Quantum mechanics in theK-field formalism: The kepler problem (without spin)

The primary goal of this work is to use a very well-known problem (the Kepler problem) to demonstrate the procedure for the construction in theK-field formalism of the nonrelativistic approximation of the quantum mechanical model of the stationary states of the hydrogen atom neglecting the spin properties of the electron. It is shown that the standard stationary states of the hydrogen atom correspond to Lyapunov-stable trajectories of theK particle (point test particle, the classical model of the electron in the atom). In spite of the electron being considered initially as a point particle without angular momentum, the internal logic of quantum mechanics in theK-field formalism requires the existence of the spin characteristics for the quantum mechanical model of the electron in the Kepler problem, even in the nonrelativistic approximation. Tomsk Polytechnic Institute. Translated fromIzvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 59–64, July, 1998.     

Features of the bremsstrahlung accompanying collisions with a hydrogen atom in an excited state

The features of the bremsstrahlung appearing during a collision of a fast charged particle with a hydrogen atom (or hydrogenic ion) in an excited state are investigated. It is shown that the emission spectrum of photons with energies greater than the ionization potential of a given excited state (except the 2s state) displays narrow lines, which are caused by de-excitation of the atom in an intermediate state. It is demonstrated that the scattering of a charged particle on an excited hydrogen atom produces a feature which is not observed in the case of scattering on a ground-state hydrogen atom. Expressions are obtained for the generalized dynamic polarizability of the hydrogen atom and hydrogenic ions in the 1s, 2s, and 3s states. A method is developed for deriving expressions for the generalized dynamic polarizabilities of other excited states through the use of the Coulomb Green’s function and representation of the electronic wave function in terms of the differentiation of the generating functions of Laguerre polynomials. The bremsstrahlung cross sections for electrons and positrons colliding with hydrogen atoms in the 1s, 2s, and 3s states are calculated. Zh. Tekh. Fiz. 69, 7–13 (October 1999)     

Antiproton-hydrogen scattering at low-eV energies

In the scattering of negative particles other than the electron by atoms at lab-frame energies around 10 eV, an elastic process termed “brickwall scattering” might lead to a high probability for scattering angles around 180°. For an antiproton slowing in hydrogen, this backward scattering would result in the loss of nearly all of its energy in a single collision, since it and a hydrogen atom have nearly the same mass. Such energy loss would have a significant effect on the energy distribution of antiprotons at energies where capture by the protons of hydrogen is possible and might, thereby, affect the capture rate and the distribution of capture states. In the semiclassical treatment of the problem with an adiabatic potential energy, brickwall scattering is indeed present, and with a substantial cross section. However, this model appears to underestimate inelastic processes. Based on calculations for negative muons on hydrogen atoms, these processes appear to occur for about the same impact parameters as brickwall scattering and thus substantially reduce its effect.     

Mechanisms for long-range forces in the “three atoms+electron” system

The Born-Oppenheimer approximation is used to obtain an equation for the effective interaction of three atoms bound by a single electron. For low binding energies long-range forces arise between the atoms in an “electron + atom pair” that lead to bound states when the size of the three-atom cluster is several tens of angstroms. A system made up of alkali metal atoms is considered as an example. Zh. éksp. Teor. Fiz. 111, 1229–1235 (April 1997)     

Features of the structure and properties of β-FeSi<Subscript>2</Subscript> nanofilms and a β-FeSi<Subscript>2</Subscript>/Si interface

The electronic, geometric, and magnetic structure of nanofilms of the β phase of iron disilicide FeSi₂ with the (001), (100), and (010) surfaces have been simulated through density functional calculations. A substantial reconstruction of the (001) surface terminated with silicon atoms has been observed, which was accompanied by an increase in the surface symmetry and appearance of “squares” of silicon atoms. Analysis of the electron density of states (DOS) and spin DOS projected on the contributions of layers of atoms (LSDOS) indicates that all plates have metallic properties. The main contribution near the Fermi level comes from the surface iron layers and it decreases rapidly with an increase in the distance from the surface of the plate. Analysis of the calculated effective magnetic moments of atoms shows that the surface layers in the plates have a significant magnetic moment, in particular, iron layers on the (001) surface (1.89 μ_B/atom). The moments of atoms decrease rapidly with an increase in their distance from the surface. The electron and geometric regions of a (001)Si/FeSi₂ interface have been studied. Analysis of the LSDOS shows that the surface conducting state mainly determined by the contribution from the near-surface silicide layers is implemented in this region. The possibility of the formation of the perfect and sharp Si/FeSi₂ interface has been demonstrated.     

Moment coupling in the interaction of atoms and their ions with a 3<Emphasis Type="Italic">d</Emphasis>-electron shell

The moment coupling of an interacting ion and an atom with a 3d-electron shell is analyzed for the ground state of identical atoms and ions where resonant charge exchange proceeds with transition of a 4s-electron. The interaction of the ion charge with the atom quadrupole moment is important for this system along with the exchange interactions and spin-orbit interactions inside an isolated atom and an ion. The quadrupole moment for 3d-atoms in the ground states is evaluated. The hierarchy of interactions in a molecular ion is analyzed depending on ion-atom distances and is compared with the standard Hund scheme. The resonant charge exchange proceeds effectively at separations corresponding to an intermediate case between cases “a” and “c” of the Hund coupling scheme.     

Inelastic electron collisions with Rydberg atoms

The standard classical method of computer simulation is used for evaluation of the inelastic cross section in electron collisions with a highly excited (Rydberg) atom. In the course of collision, the incident and bound electrons move along classical trajectories in the Coulomb field of the nucleus, and the scattering parameters are averaged over many initial conditions. The reduced ionization cross section of a Rydberg atom by electron impact approximately corresponds to that of atoms in the ground states with valence s-electrons and coincides with the results of the previous Monte Carlo calculations. The cross section of an atom transition between Rydberg atom states as a result of electron impact is used for finding the stepwise ionization rate constant of atoms in collisions with electrons or the rate constant of three-body electron-ion recombination in a dense ionized gas because these processes are determined by kinetics of highly excited atom states. Surprisingly, the low-temperature limit of electron temperatures is realized when the electron thermal energy is lower than the atom ionization potential by about three orders of magnitude, as follows from the kinetics of excited atom states. The article is published in the original.     

单轴应变对H在α-Fe中占位及扩散的影响

采用基于密度泛函理论的第一性原理方法,研究了H在不同单轴应变下α-Fe中的间隙占位,计算了H原子的溶解能、态密度、电荷差分密度和电荷布居.结果表明:不同单轴拉压应变作用下,H原子优先占据四面体间隙(Ts)位,且随着压应变减小、拉应变增加,H原子越易溶于α-Fe.压应变使得Ts位的H获得更多的电子,而拉应变减少了这种电荷转移.应用LST/QST过渡态搜索计算垂直应变方向的扩散.八面体间隙位是邻近Ts位H的扩散过渡态.扩散激活能与应变呈线性关系,且随着压应变的增加,扩散激活能降低,扩散更容易.     

Theoretical study of the migration of the hydrogen atom adsorbed on aluminum nanowire

We study the behavior of a hydrogen atom adsorbed on aluminum nanowire based on density functional theory. In this study, we focus on the electronic structure, potential energy surface (PES), and quantum mechanical effects on hydrogen and deuterium atoms. The activation energy of the diffusion of a hydrogen atom to the axis direction is derived as 0.19 eV from PES calculations. The probability density, which is calculated by including quantum effects, is localized on an aluminum top site in both cases of hydrogen and deuterium atoms of the ground state. In addition, some excited states are distributed between aluminum atoms on the surface of the nanowire. The energy difference between the ground state and these excited states are below 0.1 eV, which is much smaller than the activation energy of PES calculations. Thus using these excited states, hydrogen and deuterium atoms may move to the axial direction easily. We also discuss the electronic structure of the nanowire surface using quantum energy density defined by one of the authors.     

High-order perturbation theory for the hydrogen atom in a magnetic field

The states of a hydrogen atom with principal quantum numbers n⩽3 in a constant uniform magnetic field ℋ are studied. Coefficients in the expansion of the energy of these states in powers of ℋ² up to the 75th order are obtained. Series for the energies of the states and the wave functions are summed to values of ℋ on the order of the atomic magnetic field. A generalization of the moment method upon which these calculations are based can be used in other cases in which a hydrogen atom is perturbed by a potential with a polynomial dependence on the coordinates. Zh. éksp. Teor. Fiz. 113, 550–562 (February 1998)     

ZrMn2（110）表面结构及吸氢机理的第一性原理研究

采用基于密度泛函理论(DFT)的平面波赝势(PW-PP)方法,研究了ZrMn2（110）清洁表面结构和氢原子在表面的吸附。弛豫表面结构的计算结果表明表面结构的最表层为曲面,且表面结构的原子间隙变小。由1Zr2Mn原子组成的空位是氢原子吸附在ZrMn2（110）表面的最佳吸附位,吸附能为3.352 eV,氢原子吸附后离表面的距离为1.140 Å。Mulliken电荷布居分析表明吸附的氢原子与表面原子的相互作用主要是接近氢原子的第一层原子与氢原子的相互作用。过渡态计算表明被吸附的氢原子进入表面内部需克服的最大势垒为1.033 eV。     

Pulsed magnetooptic compression of cold atoms

A method is proposed for increasing the density of cold atoms. The method is based on pulsed laser irradiation of the atoms in a nonuniform magnetic field. The interaction conditions under which the velocity of an atom is damped to a value that depends only on the magnitude of the magnetic field and the position of the atom at the moment it is irradiated by the laser field are found. The atom completely loses all memory of its initial coordinates and velocity. In a three-dimensional interaction geometry an irradiated atomic ensemble transforms into an ensemble contracting toward the origin. The basic physical processes accompanying the compression of atoms are studied. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 327–331 (10 September 1997)     

Atom as a “dressed” nucleus

We show that the electrostatic potential of an atomic nucleus “seen” by a fast charged projectile at short distances is quantum mechanically smeared due to nucleus motion around the atomic center of inertia. For example, the size of the “positive charge cloud” in the Hydrogen ground state is much larger than the proper proton size. For target atoms in excited initial states, the effect is even larger. The elastic scattering at large angles is generally weaker than the Rutherford scattering since the effective potential at short distances is softer than the Colombian one due to a natural “cutoff”. In addition, the large-angle scattering leads to target atom excitations due to pushing the nucleus (⇒ inelastic processes). The Rutherford cross section is in fact inclusive rather than elastic. These results are analogous to those from QED. Non-relativistic atomic calculations are presented. The difference and the value of these calculations arise from nonperturbatively (exact) nucleus “dressing” that immediately leads to correct physical results and to significant technical simplifications. In these respects a nucleus bound in an atom is a simple but rather realistic model of a “dressed” charge in the QFT. This idea is briefly demonstrated on a real electron model (electronium) which is free from infinities.      

Magnetic trapping of strongly-magnetized Rydberg atoms

Effective magnetic moments of drift Rydberg atoms in strong magnetic fields are obtained for different energy and angular-momentum states. Classical two-body trajectory calculations and quantum-mechanical one-body calculations are employed. For heavy atoms such as rubidium, the trapping dynamics can largely be explained by the net magnetic moment due to the cyclotron and the magnetron motion of the Rydberg electron. In light Rydberg atoms such as hydrogen, the intrinsic two-body nature of the dynamics becomes manifest in that the ionic motion significantly contributes to the effective magnetic moment. Also, light drift Rydberg atoms exhibit an anisotropic response to field-inhomogeneities parallel and transverse to the magnetic-field lines. The results are relevant to magnetic trapping of Rydberg atoms in strong-magnetic-field atom traps.     

Observation of a Rydberg series in H+H-: a heavy Bohr atom

We report on the realization of a heavy "Bohr atom," through the spectroscopic observation of a Rydberg series of bound quantum states at principal quantum numbers n=140 to 230. The system is made heavy by replacing an electron inside a hydrogen atom by a composite H- particle, thus forming a H+H- Coulombically bound system obeying the physical laws of a generalized atom with appropriate mass scaling.     

A computational NMR study of nitrogen substitutional impurity in the armchair BeO nanotube

The properties of nitrogen doped model of (5, 5) armchair beryllium monoxide nanotubes (BeONTs) have been investigated by density functional theory (DFT) and chemical shift parameters were calculated. A BeONT consisting of 60 Be, 60 atoms of O, and having a length of 1.67 nm was considered and each end of the nanotube was capped by 10 hydrogen atoms. The calculated results indicate that by replacing an O atom by N atom (N_O-doping), the chemical shift (CS) parameters of ⁹Be and ¹⁷O atoms are un-affected but replacing a Be atom with N (N_Be-doping) affects the CS parameters of O atoms. These results imply that role of nitrogen as an electron acceptor is more significant in the structure for which it dopes a Be atom.     

Mn掺杂ZnS(110)表面的电子结构和磁性

采用基于密度泛函理论的第-性原理方法,研究Mn掺杂ZnS(110)表面的电子结构和磁性.计算分析不同掺杂组态的几何参数、形成能、磁矩、电子态密度以及电荷密度.结果表明:单个Mn原子掺杂,替位于表面第二层的Zn原子时体系形成能最低,说明该层是最稳定的掺杂位置.对于两个Mn原子的掺杂,当Mn与Mn之间呈反铁磁耦合时体系最稳定.体系的总磁矩和自由Mn原子的磁矩差别很小,但是Mn原子的局域磁矩却依赖于Mn原子的3d态和近邻S原子的3p态的杂化作用,即受周围S原子环境的变化影响较大.此外,分析电荷密度图得出Mn原子替换Zn原子后与S原子形成了更强的共价键.     

Selected Problems of Relativistic Quantum Mechanics and Atomic Physics

The paper presents a brief review of the scientific work performed by the authors in the field of quantum mechanics and atomic, laser, and mathematical physics. The following problems are considered: the semiclassical theory of tunneling and multiphoton ionization of atoms and ions in a strong electromagnetic field; generalization of the Keldysh ionization theory to the relativistic case; calculation of the Coulomb corrections to the ionization rate of atoms for arbitrary values of the adiabaticity parameter γ: from γ ≪ 1 (the adiabatic region) to γ ≫ 1, when the laser field changes its direction and magnitude many times during the time of flight of the electron through the barrier; the Lorentz ionization of atoms moving in a constant magnetic field; the WKB approximation and the imaginary time method for describing electron tunneling through a time-varying barrier; the Stark effect in a strong field; the energy spectrum of a hydrogen atom in a strong and superstrong magnetic field; quantization with account of the barrier transparency; creation of electron-positron pairs from vacuum in a constant electric or intense pulsed (laser) field and the dependence of the number of pairs on the intensity and frequency of the laser field; the Feynman method of disentanglement of noncommuting operators and its applications: transitions between atomic states in an alternating magnetic field (the Majorana problem); a quantum oscillator with time-dependent frequency; and a singular oscillator. The mathematical problems of quantum mechanics are considered: the fall of a particle to the center; modification of the Bohr-Sommerfeld quantization condition for potentials with a barrier and the Kramers matching conditions; divergence of perturbation series and their summation; eigenvalues of the Casimir operators for irreducible representations of Lie groups, including the SU(2), SU(3), and SU(6) groups, which are widely used in physics.     

Band structure calculations for Heusler phase Co2YBi and half-Heusler phase CoYBi (Y=Mn, Cr)

We have studied the electron structure and magnetic properties of Heusler phase Co₂YBi and half-Heusler phase CoYBi (Y=Mn, Cr) by using the full-potential linearized-augmented plane-wave (FLAPW) method. Co₂MnBi and Co₂CrBi are predicted to be half-metallic magnetism with a total magnetic moment of 6 and 5 μ_B, respectively, well consistent with the Slater-Pauling rule. We also predict CoMnBi to be half-metallic magnetism with a slight compression. The gap origin for Co₂MnBi and Co₂CrBi is due to the 3d electron splitting of Mn (Cr) and Co atoms, and the gap width depends on Co electron splitting. The atom coordination surroundings have a great influence on the electron structure, and consequently the Y site in the X₂YZ structure has a more remarkable electron splitting than the X site due to the more symmetric surroundings. The investigation regarding the lattice constant dependence of magnetic moment shows that the Co magnetic moment exhibits an opposite behavior with the change of the lattice constant for Heusler and half-Heusler alloys, consequently leading to the different variation trends for total magnetic moment. The variation of total and atom magnetic moment versus lattice constant can be explained by the extent of 3d electron splitting and localization of Mn (Cr) and Co atoms for both the series of alloys.