Relativistic Linear Response Wave Functions and Dynamic Scattering Tensor for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>States in Hydrogenlike Atoms

Yakhontov, V L

doi:10.1103/physrevlett.91.093001

Cited by 18 publications

(19 citation statements)

References 19 publications

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“…states with n ′ = n and |κ ′ | = |κ|, must be excluded in the hydrogenic case. Moreover, in this case, we also exclude almost degenerate states with n ′ = n but |κ ′ | = |κ| because their small finestructure energy differences are significantly affected by the Lamb shift and require a separate treatment [8,21] (see Sec. IV A).…”

Section: B Relativistic Polarizabilitiesmentioning

confidence: 99%

Relativistic polarizabilities with the Lagrange-mesh method

2014

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Relativistic dipolar to hexadecapolar polarizabilities of the ground state and some excited states of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the Lagrange-mesh method. This approach is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. The partial polarizabilities conserving the absolute value of the quantum number κ are also numerically exact with small numbers of mesh points. The ones where |κ| changes are very accurate when using three different meshes for the initial and final wave functions and for the calculation of matrix elements. The polarizabilities of the n = 2 excited states of hydrogenic atoms are also studied with a separate treatment of the final states that are degenerate at the nonrelativistic approximation. The method provides high accuracies for polarizabilities of a particle in a Yukawa potential and is applied to a hydrogen atom embedded in a Debye plasma.

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Section: B Relativistic Polarizabilitiesmentioning

confidence: 99%

Relativistic polarizabilities with the Lagrange-mesh method

2014

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“…If we absorb in our definition of α TL (ω) relativistic corrections to the dipole polarizability of relative order α 2 QED (see Ref. [18]) and all radiative corrections without cuts in the self-energy photon lines (of relative order α 3 QED , see Refs. [16,[19][20][21]), then we can write Eq.…”

Section: Length Gaugementioning

confidence: 99%

Functional form of the imaginary part of the atomic polarizability

Pachucki

2015

Eur. Phys. J. D

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The dynamic atomic polarizability describes the response of the atom to incoming electromagnetic radiation. The functional form of the imaginary part of the polarizability for small driving frequencies ω has been a matter of long-standing discussion, with both a linear dependence and an ω 3 dependence being presented as candidate formulas. The imaginary part of the polarizability enters the expressions of a number of fundamental physical processes which involve the thermal dissipation of energy, such as blackbody friction, and non-contact friction. Here, we solve the longstanding problem by calculating the imaginary part of the polarizability in both the length (" d · E") as well as the velocity-gauge (" p · A") form of the dipole interaction, verify the gauge invariance, and find general expressions applicable to atomic theory; the ω 3 form is obtained in both gauges. The seagull term in the velocity gauge is found to be crucial in establishing gauge invariance.

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“…This approximation was also made in Ref. [14]. Field-configuration dependent corrections are discussed in Sec.…”

Section: B Leading (Nonrelativistic) Dynamic Stark Shiftmentioning

confidence: 80%

“…By contrast, in a weak laser field, the atom-laser interaction can be treated perturbatively. The perturbative effect of a time varying electric field is commonly referred to as the dynamic or ac ("alternating current") Stark shift [11,14].…”

Section: Introductionmentioning

confidence: 99%

Relativistic and radiative corrections to the dynamic Stark shift: Gauge invariance and transition currents in the velocity gauge

Adhikari

2018

Phys. Rev. A

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We investigate the gauge invariance of the dynamic (ac) Stark shift under "hybrid" gauge transformations from the "length" ( E · r) to the "velocity" ( A· p) gauge. By a "hybrid" gauge transformation, we understand a transformation in which the scalar and vector potentials are modified, but the wave function remains unaltered. The gauge invariance of the leading term is well known, while we here show that gauge invariance under perturbations holds only if one takes into account an additional correction to the transition current, which persists only in the velocity gauge. We find a general expression for this current, and apply the formalism to radiative and relativistic corrections to the dynamic Stark effect, which is described by the sum of two polarizability matrix elements.

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Relativistic Linear Response Wave Functions and Dynamic Scattering Tensor for thens1/2States in Hydrogenlike Atoms

Cited by 18 publications

References 19 publications

Relativistic polarizabilities with the Lagrange-mesh method

Relativistic polarizabilities with the Lagrange-mesh method

Functional form of the imaginary part of the atomic polarizability

Relativistic and radiative corrections to the dynamic Stark shift: Gauge invariance and transition currents in the velocity gauge

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