A reduced green function of the Dirac equation with a coulomb potential. Second order Zeeman effect

Manakov, N. L.; Zapryagaev, S. A.

doi:10.1016/0375-9601(76)90536-3

Cited by 18 publications

(10 citation statements)

References 3 publications

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“…Levinger (1952) Cromer (1965b); Cromer and Waber (1965) Ooyle and Turner (1967,1968) Cromer and Liberman (1970) .0'verblZf (1977) Hubbell and 0verb~ (1979) Jensen (1980) Cromer and Liberman (1981) Analytical Mott (1929,1932) Moeller (1932) Bethe and Heitler (1934) Massey and Mohr (1941) Bethe and Maximon (1948) Khuri and Treiman (1958) Johnson et al (1964) Bunyan and Schonfelder (1965) Mott and Massey (1965) Browne and Bauer (1966) Schonfelder (1966) Dawson (1967) Doyle and Turner (1967, (1968) D.W. Walker (1969,1970,1975) D.W. Walker (1971) Jones (1974,1975) D.W. Walker (1974) Chang (1975) Davidovic and Moiseiwitsch (1975) Fano et al (1976) Chang (1977b) Pratt et al (1977) Almaliev and Batkin (1978) Oh and Macek (1978) Polarization of electrons by double scattering from atomic potentials. Inß~r-shell ionization of heavy elements Ndefru et al (1980); by slow and fast electrons.…”

Section: Reference Commentsmentioning

confidence: 96%

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Relativistic Theory of Atoms and Molecules

Pyykkö

1986

Lecture Notes in Chemistry

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Section: Reference Commentsmentioning

confidence: 96%

“…Casimir and Polder (1948) Dzyaloshinskii et al (1961) Hirschfe1der (1967) Certain and Bruch (1972) Varandas (1974) Michels (1976) Power (1978) Easa and Yousif (1982): Easa and Shukla (1983): Yousif and Easa (1982) Fischbach and Nakagawa (1984) Koga (1985) Retard 27 ion effects on London forces:…”

Section: Reference Commentsmentioning

confidence: 98%

Relativistic Theory of Atoms and Molecules

Pyykkö

1986

Lecture Notes in Chemistry

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“…The first group used the integral representation of the radial parts of the first-order Dirac-Coulomb Green function, whereas the second one exploited the Sturmian expansion of the second-order Dirac-Coulomb Green function, proposed by them at the beginning of the 1970's [4,5]. A few years later, Manakov et al extended their considerations to states with zero radial quantum number [6][7][8] (see also Ref. [9]).…”

Section: Introductionmentioning

confidence: 99%

Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

Stefańska

2015

Phys. Rev. A

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The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a pointlike, spinless and motionless nucleus of charge Ze. The result has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with 1 Z 137 and compare them with data available in the literature.

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“…Typically, such problems are solved using perturbation theory. See, e.g., the PT calculations of the second-order Zeeman effect in hydrogen-like ions [42][43][44][45][46][47], the second-and third-order Zeeman effects in boron-like ions [23][24][25][26][27], and the Zeeman splitting in hydrogen-, lithium-, and boron-like ions with nonzero nuclear spin [16][17][18][19][20][21][22]. Here we demonstrate application of the non-perturbative A-DKB method and compare the results with the PT calculations.…”

Section: Higher-order Contributions To the Zeeman Splittingmentioning

confidence: 89%

Helium-like ions in magnetic field: application of the nonperturbative relativistic method for axially symmetric systems

Volchkova,

Agababaev,

Glazov

et al. 2020

Preprint

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Dirac equation for an electron bound by a nucleus in the presence of external axially symmetric field can be solved numerically by using the dual-kinetic-balance conditions imposed on the finite basis set (A-DKB method [Rozenbaum et al., Phys. Rev. A 89, 012514 (2014)]). We present the application of this method to describe helium-like ions exposed to homogeneous external magnetic field. The second-order Zeeman shift and the nuclear magnetic shielding constant are evaluated for the ground state, including the leading contribution of the interelectronic interaction. The A-DKB values are compared with the direct calculations by perturbation theory. The results for the nuclear magnetic shielding can serve for accurate determination of the nuclear magnetic moments.The quadratic contribution to the Zeeman effect can be relevant for high-precision measurements of the transition energies in helium-like ions.

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A reduced green function of the Dirac equation with a coulomb potential. Second order Zeeman effect

Cited by 18 publications

References 3 publications

Relativistic Theory of Atoms and Molecules

Relativistic Theory of Atoms and Molecules

Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

Helium-like ions in magnetic field: application of the nonperturbative relativistic method for axially symmetric systems

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