A long-distance effective theory of hydrogen-like atoms, dubbed the relativistic Ritz approach was recently introduced and some its theoretical consequences were explored. In this article, the relativistic Ritz approach is used to fit extant measurements of atomic hydrogen and deuterium transitions using information-theoretic analyses. As a result, the fine-structure constant ($α$), a fundamental parameter of the Standard Model, may be determined simultaneously with the ionization energies of hydrogen and deuterium, $E_I^{\text{(H)}}$ and $E_I^{\text{(D)}}$. The best hydrogen analysis yields $α^{-1} = 137.035\,999\,185(25)$, in good agreement with the value obtained by other methods and without relying on a separately determined Rydberg constant. From the same analysis, I find that $E_I^{\text{(H)}} = 13.598\,434\,599\,684(25)\,\text{eV}$, an improvement of two orders of magnitude in precision compared to previous determinations and in agreement with the Standard Model prediction at 1.8 parts per trillion. The best deuterium analysis yields $E_I^{\text{(D)}} = 13.602\,134\,636\,543(31)\,\text{eV}$, agreeing with the Standard Model at 2.3 parts per trillion. This study demonstrates how the relativistic Ritz approach can be used for testing the Standard Model with the spectra of hydrogen-like atoms.
My previous calculations of the Lamb shift in muonic hydrogen are reviewed and compared with other work. In addition, numerical results for muonic deuterium are presented.
We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g-factor of the electron, which was previously the most accurate prediction of QED.
We calculate the cross-damping frequency shift of a laser-induced two-photon transition monitored through decay fluorescence, by adapting the analogy with Raman scattering developed by Amaro et al. [P. Amaro et al., PRA 92, 022514 (2015)]. We apply this method to estimate the frequency shift of the 1S-3S transition in hydrogen and deuterium. Taking into account our experimental conditions, we find a frequency shift of less than 1 kHz, that is smaller than our current statistical uncertainty.
The triatomic hydrogen ion (H$_3^+$) has spurred tremendous interest in astrophysics in recent decades, and Rydberg states of H$_3$ have also maintained an important role for understanding H$_3^+$ experiments. In a previous study [J. Chem. Phys. \textbf{133}, 234302 (2010)], radiative transitions between neutral H$_3$ Rydberg states were calculated at wavelengths near 7 microns, and could be compared with mid-infrared laser lines observed in hydrogen/rare gas discharges. The present study extends the investigation to wavelengths near 10 -- 13 microns. Rydberg states of D$_3$ are also treated.
We report the first direct observation of excited state muon transfer in hydrogen/deuterium mixtures by direct measurement of q_1s, the probability that a mu-p atom, which is initially formed in an excited state, reaches the 1s ground state. The dependence of q_1s on deuterium concentration c_d was measured for two different densities at cryogenic temperatures using charge coupled devices (CCDs) to detect the muonic X rays. First results based on the analysis of the K_alpha-lines of the two isotopes are presented.
The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic foundation. Here I present a long-distance relativistic effective theory describing hydrogen-like systems with arbitrary mass ratios, thereby extending the canonical Ritz-like approach. Fitting the relativistic theory to the hydrogen energy levels predicted by bound-state QED indicates that it is superior to the canonical, nonrelativistic approach. An analytic analys…
We study the 1S-3S two-photon transition of hydrogen in a thermal atomic beam, using a homemade cw laser source at 205 nm. The experimental method is described, leading in 2017 to the measurement of the 1S-3S transition frequency in hydrogen atom with a relative uncertainty of $9 \times 10^{-13}$. This result contributes to the "proton puzzle" resolution but is in disagreement with the ones of some others experiments. We have recently improved our setup with the aim of carrying out the same measurement in deuterium. With the improved detection system, we have observed a broadened fluorescence …
A counterintuitive scheme to produce ultracold hydrogen via fragmentation of laser cooled diatomic hydrides is presented where the final atomic H temperature is inversely proportional to the mass of the molecular parent. In addition, the critical density for formation of a Bose-Einstein Condensate (BEC) at a fixed temperature is reduced by a factor ratio hydrogen mass: parent mass raised to power 3/2 over directly cooled hydrogen atoms. The narrow Feshbach resonances between a singlet S atom and hydrogen are well suited to a tiny center of mass energy release necessary during fragmentation. Wi…
Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of phot…
The radiative correction to the nuclear charge radius contribution to the Lamb shift of order $α(Zα)^5m_r^3<r^2>$ is calculated. In view of the recent high precision experimental data, this theoretical correction produces a significant contribution to the hydrogen-deuterium isotopic shift.
The ASACUSA collaboration is developing a polarized beam of antihydrogen atoms to precisely determine the ground-state hyperfine structure for studies of CPT and Lorentz invariance. Using a beam of ordinary hydrogen, measurements of both the $σ$ and $π$-transition have been performed, investigating orientation-dependent SME coefficients. Furthermore a first hyperfine experiment with a beam of deuterium is being prepared.
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.
We present a detailed study about ion-atom-atom three-body recombination in hydrogen and deuterium plasmas based on classical trajectory calculations in hyperspherical coordinates. Our results, due to the predominant role of the long-range charged-induced dipole interaction, indicate that H$_2^+$ and D$_2^+$ are the main reaction products in the case of hydrogen and deuterium plasmas, respectively. Besides, we find a more steep energy-dependent reaction rate when the collision energy surpasses the dissociation energy of the molecular ion, thus entering a new dynamical regime dominated by short…
The prospects of tests of CPT symmetry using precision spectroscopy of antihydrogen are discussed with special emphasis on the ground-state hyperfine structure, a measurement of which is the aim of the ASACUSA collaboration at the AD/ELENA facility of CERN. Ongoing parallel experiments using hyperfine spectroscopy of hydrogen and deuterium aiming at studying Lorentz invariance by determining coefficients of the Standard Model Extension framework are described.
A theoretical study of the intense-field single ionization of molecular hydrogen or deuterium oriented either parallel or perpendicular to a linear polarized laser pulse (400 nm) is performed for different internuclear separations and pulse lengths in an intensity range of $(2-13)\times10^{13} $W cm$^{-2}$. The investigation is based on a non-perturbative treatment that solves the full time-dependent Schrödinger equation of both correlated electrons within the fixed-nuclei and the dipole approximation. The results for various internuclear separations are used to obtain the ionization yields of…
We determine the Zemach moments of hydrogen and deuterium for the first time using only the world data on elastic electron-proton and electron-deuteron scattering. Such moments are required for the calculation of the nuclear corrections to the hyperfine structure of these hydrogenic atoms. We compare the resulting HFS predictions to the available high-precision data and provide an estimate of the size of the nuclear polarization corrections necessary to produce agreement between experimental HFS and theoretical calculations.
The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Zalpha)^4 mu^3/m_N^2 is evaluated for muonic hydrogen and deuterium, and muonic helium ions (mu is the reduced mass and m_N is the nuclear mass). Relativistic corrections to vacuum polarization of order alpha (Zalpha)^4 mu are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to vacuum polarization of order alpha (Zα)^5 ln^2(Zalpha) mu^2/m_…
We consider the most accurate tests of bound state QED theory of the hyperfine splitting in two-body atoms related to the HFS interval of the 1s state in muonium and positronium and the 2s state in hydrogen, deuterium and the helium-3 ion. We summarize their QED theory and pay special attention to involved effects of strong interactions and to recent optical measurements of the 2s HFS interval in hydrogen and deuterium. We present results for specific ratios of the 1s-2s frequencies in hydrogen and deuterium which happen to be among the most accurately measured and calculated quantities.
The HERMES hydrogen and deuterium nuclear-polarized gas targets have been in use since 1996 with the polarized electron beam of HERA at DESY to study the spin structure of the nucleon. Polarized atoms from a Stern-Gerlach Atomic Beam Source are injected into a storage cell internal to the HERA electron ring. Atoms diffusing from the center of the storage cell into a side tube are analyzed to determine the atomic fraction and the atomic polarizations. The atoms have a nuclear polarization, the axis of which is defined by an external magnetic holding field. The holding field was longitudinal dur…
The formation and various disintegration modes of $2s$ states for muonic hydrogen and deuterium atoms at kinetic energies both above and below the $2s-2p$ threshold are studied. The cross sections of the collision-induced radiative quenching, elastic scattering, and Coulomb deexcitation of $(μ^- p)_{2s}$ and $(μ^- d)_{2s}$ atoms in collisions with ordinary hydrogen and deuterium atoms at collision energies below the $2s-2p$ threshold are calculated in the framework of the close-coupling approach. The basis set includes all open and closed channels corresponding to exotic-atom states with princ…
Theoretical investigations of the hyperfine structure of the hydrogen molecular ion (one electron and two protons) are discussed. The nuclear spin-rotation interaction has been found to be of the same sign as in the hydrogen molecule and the hyperfine transition frequencies can be accurately predicted. With measurements of the hyperfine structure of the deuterium molecular ion (or of HD+) it should be possible to obtain a value of the deuteron quadrupole moment that could be compared with the values obtained from the deuterium molecule and from nuclear theory.
Recently, the production of ultrahigh-density (~10^{19}cm^{-3}) spin-polarized deuterium (SPD) atoms was demonstrated, from the photodissociation of deuterium iodide, but the upper density limit was not determined. Here, we present studies of spin-polarized hydrogen (SPH) densities up to 10^{20} cm^{-3}, by photodissociating 5 bar of hydrogen chloride with a focused 213 nm, 150 ps laser pulse. We extract the depolarization cross-section of hydrogen and chlorine atom collisions, which is the main depolarization mechanism at this high-density regime, to be σ_{HCl} = 7(2) x 10^{-17}cm^2. We discu…
Contributions to the energy levels in light muonic atoms and, in particular, to the Lamb shift fall into a few well-distinguished classes. The related diagrams are calculated using different approaches. In particular, there is a specific kind of non-relativistic contributions. Here we consider such corrections to the Lamb shift in order $α^5m_μ$. These contributions are due to free vacuum polarization loops as well as to various effects of light-by-light scattering. The closed loop in the related diagrams is an electronic one, which allows a non-relativistic consideration of the muon. Both kin…
We discuss how measurements of fluctuations in the absorption of cosmic microwave background (CMB) photons by neutral gas during the cosmic dark ages, at redshifts z ~ 7--200, could reveal the primordial deuterium abundance of the Universe. The strength of the cross-correlation of brightness-temperature fluctuations due to resonant absorption of CMB photons in the 21-cm line of neutral hydrogen with those due to resonant absorption of CMB photons in the 92-cm line of neutral deuterium is proportional to the fossil deuterium to hydrogen ratio [D/H] fixed during big bang nucleosynthesis (BBN). A…
The analytic form of the electrostatic potential felt by a slowly moving test charge in quantum plasma is being derived. It has been shown that the potential composed of two parts: Debye-Huckel screening term and near-field wake potential which depends on the velocity of the test charge and the number density of the plasma electrons. Rayleigh-Ritz variational calculation has been done to estimate precise energy eigenvalues of hydrogen-like ion under such plasma environment. A detailed analysis shows that the energy levels are gradually moves to the continuum with increasing plasma electron den…
Nuclear-polarizability corrections that go beyond unretarded-dipole approximation are calculated analytically for hydrogenic (atomic) S-states. These retardation corrections are evaluated numerically for deuterium and contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our results are in agreement with one previous numerical calculation, and the retardation corrections completely account for the difference between two previous calculations. The uncertainty in the deuterium polarizability correction is substantially reduced. At the level of 0.01 kHz for deuterium, only th…
In this work, we consider the thermal correction to the hyperfine interaction in hydrogen, deuterium, and the $^3$He$^+$ ion. This correction is effectively described by one-loop Feynman graphs in the framework of the quantum electrodynamics theory for bound states at a finite temperature. A simple analysis shows the importance of the obtained results for future prospects for measuring hyperfine splitting. In addition, the application for testing the time variation of fundamental constants is briefly discussed.
Nuclear-size corrections of order $(Z α)^5$ and $(Z α)^6$ to the S-state levels of hydrogenic atoms are considered. These nuclear-elastic contributions are somewhat smaller than the polarizability (nuclear-inelastic) corrections for deuterium, but are of comparable or larger size for the hydrogen case. For deuterium the (attractive) nonrelativistic $(Z α)^5$ correction to the 2S-1S transition is 0.49 kHz, while the (repulsive) relativistic $(Z α)^6$ contribution is -3.40 kHz. For the proton the corresponding corrections are 0.03 kHz and -0.61 kHz, respectively. The $(Z α)^5$ contribution large…
The muonic hydrogen experiment measuring the $2P-2S$ transition energy [R. Pohl {\em et al.}, Nature {\bf 466}, 213 (2010)] is significantly discrepant with theoretical predictions based on quantum electrodynamics. A possible approach to resolve this conundrum is to compare experimental values with theoretical predictions in another system, muonic deuterium $μ$D. The only correction which might be questioned in $μ$D is that due to the deuteron polarizability. We investigate this effect in detail and observe cancellation with the elastic contribution. The total value obtained for the deuteron s…
GRASIAN: Shaping and characterization of the cold hydrogen and deuterium beams for the forthcoming first demonstration of gravitational quantum states of atoms
Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences（奥地利科学院斯特凡·迈耶亚原子物理研究所）；Institute for Particle Physics and Astrophysics, eth（苏黎世联邦理工学院粒子物理与天体物理研究所）；Department of Physics and Astronomy, University of Turku（图尔库大学物理与天文系）；Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Université, Collège de France（索邦大学卡斯特尔-布罗塞尔实验室（CNRS、巴黎高等师范学院-PSL大学、法兰西公学院））；Institut Max von Laue - Paul Langevin（马克斯·冯·劳厄-保罗·朗之万研究所）
From the comparison between the experimental and theoretical results for the energy difference between 2s1/2 and 2p1/2 states in hydrogen and hydrogen-like ions with different values of Z, we estimate bounds for the presence of an extra fractional dimension. These bounds are higher when we work with muonic hydrogen and muonic deuterium, which open the possibility that future measurements of the Lamb shift in muonic atoms with one electron and higher values of Z may show evidence of the extra dimension.
