Muonic Atoms and the Nuclear Structure

Abstract

High-precision laser spectroscopy of atomic energy levels enables the measurement of nuclear properties. Sensitivity to these properties is particularly enhanced in muonic atoms which are bound systems of a muon and a nucleus. Exemplary is the measurement of the proton charge radius from muonic hydrogen performed by the CREMA collaboration which resulted in an order of magnitude more precise charge radius as extracted from other methods but at a variance of 7 standard deviations. Here, we summarize the role of muonic atoms for the extraction of nuclear charge radii, we present the status of the so called "proton charge radius puzzle", and we sketch how muonic atoms can be used to infer also the magnetic nuclear radii, demonstrating again an interesting interplay between atomic and particle/nuclear physics.

Muonic vacuum polarization correction to the bound-electron $g$-factor

“…This situation is similar to the case of the muonic VP contribution to atomic binding energies [29]. Recent or projected improvements of proton distribution parameters by, e.g., collinear laser spectroscopy [30], x-ray spectroscopy of muonic atoms [31] or by electron-ion collision spectroscopy [32] are anticipated to help with the experimental identification of the dominant muonic VP effect. Furthermore, one may alternatively consider a weighted difference of g-factors in different charge states with the same Z, in analogy with [7,9,33].…”

“…(3) shows that for several elements, the dominant (electric loop) muonic and hadronic VP effects will be identifiable in experimental g-factors after an improvement of nuclear radii by approx. a factor of 5 via, e.g., the methods mentioned above [30][31][32]. The hadronic ML correction, as it is in leading order described by a virtual light-by-light scattering diagram, is much more complicated to calculate.…”

Chiral perturbation theory of hyperfine splitting in muonic hydrogen

“…6 of Ref. [6]) could enhance our understanding of the proton structure. Such experiment requires a precise theoretical prediction for the 1S HFS, because the transition is very narrow.…”

Experimental determination of the energy dependence of the rate of the muon transfer reaction from muonic hydrogen to oxygen for collision energies up to 0.1 eV

“…The ground-state hyperfine splitting of pμ, E hfs ∼ 0.182 eV, turns out to be in the infrared optical range, thus enabling the application of laser spectroscopy techniques. A number of experimental proposals for the measurement of E hfs have been put forward in recent years [42][43][44][45][46][58][59][60]. This was stimulated the need for new data on proton electromagnetic that had become an issue with the proton charge determination from the Lamb shift in muonic hydrogen [61].…”

“…The experimental investigations of (3) in the 1990s led to the two-step model [39] for the rate of the process, which was consistent with the then available data from measurements at room temperature. The interest in the subject was revived a few years later in relation to the projects to measure the hyperfine splitting in the ground state of muonic hydrogen [42][43][44][45][46] and extract out of it the value of the electromagnetic Zemach radius of the proton [47,48]. In a series of advanced theoretical calculations [24,25,29] significant progress was achieved in the quantitative description of the process (3) for energies up to 10 eV, but these theoretical results necessitate experimental verification.…”