The 7σ discrepancy between the proton rms charge radius from muonic hydrogen and the CODATA-2010 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we ...review the theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S–2P transition frequencies measured in muonic hydrogen; see Pohl et al. (2010) 9 and Antognini et al. (2013) 71.
► We update the theory of Lamb shift and hyperfine splitting in muonic hydrogen. ► We found no large error or missing contribution larger than 0.001 meV. ► We critically discuss the proton-structure-dependent contributions. ► The proton radius puzzle still remains.
A multipass laser cavity is presented which can be used to illuminate an elongated volume from a transverse direction. The illuminated volume can also have a very large transverse cross section. ...Convenient access to the illuminated volume is granted. The multipass cavity is very robust against misalignment, and no active stabilization is needed. The scheme is suitable for example in beam experiments, where the beam path must not be blocked by a laser mirror, or if the illuminated volume must be very large. This cavity was used for the muonic-hydrogen experiment in which 6 μm laser light illuminated a volume of 7 × 25 × 176 mm3, using mirrors that are only 12 mm in height. We present our measurement of the intensity distribution inside the multipass cavity and show that this is in good agreement with our simulation.
The present knowledge of Lamb shift, fine- and hyperfine structure of the 2S and 2P states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several 2S −2P ...transition frequencies in muonic deuterium (μd). A term-by-term comparison of all available sources reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift, which are essential for a determination of the deuteron rms charge radius from μd. Apparent discrepancies between different sources are resolved, in particular for the difficult two-photon exchange contributions. Problematic single-sourced terms are identified which require independent recalculation.
Theory of the n = 2 levels in muonic helium-3 ions Franke, Beatrice; Krauth, Julian J.; Antognini, Aldo ...
The European physical journal. D, Atomic, molecular, and optical physics,
12/2017, Letnik:
71, Številka:
12
Journal Article
Recenzirano
Odprti dostop
The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several 2S → ...2P transition frequencies in the muonic helium-3 ion,
μ
3He+. This ion is the bound state of a single negative muon
μ
-
and a bare helium-3 nucleus (helion),
3
He
++
. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting. These values are essential for the determination of the helion rms charge radius and the nuclear structure effects to the hyperfine splitting in
μ
3He+. With this review we continue our series of theory summaries in light muonic atoms see A. Antognini et al., Ann. Phys.
331
, 127 (2013); J.J. Krauth et al., Ann. Phys.
366
, 168 (2016); and M. Diepold et al.
arXiv:1606.05231
(2016).
Graphical abstract
Laser spectroscopy of muonic deuterium Pohl, Randolf; Nez, François; Fernandes, Luis M. P. ...
Science (American Association for the Advancement of Science),
08/2016, Letnik:
353, Številka:
6300
Journal Article
Recenzirano
Odprti dostop
The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius rd and the polarizability serve as important ...benchmarks for understanding the nuclear forces and structure. Muonic deuterium μd is the exotic atom formed by a deuteron and a negative muon μ⁻. We measured three 2S-2P transitions in μd and obtain rd = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value rd = 2.1424(21) fm. The μd value is also 3.5σ smaller than the rd value from electronic deuterium spectroscopy. The smaller rd, when combined with the electronic isotope shift, yields a "small" proton radius rp, similar to the one from muonic hydrogen, amplifying the proton radius puzzle.
The energy levels of hydrogen-like atomic systems are shifted
slightly by the complex structure of the nucleus, in particular by the
finite size of the nucleus. These energy shifts are vastly ...magnified in
muonic atoms and ions, i.e. the hydrogen-like systems formed by a negative
muon and a nucleus. By measuring the 2S-2P energy splitting in muonic
hydrogen, muonic deuterium and muonic helium, we have been able to
deduce the p, d,
^3
3
He
and
^4
4
He
nuclear charge radii to an unprecedented accuracy. These radii provide
benchmarks for hadron and nuclear theories, lead to precision tests of
bound-state QED in regular atoms and to a better determination of the
Rydberg constant.
Accurate knowledge of the charge and Zemach radii of the proton is essential, not only for understanding its structure but also as input for tests of bound-state quantum electrodynamics and its ...predictions for the energy levels of hydrogen. These radii may be extracted from the laser spectroscopy of muonic hydrogen (μp, that is, a proton orbited by a muon). We measured the $2{\mathrm{S}}_{1/2}^{\mathrm{F}=0}-2{\mathrm{P}}_{3/2}^{\mathrm{F}=1}$ transition frequency in μp to be 54611.16(1.05) gigahertz (numbers in parentheses indicate one standard deviation of uncertainty) and reevaluated the $2{\mathrm{S}}_{1/2}^{\mathrm{F}=1}-2{\mathrm{P}}_{3/2}^{\mathrm{F}=1}$ transition frequency, yielding 49881.35(65) gigahertz. From the measurements, we determined the Zemach radius, r Z = 1.082(37) femtometers, and the magnetic radius, r M = 0.87(6) femtometer, of the proton. We also extracted the charge radius, r E = 0.84087(39) femtometer, with an order of magnitude more precision than the 2010-CODATA value and at 7σ variance with respect to it, thus reinforcing the proton radius puzzle.
We provide an up to date summary of the theory contributions to the 2S → 2P Lamb shift and the fine structure of the 2P state in the muonic helium ion (μ{sup 4}He){sup +}. This summary serves as the ...basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the {sup 3}He–{sup 4}He isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of n=2 theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.
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