Influence of external electric fields on multi-photon transitions between the 2s, 2p and 1s levels for hydrogen and anti-hydrogen atoms and hydrogen-like ions
D. Solovyev, L. Labzowsky, G. Plunien, V. Sharipov
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 also evaluated and possible applications of the results are discussed.
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 …
In this work, analytical formulas for the static multipole polarizabilities of hydrogen-like ions are derived by using the analytical wave functions and the reduced Green function and by applying a numerical fitting procedure. Our results are then applied to the studies of blackbody radiation shifts to atomic energy levels at different temperatures. Our analytical results can be served as a benchmark for other theoretical methods.
We develop {\it ab initio} relativistic QED theory for elastic electron scattering on hydrogen-like highly charged ions for impact energies where, in addition to direct (Coulomb) scattering, the process can also proceed via formation and consequent Auger decay of autoionizing states of the corresponding helium-like ions. Even so the primary goal of the theory is to treat electron scattering on highly charged ions, a comparison with experiment shows that it can also be applied for relatively light ions covering thus a very broad range of the scattering systems. Using the theory we performed cal…
Approximate scaling laws with respect to the nuclear charge are introduced for the time-dependent Dirac equation describing hydrogen-like ions subject to laser fields within the dipole approximation. In particular, scaling relations with respect to the laser wavelengths and peak intensities are discussed. The validity of the scaling relations is investigated for two-, three-, four-, and five-photon ionization of hydrogen-like ions with the nuclear charges ranging from $Z=1$ to $92$ by solving the corresponding time-dependent Dirac equations adopting the properly scaled laser parameters. Good a…
We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $mα^7 \ln(α)$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $mα^6$-order relativistic correction, for the case of H$_2^+$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.
We review recent experiments on HD$^+$ spectroscopy. The reduced proton-deuteron mass to electron mass ratio, $μ_{pd}/m_e$, is inferred from the comparison of theory and experiment. Theoretical issues related to the calculations of the spin structure, which are currently the main limiting factor of theoretical accuracy, are discussed.
The two-loop self-energy correction to the Lamb shift of hydrogen-like ions is calculated for the $1s$, $2s$, and $2p_{1/2}$ states and nuclear charge numbers $Z = 30$-$100$. The calculation is performed to all orders in the nuclear binding strength parameter $Zα$. As compared to previous calculations of this correction, numerical accuracy is improved by an order of magnitude and the region of the nuclear charges is extended. An analysis of the $Z$-dependence of the obtained results demonstrates their consistency with the known $Zα$-expansion coefficients.
We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous work. In particular, one-loop and two-loop QED corrections at $mα^7$ and $mα^8$ orders are recalculated in the framework of the adiabatic approximation, with systematic inclusion of corrections associated with vibrational motion. Improved theoretical transitions frequencies are obtained and found to be in very good agreement with recent high-precision spectr…
We present a theoretical investigation of the radiative recombination of twisted Bessel electrons with initially hydrogen-like (finally helium-like) heavy ions. In our study, we focus especially on the linear polarization of x-ray photons emitted in the electron capture into the ground $1s^2_{1/2}$ ionic state. Particular emphasis is placed on the question of how this polarization is affected if incident hydrogen-like ions are themselves spin-polarized. To explore such a "polarization transfer" we apply the density matrix theory and derive the Stokes parameters of recombination x-rays for the …
The total two-photon decay rate of hydrogen-like ions is studied using relativistic quantum electrodynamics. In particular, we analyse how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$-splines is used for the generation of quasi-complete atomic spectra and, hence, of the relativistic Green's function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2s_{1/2} \to 1s_{1/2} + 2γ$ and $2p_{1/2} \to 1s_{1/2} + 2γ$ decay of hydrogen-like ions …
Parametrization of the angular correlation and degree of linear polarization in two-photon decays of hydrogen-like ions
在二阶微扰理论和狄拉克相对论方程的框架下，研究了类氢离子的双光子衰变。特别注意的角度相关的发射的光子，以及两个光子之一的线性偏振的程度，如果第二个是刚刚观察到给定的角度。角相关和线性偏振度的表达式展开的$\cosθ$ -多项式，其系数取决于原子序数和能量共享的发射光子。包括更高的（电和磁）多极后，超出电偶极子近似的发射光子对的影响进行了讨论。沿着整个氢等电子序列（$1\le Z \le 100$），对跃迁$2s_{1/2}\rightarrow1s_{1/2}$、$3d_{3/2}\rightarrow1s_{1/2}$和$3d_{5/2}\rightarrow1s_{1/2}$进行系数计算。
New method for highly accurate calculations of the photodetachment cross-sections of the negatively charged hydrogen ions
本文提出了一种计算负氢离子光剥离截面的新方法。这种有效的，快速的和数值稳定的方法是基于使用的瑞利公式的球贝塞尔函数。利用为负电荷氢离子${}^{\infty}$ H $^{-}$，${}^{1}$ H $^{-}$（protium），${}^{2}$ H $^{-}$（deuterium D $^{-}$）和${}^{3}$ H $^{-}$（tritium T $^{-}$）构造的高精度、真实相关的变分波函数，测定了这些离子的光剥离截面.我们的方法允许一个调查的负电荷的氢离子的光剥离的问题完全，即没有任何限制的数值的光电子动量$p_e$。
Bound state properties and photodetachment of the negatively charged hydrogen ions
考虑了负氢离子H $^{-}$对恒星辐射光谱中红外和可见光辐射的吸收。导出了负电荷氢离子光剥离截面的显式表达式。以高精度和大量的光电子动量/能量测定了${}^{\infty}$ H $^{-}$、${}^{3}$ H $^{-}$（或T $^{-}$）、${}^{2}$ H $^{-}$（或D $^{-}$）和${}^{1}$ H $^{-}$离子的光电子横截面。我们介绍的标准，可用于评估的氢离子（S）的高精度波函数的整体质量。这些标准之一是基于对带负电荷的氢离子中的最低阶QED校正的高度精确计算，所述氢离子包括${}^{1}$ H $^{-}$（protium）、${}^{2}$ H $^{-}$（deuterium）、${}^{3}$ H $^{-}$（tritium）和具有无限重核的模型离子${}^{\infty}$ H $^{-}$。本文发展了一种计算不同阶贝塞尔函数的三体积分的有效方法。对带负电荷的氢离子的光剥离截面进行了初步的计算。本文简要地讨论了中性氢原子场中的逆韧致辐射。
Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We …
High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for the lowlying vibrational-rotational states of hydrogen molecular ions
Electronic stopping cross sections (SCS) of nickel, silicon and nickel-silicon alloys for protons and helium (He) ions are studied in the regime of medium and low energy ion scattering, i.e., for ion energies in the range from 500 eV to 200 keV. For protons, at velocities below the Bohr velocity the deduced SCS is proportional to the ion velocity for all investigated materials. In contrast, for He ions non-linear velocity scaling is observed in all investigated materials. Static calculations using density functional theory (DFT) available from literature accurately predict the SCS of Ni and Ni…
We consider the application of a basic principle of quantum theory, the tracelessness of a certain class of hamiltonians, to the precision spectroscopy of the molecular hydrogen ions. We show that it is possible to obtain the spin-averaged transition frequencies between states from a simple weighted sum of experimentally accessible spin-dependent transition frequencies. We discuss the cases ${\rm H}_{2}^{+}$ and ${\rm HD}^{+}$, which are distinct in the multipole character of their rovibrational transitions. Inclusion of additional frequencies permits canceling also the electric quadrupole shi…
