Relativistic corrections to the Bethe sum rule

Leung, P. T.; Long, S. A. T.

doi:10.1103/physreva.33.2827

Cited by 20 publications

(20 citation statements)

References 13 publications

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“…Shortly thereafter, Leung, Rustgi, and Long [33] considered relativistic corrections to the Bethe sum rule. In a non-relativistic theory, this sum can be readily evaluated exactly including all multipoles:…”

Section: Review Of Early Workmentioning

confidence: 99%

“…I will discuss the FWT [31], derive a formally exact expression for the sum rule, and then explain why the results of [33,35] are only valid when q is small. I will also show how to obtain an exact treatment of the q-dependence of the Bethe sum rule, using an FWT-type transformation introduced by Douglas and Kroll [38].…”

Section: Recent Advances 41 Relativistic Bethe Sum Rulementioning

confidence: 99%

“…Other sums, involving various moments of the energy transfer, were also evaluated [35]. It was suggested in [33] that use of a no-pair Hamiltonian [36] and/or field-theoretic techniques might be useful for consideration of many-electron atoms. Such techniques were later used by Aucar, Oddershede, and Sabin [37] in their work on the relativistic corrections to the Bethe sum.…”

Section: Review Of Early Workmentioning

confidence: 99%

“…al. [33] used an approach similar to that of [27], performing the FWT on H D for a one-electron system, obtaining…”

Section: Review Of Early Workmentioning

confidence: 99%

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Aspects of Relativistic Sum Rules

Cohen¹

2004

Theory of the Interaction of Swift Ions With Matter. Part 2

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The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques are described, along with a discussion of the source of difficulties inherent in such relativistic calculations. A connection is pointed out between certain sum rules for atomic interactions with charged particles and those for interactions with photons.

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Section: Review Of Early Workmentioning

confidence: 99%

Section: Recent Advances 41 Relativistic Bethe Sum Rulementioning

confidence: 99%

Section: Review Of Early Workmentioning

confidence: 99%

“…al. [33] used an approach similar to that of [27], performing the FWT on H D for a one-electron system, obtaining…”

Section: Review Of Early Workmentioning

confidence: 99%

See 2 more Smart Citations

Aspects of Relativistic Sum Rules

Cohen¹

2004

Theory of the Interaction of Swift Ions With Matter. Part 2

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“…[40] We wish to only observe the positive energy states from an electron in an atom or molecule, and therefore, we must project out the positive energy states. For a single electron system, the positive energy TRK sum rules to lowest-relativistic order (ordered in 1/c) have previously been derived [41][42][43] using a Foldy-Wouthuysen (FW) transformation, [44] …”

Section: Theorymentioning

confidence: 99%

Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients

Dawson

2015

Phys. Rev. A

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The effects of small relativistic corrections to the off-resonant polarizability, hyperpolarizability, and second hyperpolarizability are investigated. Corrections to linear and nonlinear optical coefficients are demonstrated in the three-level ansatz, which includes corrections to the Kuzyk limits when scaled to semi-relativistic energies. It is also shown that the maximum value of the hyperpolarizability is more sensitive than the maximum polarizability or second hyperpolarizability to lowest-order relativistic corrections. These corrections illustrate how the intrinsic nonlinear-optical response is affected at semi-relativistic energies.

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