Muonic hydrogen

Muonic hydrogen is an exotic atom in which a muon is bound to a proton . Since the muon is about 200 times heavier than the electron , which is bound to a proton in normal hydrogen , the energy spectrum differs significantly from the hydrogen spectrum . Because of the mean lifetime of the muon of about 2.2 · 10 ⁻⁶  s, the lifetime of muonic hydrogen is also limited to the order of a millionth of a second.

Physical Properties

Due to the high mass of the muon, the distance between it and the proton is much smaller than with normal hydrogen:

• the Bohr radius of normal hydrogen is , with the Compton wavelength of the electron and the fine structure constant ${\displaystyle a_{0}={\frac {\lambda _{\mathrm {e} }}{2\pi \alpha }}\approx 21{,}8\lambda _{\mathrm {e} }}$
  ${\displaystyle \lambda _{\mathrm {e} }}$
  ${\displaystyle \alpha ,}$
• while the Bohr radius of muonic hydrogen is only about one-thirtieth of this value: ${\displaystyle a_{0,\mathrm {myonisch} }\approx 0{,}73\lambda _{\mathrm {e} }.}$

The Compton wavelength of the electron is the typical length scale for the vacuum polarization , therefore this is pronounced in myonischem hydrogen significantly higher than in normal hydrogen and the Lamb-shift is the dominant correction of the difference in energy of 2p and 2s - level . Clearly speaking, the muon in the spherically symmetrical 2s level has a certain non-zero probability of being “inside the proton”, in this case it does not “see” its electrical charge - the muon in the 2p level, on the other hand, has zero probability of being with the proton.

Due to the small distance between the muon and the proton, the size of the proton can be measured, since the finite size influences the energy levels. A measurement in 2010 gave the value 0.84184 (67)  fm for the proton radius , which deviates significantly from the previous measured values, but is much more precise. Measurements carried out by the same working group in 2013 provide an even more precise measured value with a proton radius of 0.84087 (39) fm, which, however, is still based on the value of the proton radius of 0.8775 (51) fm determined by scattering measurements on electronic hydrogen deviates. This could be an indication of a new physics , since the Standard Model has not yet been able to explain this deviation.

Individual evidence

1. ↑ Randolf Pohl et al .: The size of the proton . In: Nature . tape 466 , no. 7303 , 2010, p. 213-216 , doi : 10.1038 / nature09250 .
2. ↑ Randolf Pohl et al .: Muonic hydrogen and the proton radius puzzle . In: Annual Review of Nuclear and Particle Science . Vol. 63, 2013, pp. 175-204 , doi : 10.1146 / annurev-nucl-102212-170627 , arxiv : 1301.0905v2 .
3. ↑ Randolf Pohl, Jan C. Bernauer: The Proton Paradox . In: Spectrum of Science . April, 2014, p. 48-55 .