Closed summation of large perturbation orders: the s-d series for hydrogen in a magnetic field

Schmidt, Heinar

doi:10.1088/0953-4075/24/13/010

Cited by 6 publications

(8 citation statements)

References 15 publications

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“…The cross-sections used in this study are those of Schmidt [5] as shown in figure 1. In these cross-sections, anisotropic elastic collisions are employed with the first three partial crosssection differences, σ 0 − σ l (l 3) specified.…”

Section: Electrons In Methanementioning

confidence: 99%

“…Suffice to say that periodic behaviour of electron properties in drift tubes is quite common, and can be explained physically in exactly the same way as for the Franck-Hertz experiment. In this paper, we consider a formalism suitable for dealing with both ions and electrons, and give results for electrons undergoing both conservative and nonconservative collisions, taking as examples methane gas [5] and the Lucas-Saelee model [6], respectively. The former is particularly interesting, since it exhibits marked negative differential conductivity (NDC), and requires a distinctly 'multi-term' analysis [2,[7][8][9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis

Li¹,

White²,

Robson³

2002

J. Phys. D: Appl. Phys.

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In reference (Robson R E, Li B and White R D 2000 J. Phys. B: At. Mol. Opt. Phys. 33 507), we revisited the Franck–Hertz experiment, and gave solutions of the Boltzmann equation describing the spatially-resolved relaxation profiles of a non-hydrodynamic swarm of electrons streaming at a steady rate from a plane source into mercury vapour. In this paper, we extend this study to other cases and develop a formalism for both ions and electrons and consider situations where both conservative and non-conservative collisions may take place. As in Robson et al (2000), we employ a `two-temperature' Burnett function representation of operators in velocity space in the Boltzmann equation. Configuration space is represented by a finite mesh of points and a finite difference technique is developed accordingly. Boundary conditions are specified for the general problem and techniques for solving the resulting large system of algebraic equations are discussed. The importance of a `multi-term' analysis and the existence of negative differential conductivity (NDC) under non-hydrodynamic conditions is displayed by considering electrons in methane. The explicit effect of ionization on the spatial relaxation profiles is considered along with a study on the importance of treating ionization as a true non-conservative process as opposed to another inelastic process. The spatial relaxation profiles are compared with predictions from eigenvalue theory.

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Section: Electrons In Methanementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis

Li¹,

White²,

Robson³

2002

J. Phys. D: Appl. Phys.

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“…For the ground state this regime is roughly given by γ = 0.2 − 20 (γ = B/B 0 is the magnetic field strength in atomic units, B 0 = hc/ea 2 0 = 2.3505•10 5 T). Both early [13] and more recent works [4,[14][15][16][17] on the hydrogen atom have used different approaches for relatively weak fields (the Coulomb force prevails over the magnetic force) and for very strong fields (the Coulomb force can be considered as weak in comparison with the magnetic forces which is the socalled adiabatic regime). In the latter regime the motion of the electron parallel to the magnetic field is dominated [18] by a 1D quasi-Coulomb potential including a parameter which depends on the magnetic field strength.…”

Section: Introductionmentioning

confidence: 99%

Ground state of the carbon atom in strong magnetic fields

Ivanov

Schmelcher

1999

Phys. Rev. A

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The ground and a few excited states of the carbon atom in external uniform magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for field strengths ranging from zero up to 2.35 · 10 9 T. With increasing field strength the ground state undergoes six transitions involving seven different electronic configurations which belong to three groups with different spin projections Sz = −1, −2, −3. For weak fields the ground state configuration arises from the field-free 1s 2 2s 2 2p02p−1, Sz = −1 configuration.With increasing field strength the ground state involves the four Sz = −2 configurations

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“…With increasing degree of excitation the domain of the intermediate fields lowers correspondingly and becomes, as a rule, wider on a logarithmic scale of γ. Both early [15] and more recent works [5,[16][17][18][19] on the hydrogen atom have used different approaches for relatively weak fields (the Coulomb force prevails over the magnetic force) and for very strong fields where the Coulomb force can be considered as weak in comparison with the magnetic forces (adiabatic limit). In early works the Coulomb field was considered in this limit actually as perturbation for a free electron in a superstrong magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Ground state of the lithium atom in strong magnetic fields

Ivanov

Schmelcher

1998

Phys. Rev. A

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The ground and some excited states of the Li atom in external uniform magnetic fields are calculated by means of our two-dimensional mesh Hartree-Fock method for field strengths ranging from zero up to 2.35 ϫ10 8 T. With increasing field strength, the ground state undergoes two transitions involving three different electronic configurations: for weak fields, the ground-state configuration arises from the field-free 1s 2 2s configuration; for intermediate fields, it arises from the 1s 2 2p Ϫ1 configuration, and in high fields, the 1s2 p Ϫ1 3d Ϫ2 electronic configuration is responsible for the properties of the atom. The transition field strengths are determined. Calculations on the ground state of the Li ϩ ion allow us to describe the fielddependent ionization energy of the Li atom. Some general arguments on the ground states of multielectron atoms in strong magnetic fields are provided.

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Closed summation of large perturbation orders: the s-d series for hydrogen in a magnetic field

Cited by 6 publications

References 15 publications

Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis

Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis

Ground state of the carbon atom in strong magnetic fields

Ground state of the lithium atom in strong magnetic fields

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