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.
The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the ...electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S-2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering
, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle
, in line with recent determinations of the proton charge radius
, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.
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 size of the proton dos Santos, Joaquim M. F; Fernandes, Luis M. P; Liu, Yi-Wei ...
Nature (London),
07/2010, Letnik:
466, Številka:
7303
Journal Article
Recenzirano
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 experiments. The present most accurate value of rp (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants. This value is based mainly on precision spectroscopy of atomic hydrogen 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 constant). 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 shift (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 calculations 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 value 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.
Line shape analysis of the Kβ transition in muonic hydrogen Covita, Daniel S.; Anagnostopoulos, Dimitrios F.; Fuhrmann, Hermann ...
The European physical journal. D, Atomic, molecular, and optical physics,
2018/4, Letnik:
72, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The K
β
transition in muonic hydrogen was measured with a high-resolution crystal spectrometer. The spectrum is shown to be sensitive to the ground-state hyperfine splitting, the corresponding ...triplet-to-singlet ratio, and the kinetic energy distribution in the 3
p
state. The hyperfine splitting and triplet-to-singlet ratio are found to be consistent with the values expected from theoretical and experimental investigations and, therefore, were fixed accordingly in order to reduce the uncertainties in the further reconstruction of the kinetic energy distribution. The presence of high-energetic components was established and quantified in both a phenomenological, i.e. cascade-model-free fit, and in a direct deconvolution of the Doppler broadening based on the Bayesian method.
Graphical abstract
Pionic deuterium Strauch, Th; Amaro, F. D.; Anagnostopoulos, D. F. ...
The European physical journal. A, Hadrons and nuclei,
07/2011, Letnik:
47, Številka:
7
Journal Article
Recenzirano
Odprti dostop
The strong-interaction shift
ε
1
s
π
D
and broadening
Γ
1
s
π
D
in pionic deuterium have been determined in a high statistics study of the
π
D(3
p
-1
s
) 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
ε
1
s
π
D
= (−2356 ± 31) meV (repulsive) and
Γ
1
s
π
D
meV yielding for the complex
π
D scattering length
a
π
D
= −(24.99±0.33)+
i
(6.22
−0.26
+0.12
) × 10
−3
m
π
−1
. From the imaginary part, the threshold parameter for pion production is obtained to be
α
= (251
−11
+5
)
μ
b. This allows, in addition, and by using results from pion absorption in
3
He at threshold, the determination of the effective couplings
g
0
and
g
1
for
s
-wave pion absorption on isoscalar and isovector
NN
pairs.
We plan to measure several 2S-2P transition frequencies in mu He-4(+) and mu He-3(+) by means of laser spectroscopy with an accuracy of 50 ppm. This will lead to a determination of the corresponding ...nuclear rms charge radii with a relative accuracy of 3 x 10(-4), limited by the uncertainty of the nuclear polarization contribution. First, these measurements will help to solve the proton radius puzzle. Second, these very precise nuclear radii are benchmarks for ab initio few-nucleon theories and potentials. Finally when combined with an ongoing measurement of the 1S-2S transition in He+, these measurements will lead to an enhanced bound-state QED test of the 1S Lamb shift in He+.
Laser spectroscopy of muonic hydrogen Pohl, Randolf; Antognini, Aldo; Amaro, Fernando D. ...
Annalen der Physik,
09/2013, Letnik:
525, Številka:
8-9
Journal Article
Recenzirano
Odprti dostop
Muonic hydrogen (μp) is a very sensitive probe of the proton structure. Laser spectroscopy of two 2S‐2P transitions in μp was used to determine both the Lamb shift and the hyperfine splitting of the ...2S state in μp. The rms charge radius of the proton, Rch=0.84087(39) fm, was extracted from the Lamb shift. The Zemach radius of the proton, RZ=1.082(37) fm, was obtained from the 2S‐hyperfine splitting. This article summarizes the previously published findings.
Muonic hydrogen (μp) is a very sensitive probe of the proton structure. Laser spectroscopy of two 2S‐2P transitions in μp was used to determine both the Lamb shift and the hyperfine splitting of the 2S state in μp. The rms charge radius of the proton, Rch = 0.84087(39) fm, was extracted from the Lamb shift. The Zemach radius of the proton, RZ = 1.082(37) fm, was obtained from the 2S‐hyperfine splitting. This article summarizes the previously published findings.
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