We make a comparison between the energy levels of the hydrogen atom, calculated by using standard methods, and that by using a modified Coulomb potential due to the interaction between the magnetic moments of the proton and electron. In this later method we use to ways. One is that in which we solve the Schroedinger equation with the modified Coulomb potential and some constraint conditions. The other is that in which we expand the modified Coulomb potential in Taylor series. The obtained results show that the first way gives a better agreement with experimental data.
The proton structure effects, including finite size, polarizability and self-energy is considered and their influence on energy levels of muonic hydrogen is recalculated. A new theoretical prediction for the Lamb shift is presented together with improved values of all known QED contributions.
The "proton radius puzzle" was recently solved by reducing the four-standard deviation discrepancy between the results for electronic hydrogen ($H$) and muonic hydrogen ($μH$) atoms to $3.3$ value. The value of the root-mean-square radius of the proton ($r_p$), extracted from experiments on measuring the one-photon $2s-4p$ transition and the Lamb shift in hydrogen, is now $0.8335(95)$ fm, that is in good agreement with the muonic hydrogen experiments, $0.84087(39)$ fm. Even so, these values deviate significantly from the CODATA value, which is determined as the average using the results for va…
High resolution spectroscopy of the hydrogen atom takes on particular importance in the new SI, as it allows to accurately determine fundamental constants, such as the Rydberg constant and the proton charge radius. Recently, the second most precisely measured transition frequency in hydrogen, 1S - 3S, was obtained in our group. In the context of the Proton Radius Puzzle, this result calls for further investigation.
We study the proton-hydrogen collision in the energy range from 0 to 5 K where the hyperfine structure of the hydrogen atom is important. The proper multichannel treatment of the hyperfine structure is found to be crucial at cold temperatures compared to the elastic approximation used for higher temperatures. Both elastic and hyperfine-changing inelastic processes are investigated using the newly developed multichannel quantum-defect theory (MQDT) as well as the traditional coupled-channel numerical method. Cross section results from the two methods coincide well throughout the energy range. T…
The current status of the determination of corrections to the hyperfine splitting of the ground state in hydrogen is considered. Improved calculations are provided taking into account the most recent value for the proton charge radius. Comparing experimental data with predictions for the hyperfine splitting, the Zemach radius of the proton is deduced to be $1.045(16)$ fm. Employing exponential parametrizations for the electromagnetic form factors we determine the magnetic radius of the proton to be $0.778(29)$ fm. Both values are compared with the corresponding ones derived from the data obtai…
We consider excitation of highly charged hydrogen-like ions by the impact of equivelocity electrons and protons. The kinetic energy of the protons is more than three orders of magnitude larger than that of the equivelocity electrons. It is shown, however, that despite this fact, the electrons can be much more effective in inducing excitation at collision velocities (slightly) above the threshold for electron impact excitation. The basic reason for this is the strong distortion of the motion of the electron by the attractive field of the nucleus of the highly charged ion.
Feasibility of extracting the proton weak charge from quantum-control measurements of atomic parity violation on the $2s-3s$ or $2s-4s$ transition in hydrogen
本文提出通过氢的 $2s-3s$ 或 $2s-4s$ 跃迁量子控制方案测量原子宇称破坏，以提取质子弱电荷，应对近期 W 玻色子质量异常，并评估了相关计算近似的准确度。
We present a new measurement of the $1S-3S$ two-photon transition frequency of hydrogen, realized with a continuous-wave excitation laser at 205 nm on a room-temperature atomic beam, with a relative uncertainty of $9\times10^{-13}$. The proton charge radius deduced from this measurement, $r_\text{p}=0.877(13)$ fm, is in very good agreement with the current CODATA-recommended value. This result contributes to the ongoing search to solve the proton charge radius puzzle, which arose from a discrepancy between the CODATA value and a more precise determination of $r_\text{p}$ from muonic hydrogen s…
We study electron loss from a hydrogen-like highly charged ion by the impact of equivelocity electrons and protons and also in collisions with hydrogen and helium. The collision velocity $v$ varies between $v_{min}$ and $v_{max}$, where $v_{min}$ and $v_{max}$ correspond to the energy threshold $\varepsilon_{th}$ for electron loss in collisions with a free electron and to $\approx 5 \, \varepsilon_{th}$, respectively. Our results show that in this range of $v$: i) compared to equivelocity electrons protons are more effective in inducing electron loss (due to a substantially larger volume of th…
This paper concerns the most intriguing question of modern atomic physics: determination of the proton root-mean-square (rms) charge radius ($r_p$). This problem was announced by the difference in $r_p$ values extracted from the experiments on measurement of transition frequencies in hydrogen ($H$) atom and measurement of Lamb shift in muonic hydrogen ($μH$) atom. The both experiments give the possibility for the very accurate comparison of values evaluated theoretically and experimentally. As a result of this analysis the value of proton charge radius extracted from the $μH$ experiment was fo…
The correction to the hydrogen Lamb shift due to the proton electric and magnetic polarizabilities is expressed analytically through their static values, which are known from experiment. The numerical value of the correction is $ - 71 \pm 11 \pm 7$ Hz.
The processes of electron excitation, capture, and ionization were investigated in proton collisions with atomic hydrogen in the initial $n=1$ and $n=2$ states at impact energies from 1 to 300 keV. The theoretical analysis is based on the close-coupling two-center basis generator method in the semiclassical approximation. Calculated cross sections are compared with previous results which include data obtained from classical-trajectory Monte Carlo, convergent close-coupling, and other two-center atomic orbital expansion approaches. There is an overall good agreement in the capture and excitatio…
The possible use of high-resolution rovibrational spectroscopy of the hydrogen molecular ions H + 2 and HD + for an independent determination of several fundamental constants is analyzed. While these molecules had been proposed for metrology of nuclear-to-electron mass ratios, we show that they are also sensitive to the radii of the proton and deuteron and to the Rydberg constant at the level of the current discrepancies colloquially known as the proton size puzzle. The required level of accuracy, in the 10 --12 range, can be reached both by experiments, using Doppler-free two-photon spectrosc…
Recently a high-precision measurement of the Lamb shift in muonic hydrogen has been performed. An accurate value of the proton charge radius can be extracted from this datum with a high accuracy. To do that a sufficient accuracy should be achieved also on the theoretical side, including an appropriate treatment of higher-order proton-structure effects. Here we consider a higher-order contribution of the finite size of the proton to the Lamb shift in muonic hydrogen. Only model-dependent results for this correction have been known up to date. Meantime, the involved models are not consistent eit…
Theoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high-precision determination of the proton charge radius drastically reduced the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two- and three-loop QED effects, which calls for further advances in their calculations. We review the present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen-like ions …
We show that the non-spherical charge distribution of the proton manifests itself in hydrogen hyperfine splitting as an increase (in absolute value) of the proton Zemach radius and polarization contributions.
Recently the muonic hydrogen lamb shift has been measured with unprecedented accuracy, allowing for a precise determination of the proton radius. This determination is 5 sigma away from the previous CODATA value obtained from (mainly) the hydrogen lamb shift and the electron-proton scattering. Within an effective field theory formalism, I will define the proton radius and briefly review some aspects of the theoretical prediction for the muonic hydrogen lamb shift, studying both the pure QED-like computation and the hadronic effects.
We present the leading-order prediction of baryon chiral perturbation theory for the proton polarizability contribution to the 2S hyperfine splitting in muonic hydrogen, and compare with the results of dispersive calculations.
The Lamb shift in muonic hydrogen was measured some time ago to a high accuracy. The theoretical prediction of this value is very sensitive to the proton-finite-size effects. The proton radius extracted from muonic hydrogen is in contradiction with the results extracted from elastic electron-proton scattering. That creates a certain problem for the interpretation of the results from the muonic hydrogen Lamb shift. For the latter we need also to take into account the two-photon-exchange contribution with the proton finite size involved. The only way to describe it relies on the data from the sc…
The 7 standard deviations between the proton rms charge radius from muonic hydrogen and the CODATA-10 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.
To date the magnetic radius of the proton has been determined only by means of electron-proton scattering, which is not free of controversies. Any existing atomic determinations are irrelevant because they are strongly model-dependent. We consider a so-called Zemach contribution to the hyperfine interval in ordinary and muonic hydrogen and derive a self-consistent model-independent value of the magnetic radius of the proton. More accurately, we constrain not a value of the magnetic radius by itself, but its certain combination with the electric-charge radius of the proton, namely, R_E^2+R_M^2.…
We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and pola…
We discuss the role of the so-called Darwin-Foldy term in the evaluation of the proton and deuteron charge radii from atomic hydrogen spectroscopy and nuclear scattering data. The question of whether this term should be included or excluded from the nuclear radius has been controversially discussed in the literature. We attempt to clarify which literature values correspond to which conventions. A detailed discussion of the conventions appears useful because a recent experiment [R. Pohl et al., Nature vol. 466, p. 213 (2010)] has indicated that there is a discrepancy between the proton charge r…
The recent conundrum with the proton charge radius inspires reconsideration of the corrections that enter into determinations of the proton size. We study the two-photon proton-structure corrections, with special consideration of the non-pole subtraction term in the dispersion relation, and using fits to modern data to evaluate the energy contributions. We find that individual contributions change more than the total, and present results with error estimates.
Energy-conserving, angular momentum-changing collisions between protons and highly excited Rydberg hydrogen atoms are important for precise understanding of atomic recombination at the photon decoupling era, and the elemental abundance after primordial nucleosynthesis. Early approaches to $\ell$-changing collisions used perturbation theory for only dipole-allowed ($Δ\ell=\pm 1$) transitions. An exact non-perturbative quantum mechanical treatment is possible, but it comes at computational cost for highly excited Rydberg states. In this note we show how to obtain a semi-classical limit that is a…
Proton structure effects in hydrogenic bound states are analyzed using nonrelativistic QED effective field theory. Implications for the Lamb shift in muonic hydrogen are discussed. Model-dependent assumptions in previous analyses are isolated, and sensitivity to poorly constrained hadronic structure in the two-photon exchange contribution is identified.
We present a new measurement constraining Lorentz and CPT violation of the proton using a hydrogen maser double resonance technique. A search for hydrogen Zeeman frequency variations with a period of the sidereal day (23.93 h) sets a clean limit on violation of Lorentz and CPT symmetry of the proton at the 10^{-27} GeV level.
We present new calculations of unified line profiles for hydrogen perturbed by collisions with protons. We report on new calculations of the potential energies and dipole moments which allow the evaluation of profiles for the lines of the Lyman series up to Lyman$δ$ and the Balmer series up to Balmer10. Unified calculations only existed for the lines Lyman$α$ to Lyman$γ$ and Balmer$α$ including the H$_2^+$ quasi-molecule. These data are available as online material accompanying this paper and should be included in atmosphere models, in place of the Stark effect of protons, since the quasi-mole…
The extremely precise extraction of the proton radius by Pohl et al. from the measured energy difference between the 2P and 2S states of muonic hydrogen disagrees significantly with that extracted from electronic hydrogen or elastic electron-proton scattering. This is the proton radius puzzle. The origins of the puzzle and the reasons for believing it to be very significant are explained. Various possible solutions of the puzzle are identified, and future work needed to resolve the puzzle is discussed.
We have designed a Euler approximation Monte-Carlo code for the calculation of the ionization of atomic hydrogen by protons with energies between 0.05 and 1.0 MeV. This code is used to calculate the total ionization cross sections s(E), the angular distribution double differential cross sections d2s/ (dW - dE) for electrons with energies of 150 eV ionized by 300 keV protons and the energy distribution d2s/ (dW - dE) for the ionized electrons emitted at 10o by protons of energy 300 keV. Our calculations are compared to experimental values of these quantities as well as independent calculations.…
The Lamb shift measurement and theory are now both a dynamically developing field and we give a review of the current data. Critical comparison of theory and experiment can be done using a value of the proton charge radius and we pay attention to several results of its determination.
We present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncert…
We investigate the influence of the spatial extent of the proton magnetization and charge densities on the 2S hyperfine splitting in muonic hydrogen. The use of a non-perturbative relativistic Dirac approach leads to corrections of 15% to values obtained from the perturbative treatment encapsulated by the Zemach radius, which surpass the next-leading order contribution in the perturbation series by an order of magnitude.
By solving the two-body Schordinger equation in a very high precise nonperturbative numerical (NPnum) way, we reexamine the contributions of fine, hyperfine structure splittings of muonic hydrogen based on the Breit potential. The comparison of our results with those by the first order perturbative theory ($^{1st}$PT) in the literature shows, when the structure of proton is considered, the differences between the results by the $^{1st}$PT and NPnum methods are small for the fine and hyperfine splitting of $2P$ state, while are about $-0.009$ meV and $0.08$ meV for the $F=1$ and total hyperfine…
In astrophysical regimes where the collisional excitation of hydrogen atoms is relevant, the cross sections for the interactions of hydrogen atoms with electrons and protons are necessary for calculating line profiles and intensities. In particular, at relative velocities exceeding ~1000 km/s, collisional excitation by protons dominates over that by electrons. Surprisingly, the hydrogen-proton cross sections at these velocities do not exist for atomic levels of n >= 4, forcing researchers to utilize extrapolation via inaccurate scaling laws. In this study, we present a faster and improved algo…
We demonstrate that criticisms concerning our work nucl-th/9704043, made in the recent preprint hep-ph/9903352, are unfounded. The improvements over our results claimed in hep-ph/9903352 are in fact spurious, being based mainly on misunderstandings and on dubious theoretical models.
The relevance of the electronic swap in the stopping process of proton by hydrogen is investigated. To this end, the Classical Trajectory Monte-Carlo method is used to calculate the k-stopping cross-section, i.e. the stopping cross-section given the occurrence of k-swaps during the collision. It is found that electron swaps can be used to label electron trajectories, as it seems to describe fairly well the extent of the electron-ion interaction during the collision. Depending on the ion energy, the number of swaps entering the stopping cross section may vary. In the keV range the number of swa…
We consider the proton structure corrections to hydrogen ground-state hyperfine structure, focusing on a state-of-the-art evaluation of the inelastic nucleon corrections--the polarizability corrections--using analytic fits to the most recent data. We find a value for the fractional correction Delta_{pol} of 1.3 \pm 0.3 ppm. This is 1--2 ppm smaller than the value of Delta_{pol}$ one would deduce using hyperfine splitting data and elastic proton structure corrections obtained from modern form factor fits. In addition, we discuss the derivations of the relevant formulas, paying attention to lept…
The correction to the hydrogen Lamb shift due to the proton electric and magnetic polarizabilities is expressed analytically through their static values, which are known from experiment. The numerical value of the correction to the hydrogen 1S state is $ - 71 \pm 11 \pm 7$ Hz. Correction to the H-D 1S-2S -- isotope shift due to the proton and neutron polarizabilities is estimated as $ 53 \pm 9 \pm 11$ Hz.
The goal of the FAMU experiment at RIKEN RAL is the measure of the hyperfine splitting of the ground state of the muonic hydrogen, to allow a determination of the proton Zemach radius with a precision better than $5 \times 10^{-3}$ . The comparison of this measurement with the ones done with ordinary hydrogen may help to solve the so-called "proton radius puzzle", triggered by the $6 σ$ discrepancy in the proton charge radius value as extracted from muonic Lamb shift and the value based on e-p scattering and ordinary hydrogen spectroscopy.
We comprehensively analyse the theoretical prediction for the Lamb shift in muonic hydrogen, and the associated determination of the proton radius. We use effective field theories. This allows us to relate the proton radius with well-defined objects in quantum field theory, eliminating unnecessary model dependence. The use of effective field theories also helps us to organize the computation so that we can clearly state the parametric accuracy of the result. In this paper we review all (and check several of) the contributions to the energy shift of order $α^5$, as well as those that scale like…
The production of anti-hydrogen ions in the GBAR experiment will occur via a two step charge exchange process. In a first reaction, the anti-protons from the ELENA ring at CERN will capture a positron from a positronium target producing anti-hydrogen atoms. Those interacting in the same positronium target will produce in a second step anti-hydrogen ions. This results in a dependence for the anti-ions production rate which is roughly proportional to the positronium density squared. We present a scheme to increase the anti-ions production rate in the GBAR experiment by tailoring the anti-proton …
The measurement of the 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition in muonic hydrogen by Pohl et al. and subsequent analysis has led to the conclusion that the rms radius of the proton differs from the accepted (CODATA) value by approximately 4%, corresponding to a 4.9 sigma discrepancy. We investigate the finite-size effects - in particular the dependence on the shape of the proton electric form-factor - relevant to this transition using bound-state QED with nonperturbative, relativistic Dirac wave-functions for a wide range of idealised charge-distributions and a parameterization of experime…
We calculate the amplitude T_1 for forward doubly-virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the gammaNDelta form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions o…
We explore the possibility that a new interaction between muons and protons is responsible for the discrepancy between the CODATA value of the proton radius and the value deduced from the measurement of the Lamb shift in muonic hydrogen. We show that a new force carrier with roughly MeV mass can account for the observed energy shift as well as the discrepancy in the muon anomalous magnetic moment. However, measurements in other systems constrain the couplings to electrons and neutrons to be suppressed relative to the couplings to muons and protons, which seems challenging from a theoretical po…
The uncertainty in the contribution to the Lamb shift in muonic hydrogen, $ΔE^{subt}$ arising from proton polarizability effects in the two-photon exchange diagram at large virtual photon momenta is shown large enough to account for the proton radius puzzle. This is because $ΔE^{subt}$ is determined by an integrand that falls very slowly with very large virtual photon momenta. We evaluate the necessary integral using a set of chosen form factors and also a dimensional regularization procedure which makes explicit the need for a low energy constant. The consequences of our two-photon exchange i…
The contribution from the axial-vector meson exchange to the potential of the muon-proton interaction in muonic hydrogen induced by anomalous axial-vector meson coupling to two photon state is calculated. It is shown that such contribution to the hyperfine splitting in muonic hydrogen is large and important for a comparison with precise experimental data. In the light of our result, the proton radius "puzzle" is discussed.
This PhD thesis is devoted to the low-energy structure of the nucleon (proton and neutron) as seen through electromagnetic probes, e.g., electron and Compton scattering. The research presented here is based primarily on dispersion theory and chiral effective-field theory. The main motivation is the recent proton radius puzzle, which is the discrepancy between the classic proton charge radius determinations (based on electron-proton scattering and normal hydrogen spectroscopy) and the highly precise extraction based on first muonic-hydrogen experiments by the CREMA Collaboration. The precision …
We obtain a model independent expression for the muonic hydrogen Lamb shift. This expression includes the leading logarithmic ${\cal O}(m_μα^6)$ terms, as well as the leading ${\cal O}(m_μα^5 \frac{m_μ^2}{m_ρ^2})$ hadronic effects. The latter are controlled by the chiral theory, which allows for their model independent determination. In this paper we give the missing piece for their complete expression including the pion and Delta particles. Out of this analysis and the experimental measurement of the muonic hydrogen Lamb shift we determine the electromagnetic proton radius: $r_p=0.8412(15)$ f…
We show how the "proton radius puzzle" emerging from the measurement of the Lamb shift in muonic hydrogen may be solved by means of a binding energy contribution due to an effective Yukawian gravitational potential related to charged weak interactions. The residual discrepancy from the experimental result should be mainly attributable to the need for the experimental determination of the gravitational radius of the proton. The absence of an analogous contribution in the Lamb shift of electronic hydrogen should imply the existence of generation-dependent interactions, corroborating previous pro…
We obtain a model-independent prediction for the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen. We use the relation of the Wilson coefficients of the spin-dependent dimension-six four-fermion operator of NRQED applied to the electron-proton and to the muon-proton sectors. Their difference can be reliably computed using chiral perturbation theory, whereas the Wilson coefficient of the electron-proton sector can be determined from the hyperfine splitting in hydrogen. This allows us to give a precise model-independent determination of the Wilson coefficient for th…
Determination of the proton charge radius by different methods has produced an inconsistency. The most precise value (from spectroscopy of muonic hydrogen) strongly disagrees with three less accurate values (from spectroscopy of ordinary hydrogen and deuterium, from relative measurements of the cross section of the elastic electron-proton scattering at MAMI and from evaluation of the world data on absolute measurements of e-p cross sections). Here, we question the accuracy of the determination of the proton charge radius by means of spectroscopy of ordinary hydrogen and deuterium and demonstra…
The discrepancy between the measured Lamb shift in muonic hydrogen and expectations from electron-proton scattering and regular hydrogen spectroscopy has become known as the proton radius puzzle, whose most "mundane" resolution requires a $> 5 σ$ shift in the value of the fundamental Rydberg constant. I briefly review the status of spectroscopic and scattering measurements, recent theoretical developments, and implications for fundamental physics.
Laser spectroscopy of muonic atoms has been recently used to probe properties of light nuclei with unprecedented precision. We introduce nuclear effects in hydrogen-like atoms, nucleon structure quantities (form factors, structure functions, polarizabilities) and their effects in the Lamb shift and hyperfine splitting (HFS) of muonic hydrogen ($μ$H). Updated theory predictions for the Lamb shift and HFS in $μ$H are presented. We review the challenges of the ongoing effort to measure the ground-state HFS in $μ$H and its impact on our understanding of the nucleon spin structure. To narrow down t…
We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a fit to low-$Q^2$ electron-proton elastic scattering cross section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).
