The states of hydrogen atom with principal quantum number n <= 3 and zero magnetic quantum number in constant homogeneous magnetic field H are considered. The perturbation theory series is summed with the help of Borel transformation and conformal mapping of the Borel variable. Convergence of approximate energy eigenvalues and their agreement with corresponding existing results are observed for external fields up to n^3 H ~ 5. The possibility of restoring the asymptotic behaviour of energy levels using perturbation theory coefficients is also discussed.
The largest contributions to the $n=2$ Lamb-shift, fine structure interval and $2s$ hyperfine structure of muonic hydrogen are calculated by exact numerical evaluations of the Dirac equation, rather than by a perturbation expansion in powers of $1/c$, in the framework of non-relativistic quantum electrodynamics. Previous calculations and the validity of the perturbation expansion for light elements are confirmed. The dependence of the various effects on the nuclear size and model are studied
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.
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schrödinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth order in the strength of the perturbing magnetic field. In the case of the ground state, we correct an expression for the fourth-order correction to energy available in…
We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid uncertainty relationships are maintained. We then apply such considerations to the hydrogen atom to obtain the momentum space wave functions corresponding to the position space functions in paraboloidal coordinates. The advantages and disadvantages of employing the momentum representation are explored.
We investigate the muonic hydrogen 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition through a precise, non-perturbative numerical solution of the Dirac equation including the finite-size Coulomb force and finite size vacuum polarization. The results are compared with earlier perturbative calculations of (primarily) Borie, Martynenko, and Pachucki; and experimental results recently presented by Pohl et al., in which this very comparison is interpreted as requiring a modification of the proton charge radius from that obtained in electron scattering and electronic hydrogen analyses. We find no signifi…
"Does God play dice with the Universe?" The natural width of excited hydrogen atoms are found using the Bohr's model of this atom and de Broglie's ideas. The mean life time of the excited states is a characteristic only of a statistical ensemble of many atoms.
In this paper it is shown that if one accept assumption of de Broglie that "unitary wave-particle" exists simultaneously and this coexistence is real, then one can find the mean life time of the hydrogen atom of Bohr (intensities).
The resonant spectra of hydrogen and anti-hydrogen atoms in the presence of an external electric field are compared theoretically. It is shown that nonresonant corrections to the transition frequency contain terms linear in the electric field. The existence of these terms does not violate space and time parity and leads to a difference in the resonant spectroscopic measurements for hydrogen and anti-hydrogen atoms in an external electric field. The one-photon 1s-2p and the two-photon 1s-2s resonances are investigated.
One- and two-photon transitions in the hydrogen atom are analytically evaluated in the absence and in the presence of an external electric field. The emission probabilities are different for the hydrogen and anti-hydrogen atoms due to the existence of contributions, linear in electric field. The magnitude of these contributions is evaluated within the nonrelativistic limit. The Coulomb Green function method is applied. Different nonrelativistic "forms" for the decay probabilities in combination with different gauge choices are considered. The three-photon E1E1E1 2p-1s transition probability is…
The discrete spectrum of a q-analogue of the hydrogen atom is obtained from a deformation of the Pauli equations. As an alternative, the spectrum is derived from a deformation of the four-dimensional oscillator arising in the application of the Kustaanheimo-Stiefel transformation to the hydrogen atom. A model of the 2s-2p Dirac shift is proposed in the context of q-deformations.
The Dirac equation is used to provide a relativistic calculation of the binding energy of a hydrogen-like atom confined within a penetrable spherical barrier. We take the potential to be Coulombic within the barrier and constant outside the barrier. Binding energies are derived for the ground state of hydrogen for various barrier heights and confining radii. In addition, it is shown that without the introduction of the principle quantum number $n$, all energy states of the confined relativistic hydrogen atom, determined by a single quantum number $k$, transfer into the known energy states of t…
The connection between the quantum frequency of radiation by the transition of the electron from orbit n to orbit k and frequencies of circling of electron in these orbits for the atom of hydrogen is determined.
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…
Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The relativistic dynamical polarizability of hydrogen-like atoms is calculated and analysed.
The electron impact ionization of atomic hydrogen is calculated for incident elrctron energy 76.46 eV. The Hartree-Fock approximation is used to calculate the initial state which includes both bound and continum wave functions. The final state continuum electron wave functions are obtained in the potential of hydrogen ion. The interaction between the two final state continuum electrons is approximated with the screening potential determined variationally.
We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. Depending on the choice of the external fields the atoms may acquire both dynamical and geometrical quantum mechanical phases. As an example of the former, we show first in-beam spin rotation measurements on atomic hydrogen, which are in excellent agreement with theory. Additional calculations of the behaviour of the metastable 2S states of hydrogen reveal that the geometrical phases may exhibit the signature of parity-(P-)violation. This invites for po…
Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase-space are introduced and analyzed under physical basis. The Hydrogen atom is explored in the same context. Then we add a Hénon-Heiles potential to the Hydrogen atom in order to explore chaotic features.
As the simplest atomic system, the hydrogen atom plays a key benchmarking role in laser and quantum physics. Atomic hydrogen is a widely used atomic test system for theoretical calculations of strong-field ionization, since approximate theories can be directly compared to numerical solutions of the time-dependent Schrödinger equation. However, relatively little experimental data is available for comparison to these calculations, since atomic hydrogen sources are difficult to construct and use. We review the existing experimental results on strong-field ionization of atomic hydrogen in multi-cy…
The process of recombination for the hydrogen atom in the heat bath creating the blackbody radiation is descibed within the frameworks of quantum electrodynamics. For this purpose the self-energy for unbound electron in the field of the nucleus is considered. The imaginary part of this self-energy is directly connected with the recombination cross-section. The same procedure is applied to the hydrogen atom in the field of blackbody radiation. This leads to the new thermal correction to the process of recombination for the hydrogen atom in the heat bath. This correction takes into account the f…
Some first principles that, we believe, could serve as foundation for quantum theory of extended particles are formulated. It is also shown that in the point-like particles limit the non-relativistic quantum mechanics can be restored. As an illustration the soliton model of hydrogen atom is considered.
We calculate the atomic structure of hydrogen and helium, atoms and molecules in an intense magnetic field, analytically and numerically with a judiciously chosen basis.
The nonresonant (NR) corrections are estimated for the most accurately measured two-photon transition 1s-2s in the hydrogen atom. These corrections depend on the measurement process and set a limit for the accuracy of atomic frequency measurements. With the measurement process adopted in the modern experiments the NR contribution for 1s-2s transition energy can reach 10^{-3} Hz while the experimental inaccuracy is quoted to be +/- 46 Hz.
The electric dipole moment of the hydrogen-like atom induced by a monopole moving outside the electron shell is calculated. The correction to the energy of the ground state of the hydrogen atom due to this interaction is calculated.
In this paper it is shown that if one accept assumption of de Broglie that "unitary wave-particle" exists simultaneously and this coexistence is real, then one can find the mean life time of the hydrogen atom of Bohr (intensities). Something more, the acceptance of de Broglie's ideas show that a single excited hydrogen atom decays at exactly predictable moment (after excitation). The natural width of excited hydrogen atoms are found using the Bohr's model of this atom and de Broglie's ideas. The mean life time of the excited states is a characteristic only of a statistical ensemble of many ato…
The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno-Lewis formula for…
The asymmetry of the natural line profile for transitions in hydrogen-like atoms is evaluated within a QED framework. For the Lyman-alpha $1s-2p$ absorption transition in neutral hydrogen this asymmetry results in an additional energy shift of 2.929856 Hz. For the $2s_{1/2}-2p_{3/2}$ transition it amounts to -1.512674 Hz. As a new feature this correction turns out to be process dependent. The quoted numbers refer to the Compton-scattering process.
The recoil correction to the ground state energy of hydrogenlike atoms is calculated to all orders in αZ in the range Z = 1-110. The nuclear size corrections to the recoil effect are partially taken into account. In the case of hydrogen, the relativistic recoil correction beyond the Salpeter contribution and the nonrelativistic nuclear size correction to the recoil effect, amounts to -7.2(2) kHz. The total recoil correction to the ground state energy in hydrogenlike uranium (^{238}U^{91+}) constitutes 0.46 eV.
The linear Stark effect shows that the first excited state of hydrogen atom has large permanent electric dipole moment (EDM), d(H)=3eao (ao is Bohr radius). Using special capacitors our experiments discovered that the ground state K, Rb or Cs atom is polar atom with a large EDM of the order of eao as hydrogen atom of excited state. Their capacitance(C) at different voltage (V) was measured. The C-V curve shows that the saturation polarization of K, Rb or Cs vapor has be observed when the field E more than ten to the fifth power V/m. When the saturation polarization appeared, nearly all K, Rb o…
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…
High-precision hydrogen spectroscopy is an active field which helps to determine the Rydberg constant and proton charge radius, tests bound-state QED, and can search for Beyond Standard Model (BSM) Physics. Additionally, with recent demonstrations of anti-hydrogen trapping and spectroscopy, a new line of investigation is possible whereby hydrogen can be compared to its antimatter counterpart. The next generation of precision hydrogen spectroscopy will likely require additional motional control of the atomic sample - similar to what is possible with heavier elements. Unfortunately, laser coolin…
We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. There the atoms acquire geometric (Berry) phases that exhibit a new manifestation of parity-(P-)violation in atomic physics. We provide analytical as well as numerical calculations of the behaviour of the metastable 2S states of hydrogen. The conditions for electromagnetic field configurations that allow for adiabatic evolution of the relevant atomic states are investigated. Our results provide the theoretical basis for the discussion of possible measur…
Stochastic ionization of highly excited relativistic hydrogenlike atom in the monochromatic field is considered. A theoretical analisis of chaotic dynamics of the electron based on Chirikov's criterion is given. Critical value of the external field is evaluated analytically.
We apply the non-linear Euler-Heisenberg theory to calculate the electric field inside the hydrogen atom. We will demonstrate that the electric field calculated in the Euler-Heisenberg theory can be much smaller than the corresponding field emerging from the Maxwellian theory. In the hydrogen atom this happens only at very small distances. This effect reduces the large electric field inside the hydrogen atom calculated from the electromagnetic form-factors via the Maxwell equations. The energy content of the field is below the pair production threshold.
The cosmic microwave background covers the entire universe, which suggests the absence of ay closed system, except the universe itself. In this paper, I consider the effect of the cosmic microwave background on the hydrogen atom, which must be very small, otherwise, changes in energy levels would have been measurable. But how small is small? This I compute by considering a system in an environment or bath. I derived the bath's, (in this case the CMB) effect on the hydrogen atom in the Feynman-Vernon approach to an open system. The effect is small and quantified in terms of a correction to the …
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.
We consider pionic hydrogen A_(pi p), the bound pi^- p state. Within the quantum field theoretic and relativistic covariant approach we calculate the shift and width of the energy level of the ground state of pionic hydrogen caused by strong low-energy interactions treated perturbatively. The generalization of the Deser-Goldberger-Baumann-Thirring (DGBT) formulas (Phys. Rev. 96, 774 (1954)) is given. The generalized DGBT formulas for the energy level displacement of the ground state of pionic hydrogen contain the non-perturbative and model-independent correction about 1%, caused by the relativ…
We present a design for an atomic synchrotron consisting of 40 hybrid magnetic hexapole lenses arranged in a circle. We show that for realistic parameters, hydrogen atoms with a velocity up to 600 m/s can be stored in a 1-meter diameter ring, which implies that the atoms can be injected in the ring directly from a pulsed supersonic beam source. This ring can be used to study collisions between stored hydrogen atoms and molecular beams of many different atoms and molecules. The advantage of using a synchrotron is two-fold: (i) the collision partners move in the same direction as the stored atom…
Several gage-equivalent forms (including some novel ones) of the Schroedinger equation for a hydrogenlike atom in a time-dependent electric field of a laser pulse are presented. These forms allow to develop a perturbation theory for both small and rather large intensities of the electromagnetic field.
The convergent close-coupling method is applied to the calculation of fully differential cross sections for ionization of atomic hydrogen by 15.6 eV electrons. We find that even at this low energy the method is able to yield predictive results with small uncertainty. As a consequence we suspect that the experimental normalization at this energy is approximately a factor of two too high.
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…
Superatomic hydrogen: achieving effective aggregation of hydrogen atoms at pressures lower than that of metallic hydrogen
Institute of Atomic and Molecular Physics, Jilin University（吉林大学原子与分子物理研究所）；Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University（吉林大学物理学院教育部材料模拟方法与技术重点实验室）；Institute of Theoretical Chemistry, College of Chemistry, Jilin University（吉林大学化学学院理论化学研究所）
Stochastic ionization of highly excited relativistic hydrogenlike atom in the monochromatic field is investigated. A theoretical analisis of chaotic dynamics of the relativistic electron based on Chirikov criterion is given for the cases of one- and three-dimensional atoms. Critical value of the external field is evaluated analitically. The diffusion coefficient and ionization time are calculated.
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.
The Lorentz oscillator system is studied to interpret the spectral lines of hydrogen atoms. The dielectric constant of this system is analyzed, which takes into account the electrical polarization of hydrogen atoms. This dielectric constant gives the red shift of the spectral line and the appearance of the optical spectrum dip. This dip is on the blue side of the spectral position of the shifted line. The value of this red shift and the width of this dip strongly depend on the hydrogen atom concentration and the spectral position of the not shifted line. This red shift increases with an increa…
We present a convergent variational basis-set calculational scheme for elastic scattering of positronium atom by hydrogen atom in S wave. Highly correlated trial functions with appropriate symmetry are needed for achieving convergence. We report convergent results for scattering lengths in atomic units for both singlet ($=3.49\pm 0.20$) and triplet ($=2.46\pm 0.10$) states.
Recently, a precise measurement on the bound electron g factor in hydrogen-like carbon was performed [1]. We consider the present status of the theory of the g factor of an electron bound in a hydrogen-like atom and discuss new opportunities and possible applications of the recent experiment.
We obtain the next-to-next-to-leading-log renormalization group improvement of the spectrum of Hydrogen-like atoms with massless fermions by using potential NRQED. These results can also be applied to the computation of the muonic Hydrogen spectrum where we are able to reproduce some known double logs at O(mα^6). We compare with other formalisms dealing with log resummation available in the literature.
A theoretical method for the estimation of cross sections and rates for excitation and charge transfer processes in low-energy hydrogen atom collisions with neutral atoms, based on an asymptotic two-electron model of ionic-covalent interactions in the neutral atom-hydrogen atom system, is presented. The calculation of potentials and non-adiabatic radial couplings using the method is demonstrated. The potentials are used together with the multi-channel Landau-Zener model to calculate cross sections and rate coefficients. The main feature of the method is that it employs asymptotically exact ato…
