Parity violation effects in hydrogen atom in forbidden magnetic-dipole transitions

General expressions for the probability of all strongly forbidden magnetic-dipole transitions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived in the lowest order in the parameter (αZ) in the form W _n′jl;njl ^(Ml) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, Z is the nuclear charge, and the constants D _n′n ^lj are presented in an analytical form. Using these expressions, the dependence of the degree of parity violation on the principal quantum numbers n and n′ of the lower and upper states in the ns _1/2-n′s _1/2 and np _1/2-n′p _1/2 M1 transitions is systematically analyzed. The results obtained can be used in designing experiments on parity violation in the hydrogen atom.     

Perturbation of the excited states of the hydrogen atom and hydrogen-like ions by a neutral atom

Owing to the degeneracy of the energy levels, the wavefunction of the electron in the excited states of the hydrogen atom and hydrogen-like ions perturbed by a neutral atom B is significantly different from the wavefunction of the unperturbed state. The perturbed function has a wide high maximum in the region of atom B, which is explained by multiple collisions of the electron with atom B, because the classical trajectories in the Coulomb field are closed and the size of atom B is much smaller than the size of the excited-state orbit. The radiative lifetimes of the excited states are much larger than those of unperturbed states. The orbital angular momentum L of the excited electron is strongly changed in collisions with atom B owing to the quantum interference or mixing of the temporal phases of adiabatic wavefunctions. The cross sections for such a change in the orbital angular momentum are several orders of magnitude larger than the cross sections found in early investigations in the approximation of the single collision of the electron with atom B.     

A nonlinear electrodynamical shift of spectral lines in the hydrogen atom and hydrogen-like ions

The shift of spectral lines in the hydrogen atom and hydrogen-like ions is calculated using Born-Infeld nonlinear electrodynamics. The formulas obtained show that the position of the s levels in hydrogen-like ions and muonic atoms should be most strongly affected by the nonlinearity of electrodynamics of vacuum.     

Two-quantum transitions between the fine-structure levels of a hydrogen-like atom

A study is made of the probability of two-quantum spontaneous transitions between fine-structure levels for fixed value of the principal quantum number (the radiation spectrum and the total transition probabilities are calculated) on the basis of the solution of the Dirac equation in a Coulomb field with arbitrary value of the charge of the nucleus.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 20–24, July, 1980.     

Above-threshold ionization of hydrogen and hydrogen-like ions by X-ray pulses

This paper adresses the problem of above-threshold ionization (ATI) of hydrogen interacting with an intense X-ray electromagnetic field. Two approaches have been used. In the first approach, we calculate generalized differential and total cross sections based on second-order perturbation theory for the electron interaction with a monochromatic plane wave, with the A ² and A · P contributions from the nonrelativistic Hamiltonian (including retardation) treated exactly. In the second approach, we solve the time-dependent Schrödinger equation (TDSE) for a pulsed plane wave using a spectral approach with a basis of oneelectron orbitals, calculated with L ²-integrable B-spline functions for the radial coordinate and spherical harmonics Y _lm for the angular part. Retardation effects are included up to O(1/c), they induce extra terms forcing the resolution of the TDSE in a three dimensional space. Relativistic effects [of O (1/c ²)] are fully neglected. The isoelectronic series of hydrogen is explored in the range Z = 1 ? 5 in both TDSE and perturbative approaches. Photoelectron angular distributions are obtained for photon energies of 1 keV and 3 keV for hydrogen, and photon energy of 25 keV for the hydrogenic ion B⁴⁺. Perturbative and TDSE calculations are compared.     

Magnetooptics of magnetic-dipole transitions in the rare-earth paramagnetic garnets

The Faraday effect (FE) of the rare-earth (RE) paramagnetic garnet crystals associated with magnetic-dipole (MD) transitions has been investigated theoretically over a wide temperature range 80 to 300 K. Over this temperature range, the ??gyromagnetic?? Verdet V _gm ^(m) of the Eu₃Ga₅O₁₂ (EuGG) is not a linear function of the magnetic susceptibility ?? measured along the [111] axis. We find that the nontrivial character of the temperature dependence of the MD Verdet constant V _gm ^(m) is associated with the presence of a contribution to the Faraday rotation of the Van Vleck ??mixing?? by an external magnetic field of the Eu³⁺ electronic states. The optical absorption and magnetic circular dichroism (MCD) of Eu³⁺ ion in EuGG at 85 K for the MD transition ⁷ F ₀ ?? ⁵ D ₁ were measured along the [111] axis. We show that the appearance of the MCD feature observed for the absorption line near 526.6 nm for the ⁷ F ₀ ?? ⁵ D ₁ MD absorption band may be well-explained by the contribution of Van Vleck ??mixing?? between the Stark singlet states from the ⁷ F ₀ and ⁷ F ₁ multiplet manifolds mixed by the external magnetic field H.     

氢及类氢离子光谱精细结构理论计算的改进

原子光谱数据是研究原子结构的重要参数,氢及类氢离子是原子物理和量子力学研究的理想体系.通过对氢及类氢离子光谱精细结构数据的研究发现,需要对Dirac提出的有关理论公式进行改进.本文在考虑了电子的自旋角动量与轨道角动量的耦合作用后,通过对Bohr理论中的电子运动角动量的修改,推导出单电子体系的电子速度公式,结合对Schr dinger的原子轨道能级表达式相对论效应修正,从而得出本文的氢及类氢离子光谱精细结构值的理论计算公式,应用此改进公式,所得的计算值与实验观测值符合得很好,计算结果也反映了氢及类氢离子光谱精细结构数据变化的规律性.     

Internal conversion in hydrogen-like ions

The probability of internal gamma-ray conversion is theoretically investigated for hydrogen-like ions versus the corresponding neutral atoms. The relevant calculations are performed by the relativistic Dirac-Fock method. The results reveal that the effect of multiple ionization on the coefficients of internal conversion in the K shell is maximal near the ionization threshold and for transitions of high multipole order, where this effect can be as great as a few orders of magnitude. The distinction between the coefficient of internal conversion in the K shell of a neutral atom and that in the respective hydrogen-like ion decreases with increasing transition energy, but it remains sizable for transitions of practical importance. It is found that the ionization of an atom to a hydrogen-like ion with allowance for conversion in external atomic shells may change significantly (by up to eight orders of magnitude) the lifetime of the nucleus being considered. The predicted effects can be observed in experiments with beams of relativistic heavy ions.     

High precision wavelength measurements of QED-sensitive forbidden transitions in highly charged argon ions

We present the results of an experimental study of magnetic dipole (M1) transitions in highly charged argon ions (Ar X, Ar XI, Ar XIV, Ar XV) in the visible spectral range using an electron beam ion trap. Their wavelengths were determined with, for highly charged ions, unprecedented accuracy up to the sub-ppm level and compared with theoretical calculations. The QED contributions, calculated in this Letter, are found to be 4 orders of magnitude larger than the experimental error and are absolutely indispensable to bring theory and experiment to a good agreement. This method shows great potential for the study of QED effects in relativistic few-electron systems.     

Probabilities of electric dipole transitions in the spectra of ions of the erbium isoelectronic sequence

The probabilities of the 4f ¹³6p→4f ¹³ ns (n=6 and 7) electric dipole transitions are calculated for the spectra of YbIII, LuIV, and HfV ions of the erbium isoelectronic sequence. The wave functions of the intermediate coupling scheme, which are necessary for calculating the relative line strengths, are semiempirically obtained from experimentally measured energy intervals between the fine-structure levels. To pass to the absolute values, radial integrals of transitions are used, which are evaluated with the Hartree-Fock functions.     

Resonance internal conversion in hydrogen-like ions

The resonance internal conversion effect in hydrogen-like ions is considered. For the M1 transition with an energy of 70.6 keV in ¹⁷¹Yb, the lifetime of this nucleus in the excited state decreases by five orders of magnitude as a result of deexcitation via a new channel—the resonance conversion—provided that the nuclear transition energy is equal to the energy of transition of a single 1s electron to a higher ns state. Observation of the resonance conversion in hydrogen-like ions is a powerful method for investigating their nuclear structure.     

Laser spectroscopy on forbidden transitions in trapped highly charged Ar(13+) ions

We demonstrate resonant fluorescence laser spectroscopy in highly charged ions (HCI) stored in an electron beam ion trap by investigating the dipole-forbidden 1s(2)2s(2)2p (2)P(3/2)-(2)P(1/2) transition in boronlike Ar(13+) ions. Forced evaporative cooling yielded a high resolving power, resulting in an accurate wavelength determination to λ=441.255?68(26) nm. By applying stronger cooling and two-photon excitation, new optical frequency standards based upon ultrastable transitions in such HCI could be realized in the future, e.g., for the search of time variations of the fine-structure constant.     

Radiative corrections to the magnetic-dipole transition amplitude in B-like ions

The one-electron quantum-electrodynamic corrections to the magnetic-dipole transition amplitude between the fine-structure levels (1s² 2s² 2p) ²P_3/2 - ²P_1/2 in boronlike ions are calculated to all orders in αZ. The results obtained serve for improving the theoretical accuracy of the lifetime of the (1s² 2s² 2p) ²P_3/2 level in boronlike argon.     

X-ray transitions in hydrogen-like,helium-like and lithium-like boron

The boron K X-ray spectra produced in heavy ion collisions using gas targets are reported. The observed X-ray transitions are used, to identify the one, two and three electron series of boron. The observed X-ray transition energies are found to agree well with theoretical calculations. A relatively large number of transitions involving double K-shell vacancies are observed. These transitions represent the first observation of double K-shell vacancies produced in collisions where the inner shell vacancies occur from electron promotion via molecular orbitals of the quasi-molecule formed during the collision.     

Beam-foil excitation studies of hydrogen-like ions

Ratios of initial populations of foil-excited hydrogen-like ions of He, B, C, N and O have been measured. Combined with earlier results for H obtained by Tielert they show aZ-dependence of the population process and indicate a velocity dependence as well. For the population of thenp-levels (n=2–5) of He⁺ ann-dependence ∞n ^?(3.6±0.4) has been observed.     

Relativistic correction for the Zeeman effect in a hydrogen-like atom

Based on an algebraic system of equations whose eigenvalues in the semirelativistic approximation determine the magnetic splitting of energy levels of two coupled Dirac particles with charges ±e and different masses, the splitting in extremely weak and weak magnetic fields is determined. In addition, a system of equations for charged particles with anomalous magnetic moments is given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–13, December, 2006.     

等离子体屏蔽效应对类氢离子束缚态的影响

在Debye屏蔽近似下,通过求解Schrödinger方程,计算了处于等离子体中的类氢离子的束缚态能量本征值与本征函数. 研究了氢原子和类氢Fe25+离子的n l ( n =1-4, l = 0-3)态能级随Debye 屏蔽长度λ的变化规律. 进一步,分析了等离子体屏蔽效应随主量子数n及角量子数l的变化规律, 发现对于给定的l, 等离子体屏蔽效应随主量子数n的增加而增大;对于给定的n,等离子体屏蔽效应随角量子数l 的增大而减小. 最后,我们分析了等离子体环境中类氢等电子序列离子的能级和波函数随屏蔽参数λ的变化规律,发现随着原子序数增大,等离子体屏蔽效应的影响逐渐变小.