Considering that the proton is a basic subatomic component of all ordinary matter — as well as being ubiquitous in its solo role as the hydrogen ion H+ — there are some surprising gaps in our knowledge of its structure and behaviour. A collaborative project to determine the root-mean-square charge radius of the proton to better than the 1% accuracy of the current 'best' value suggests that those knowledge gaps may be greater than was thought. The new determination comes from a technically challenging spectroscopic experiment — the measurement of the Lamb shift (the energy difference between a specific pair of energy states) in 'muonic hydrogen', an exotic atom in which the electron is replaced by its heavier twin, the muon. The result is unexpected: a charge radius about 4% smaller than the previous value. The discrepancy remains unexplained. Possible implications are that the value of the most accurately determined fundamental constant, the Rydberg constant, will need to be revised — or that the validity of quantum electrodynamics theory is called into question. Here, a technically challenging spectroscopic experiment is described: the measurement of the muonic Lamb shift. The results lead to a new determination of the charge radius of the proton. The new value is 5.0 standard deviations smaller than the previous world average, a large discrepancy that remains unexplained. Possible implications of the new finding are that the value of the Rydberg constant will need to be revised, or that the validity of quantum electrodynamics theory is called into question. The proton is the primary building block of the visible Universe, but many of its properties—such as its charge radius and its anomalous magnetic moment—are not well understood. The root-mean-square charge radius, rp, has been determined with an accuracy of 2 per cent (at best) by electron–proton scattering experiments1,2. The present most accurate value of rp (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants3. This value is based mainly on precision spectroscopy of atomic hydrogen4,5,6,7 and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of rp as deduced from electron–proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant3). An attractive means to improve the accuracy in the measurement of rp is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift10 (the energy difference between the 2S1/2 and 2P1/2 states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations11,12,13,14,15 of fine and hyperfine splittings and QED terms, we find rp = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value3 of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by −110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

/pdf/the-size-of-the-proton-1w85tmnp1f.pdf

The size of the proton

The strong interaction shift $\epsilon$ and broadening {\Gamma} in pionic deuterium have been determined in a high statistics study of the {\pi}D(3p - 1s) X-ray transition using a high-resolution crystal spectrometer The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen The hadronic broadening is related to pion absorption and production at threshold The results are \epsilon = (-2356 {\pm} 31)meV (repulsive) and {\Gamma}1s = (1171+23/-49) meV yielding for the complex {\pi}D scattering length a = [-(2499 {\pm} 033) + i (622+012/-026)]x10-3/m{\pi} From the imaginary part, the threshold parameter for pion production is obtained to be {\alpha} = (251 +5/-11) {\mu}b This allows, in addition, and by using results from pion absorption in 3He at threshold, the determination of the effective couplings g0 and g1 for s-wave pion absorption on isoscalar and isovector NN pairs

Pionic deuterium

The hadronic width of the ground state of pionic hydrogen has been redetermined by X-ray spectroscopy to be $$\varGamma ^{\pi \mathrm {H}}_{1s}=(856\,\pm \,16_\mathrm{stat}\,\pm \,22_\mathrm{sys})$$
  meV. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institute by using the cyclotron trap and a high-resolution Bragg spectrometer with spherically bent crystals. Coulomb de-excitation was studied in detail by comparing its influence on the line shape by measuring the three different transitions K
 $$\alpha $$
 , K
 $$\beta $$
 , and K
 $$\gamma $$
 at various hydrogen densities. The pion-nucleon scattering lengths and other physical quantities extracted from pionic-atom data are in good agreement with the results obtained from pion-nucleon and nucleon-nucleon scattering experiments and confirm that a consistent picture is achieved for the low-energy pion-nucleon sector with respect to the expectations of chiral perturbation theory.

/pdf/redetermination-of-the-strong-interaction-width-in-pionic-4ywfkov67g.pdf

Redetermination of the strong-interaction width in pionic hydrogen

The Lamb-shift experiment in muonic hydrogen (μ– p) aims to measure the energy difference between the atomic levels to a precision of 30 ppm. This would allow the r.m.s. proton charge radius rp to be deduced to a precision of 10–3 and open a way to check bound-state quantum electrodynamics (QED) to a level of 10–7. The poor knowledge of the proton charge radius restricts tests of bound-state QED to the precision level of about 6 × 10–6, although the experimental data themselves (Lamb-shift in hydrogen) have reached a precision of  × 10–6. Values for rp not depending on bound-state QED results from electron scattering experiments have a surprisingly large uncertainty of 2%. In our Lamb-shift experiment, low-energy negative muons are stopped in low-density hydrogen gas, where, following the μ– atomic capture and cascade, 1% of the muonic hydrogen atoms form the metastable 2S state with a lifetime of about 1 μs. A laser pulse at λ ≈ 6 μm is used to drive the 2S → 2P transition. Following the laser excitation...

/pdf/status-of-the-muonic-hydrogen-lamb-shift-experiment-1ust564qi5.pdf

Status of the muonic hydrogen Lamb-shift experiment

The subject of this thesis is the muonic hydrogen (µp) Lamb shift experiment being performed at the Paul Scherrer Institute, Switzerland. Its goal is to measure the 2S-2P energy difference in µp atoms by laser spectroscopy and to deduce the proton root ­mean­ square (rms) charge radius with 10-3 precision, an order of magnitude better than
presently known. This would make it possible to test bound-state quantum electrodynamics (QED) in hydrogen at the relative accuracy level of 10-7, and will lead to an improvement in the determination of the Rydberg constant by more than a factor of seven. Moreover it will represent a benchmark for QCD theories.

The experiment is based on the measurement of the energy difference between the 2S(F=1) and 2P(F=2) levels in µp atoms to a precision of 30 ppm, using a pulsed laser tunable
at wavelengths around 6 µm. Negative muons from a unique low energy muon beam are stopped at a rate of 70 s-1 in 0.6 hPa of hydrogen gas. Highly excited µp atoms are formed, and most of them promptly deexcite to the ground state within 100 ns. However, there is a roughly 1% probability that long­live µp(2S) atoms with a lifetime of 1.3 µs are formed.
An incoming muon triggers a pulsed, multi­stage laser system which delivers 0.2 mJ per pulse at 6 µm with 55 s-1 repetition rate. It consists of two XeCl excimer lasers followed by dye lasers which pump an oscillator ­amplifier frequency ­controlled Ti:Sa laser. Its 6 ns long pulse at 708 nm is then frequency shifted to 6 µm via third Stokes production in a Raman cell filled with hydrogen. The laser pulse has a delay of about 1.5 µs with respect to the prompt muon cascade. 

If the laser is on resonance, it induces 2S-2P transitions. The subsequent deexcitation to the 1S state emits a 1.9 keV Lyman-alpha x ray which is detected by large area avalanche photo diodes. The resonance frequency, and hence the Lamb shift and the proton radius, are determined by measuring the intensity of these x rays as a function of the laser wavelength.

A search for the 2S-2P resonance line was performed in November 2003 when a broad range of laser frequencies was scanned (49.7409 - 49.8757 THz), corresponding to proton radii between 0.844 and 0.905 fm. The result of the data analysis is that no significant 2S-2P resonance was observed. The negative result is with high probability due to the low statistics and not to an incorrect search region.
 
The first part of this thesis reports on the present status of the Lamb shift theory in µp. Following, there is a detailed description of the apparatus and analysis of the data. An estimate of the present and future laser-­induced event rates are given, together with a study of the present and future background. In the Appendices are discussed: the energy levels in hydrogen, the proton radius definition, the relevance of this experiment, the 2S state population and lifetime, and the spectroscopic properties of the 2S-2P transition.

https://edoc.ub.uni-muenchen.de/5044/1/Antognini_Aldo.pdf

The Lamb Shift Experiment in Muonic Hydrogen

The atomic cascades in mu-p and pbar-p atoms have been studied in detail using new results for the cross-sections of the scattering of highly excited exotic atoms from molecular hydrogen. The cascade calculations have been done with an updated version of the extended standard cascade model that computes the evolution in the kinetic energy from the beginning of the cascade. The resulting X-ray yields, kinetic energy distributions, and cascade times are compared with the experimental data.

Collisional deexcitation of exotic hydrogen atoms in highly excited states. II. Cascade calculations

The atomic cascades in μ-
p and 
p atoms have been studied in detail using new results for the cross-sections of the scattering of highly excited exotic atoms from molecular hydrogen. The cascade calculations have been done with an updated version of the extended standard cascade model that computes the evolution in the kinetic energy from the beginning of the cascade. The resulting X-ray yields, kinetic energy distributions, and cascade times are compared with the experimental data.

Collisional deexcitation of exotic hydrogen atoms in highly excited states: II. Cascade calculations

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Collisional deexcitation of exotic hydrogen atoms in highly excited states. II. Cascade calculations

Collisional deexcitation of exotic hydrogen atoms in highly excited states: II. Cascade calculations