Perturbation Approach to the Self Energy of non-S Hydrogenic States

氢离子 Stark 效应作为自旋-1/2 粒子八分量相对论波动方程不定度规形式体系的检验

Stark effect of hydrogenic ions as a test of the indefinite-metric formalism of the eight-component relativistic wave equation for spin-$\frac{1}{2}$ particles

该论文通过计算氢离子 Stark 位移验证了八分量相对论波动方程的不定度规形式体系，证明其与 Dirac 结果一致，并揭示了自旋-场耦合和负范数态的必要性。

兰姆位移的简化分波展开

Simplified partial wave expansion of the Lamb shift

针对兰姆位移自能计算原有分波展开法收敛慢、需数十个分波的问题，提出改进方法，用更少分波即可获准确结果，在类氢和类锂硼基态验证，还讨论了低Z类氢离子高精度计算的可能。

Two-dimensional hydrogen-like atom in a weak magnetic field

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…

Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms

We investigate the gauge invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms. It is shown that an effective treatment of the correction using a Lamb-shift "potential" leads to equivalent results in both the length as well as the velocity gauges provided all relevant correction terms are taken into account. Specifically, the relevant radiative corrections are related to the energies that enter into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition that holds between the two …

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescr…

Polarized Gaussian basis sets from one-electron ions

We demonstrate that basis sets suitable for electronic structure calculations can be obtained from simple accuracy considerations for the hydrogenic one-electron ions $Y^{(Y-1)+}$ for $Y\in[1,Z]$, necessitating no self-consistent field calculations at all. It is shown that even-tempered basis sets with parameters from the commonly-used universal Gaussian basis set (UGBS) [E. V. R. de Castro and F. E. Jorge, J. Chem. Phys. 108, 5225 (1998)] reproduce non-relativistic spin-restricted spherical Hartree-Fock total energies from fully numerical calculations to better accuracy than UGBS, which is sh…

Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of $B$ splines and $B$ polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization o…