closed electron loops is greatly enhanced, and second, the leading proton size contribution becomes the second largest individual contribution to the energy shifts after the polarization correction. 

Numerically, contribution to the 2P — 2S Lamb shift in muonic hydrogen is equal to... 

Having in mind that the data from the muonic hydrogen Lamb shift experiment will be used for measurement of the rms proton charge radius [2] it is useful to write this correction in the form... 

Nuclear size corrections of order (Za) m to the S levels were calculated in [59, 53] and were discussed above in Subsect. 6.3.2 for electronic hydrogen. Respective formulae may be directly used in the case of muonic hydrogen. Due to the smallness of this correction it is sufficient to consider only the leading logarithmically enhanced contribution to the energy shift from (6.35) [21]... 

The current surge of interest in muonic hydrogen is mainly inspired by the desire to obtain a new more precise value of the proton charge radius as a result of measurement of the 2P — 25 Lamb shift [64]. As we have seen... 

The natural linewidth of the 2P states in muonic hydrogen and respectively of the 2P — 2S transition is determined by the linewidth of the 2P — IS transition, which is equal hP = 0.077 meV. It is planned [64] to measure 2P — 2S Lamb shift with an accuracy at the level of 10% of the natural linewidth, or with an error about 0.008 meV, which means measuring the 2P — 2S transition with relative error about 4 x 10 . 

We can write the 2P — 25 Lamb shift in muonic hydrogen as a difference of a theoretical number and a term proportional to the proton charge radius squared... 

One can study muonic atoms [14,15,16]. The muon orbit lies lower and much more close to the nucleus and its energy levels are much more affected by the strong interactions. However, to determine the nuclear contributions (for e. g. the one for the Lamb shift, which is completely determined by the nuclear charge radius) it is not necessary to know the QED part with an accuracy as high as in the case of the hydrogen atom. As a result, one can try to determine the parameters due to the nuclear structure and apply them afterwards to normal atoms. 

The muon is about two hundred times heavier than the electron and its orbit lies 200 times closer to the nucleus. The nuclear structure effects scale with the mass of the orbiting particle as m3R2 (for the Lamb shift It is a characteristic value of the nuclear size) and as m R2 (for the hyperfine structure), while the linewidth is linear in m. That means, that from a purely atomic point of view the muonic atoms offer a way to measure the nuclear contribution with a higher accuracy than normal atoms. However, there are a number of problems with formation and thermalization of these atoms and with their collisions with the buffer gas. 

Lamb shift measurements on muonic hydrogen, as now pursued with a novel intense source of slow muons at the Paul Scherrer Institute [86,87] promise to yield an accurate rms charge radius of the proton, so that bound state QED can be tested to new levels of scrutiny. 

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