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Citations available: 42
Citations displayed: 1-42

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Citation 1
Accession Number
001882822
Author
Sergeev AV. Sherstyouk AI.
Title
Higher orders and structure of perturbation theory series for screened
Coulomb potential.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.82, no.4, April 1982,
pp.1070-8. USSR.
Country of Publication
USSR.
Translated Source
Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.
Abstract
An effective method is developed for calculating the higher orders in perturbation theory for potentials of the polynomial type. It is based on the transition to the problem of perturbation theory for the Fock operator with a purely discrete spectrum. Allowance for dynamic symmetry of the unperturbed operator permits one in this case to express the corrections of any order in perturbation theory as polynomials with rational coefficients. The method is employed to calculate the bound states of the Schroedinger equation with a screened Coulomb potential. The analytical properties of the solutions are investigated. Exact values of the energy in a broad range of variation of the screening parameter is obtained by the Pade technique. The real and imaginary parts of the energies of the quasi-stationary states are calculated. (34 References).
Abstract Number
A82069056
Subject Headings
Perturbation theory
Schrodinger equation
Key Phrase Identifiers
polynomial potential; perturbation theory series; screened Coulomb potential;
higher orders; Fock operator; dynamic symmetry; bound states; Schroedinger
equation; Pade technique.
Classification Codes
Functional analytical methods in quantum theory [A0365D]; Solutions of wave
equations: bound state in quantum theory [A0365G].
Treatment
Theoretical or mathematical.
CODEN
ZETFA7
Language
Russian.
ISSN
0044-4510.
Publication Type
Journal Paper.
Update Code
198200.

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Citation 2
Accession Number
002430389
Author
Sergeev AV. Sherstyuk AI.
Institution
S.I. Vavilov State Opt. Inst., USSR.
Title
Higher-order perturbation theory for the bound states of the Dirac equation
with Yukawa-type potential.
Source
Yadernaya Fizika, vol.39, no.5, May 1984, pp.1158-64. USSR.
Country of Publication
USSR.
Translated Source
Soviet Journal of Nuclear Physics (USA), vol.39, no.5, May 1984, pp.731-4.
CODEN: SJNCAS. ISSN: 0038-5506.
Abstract
The method of calculating higher orders of perturbation theory based on perturbation of the Fock operator with a purely discrete spectrum is generalized to the case of the Dirac equation with a potential of the Yukawa type. Corrections to any order of perturbation theory in the energy of an arbitrary bound state are given as finite polynomials which are determined through recurrence relations derived from the dynamical symmetry of the unperturbed problem. The authors propose a modified Pade approximant method which can be used to transform a divergent perturbation series into a rapidly convergent sequence for all bound and quasistationary states of the system. (19 References).
Abstract Number
A85046755
Subject Headings
Dirac equation
Meson field theory
Nuclear forces
Key Phrase Identifiers
nuclear forces; meson field theory; perturbation theory; bound states; Dirac
equation; Yukawa-type potential; Fock operator; discrete spectrum; finite
polynomials; recurrence relations; Pade approximant method.
Classification Codes
Relativistic wave equations and field theories [A1110Q]; Nuclear forces
[A2130].
Treatment
Theoretical or mathematical.
CODEN
IDFZA7
Language
English.
ISSN
0044-0027.
U.S. Copyright Clearance Center Code
0038-5506/84/050731-04$03.80.
Publication Type
Journal Paper.
Update Code
198500.

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Citation 3
Accession Number
002862263
Author
Vainberg VM. Mur VD. Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., USSR.
Title
Strong-field Stark effect.
Source
Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu,
vol.44, no.1, 10 July 1986, pp.9-12. USSR.
Country of Publication
USSR.
Translated Source
JETP Letters (USA), vol.44, no.1, 10 July 1986, pp.9-13. CODEN: JTPLA2. ISSN:
0021-3640.
Abstract
The Stark shifts and the widths of the ground and excited states of the hydrogen atom are calculated. Two independent calculation methods are used: a summation of a divergent perturbation-theory series and a 1/n expansion. (12 References).
Abstract Number
A87050008
Subject Headings
Atomic excited states
Atomic spectral line breadth
Hydrogen neutral atoms
Perturbation theory
Stark effect
Key Phrase Identifiers
ground state width; excited states width; Stark shifts; divergent
perturbation-theory series; H atom.
Classification Codes
Stark effect in atoms [A3260S]; Atomic line shapes, widths, and shifts
[A3270J].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
PZETAB
Language
English.
ISSN
0370-274X.
U.S. Copyright Clearance Center Code
0021-3640/86/130009-05$01.00.
Publication Type
Journal Paper.
Update Code
198700.

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Citation 4
Accession Number
003123826
Author
Vainberg VM. Mur VD. Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, USSR.
Title
Stark effect for the Rydberg states of the hydrogen atom.
Source
Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu,
vol.46, no.5, 10 Sept. 1987, pp.178-82. USSR.
Country of Publication
USSR.
Translated Source
JETP Letters (USA), vol.46, no.5, 10 Sept. 1987, pp.225-30. CODEN: JTPLA2.
ISSN: 0021-3640.
Abstract
The Stark shifts and the widths of highly excited (n=15-30) states of a hydrogen atom in a strong electric field, which is higher than the classical ionization threshold of an atom, are calculated. The results of the calculations are in agreement with the experiment. (11 References).
Abstract Number
A88060313
Subject Headings
Atomic excited states
Hydrogen neutral atoms
Ionisation of atoms
Stark effect
Key Phrase Identifiers
excited state width; Rydberg states; Stark shifts; strong electric field;
classical ionization threshold; atom; H.
Classification Codes
Excited states of atoms and molecules [A3150]; Stark effect in atoms
[A3260S].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
PZETAB
Language
English.
ISSN
0370-274X.
U.S. Copyright Clearance Center Code
0021-3640/87/170225-06$01.00.
Publication Type
Journal Paper.
Update Code
198800.

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Citation 5
Accession Number
003195961
Author
Vainberg VM. Mur VD. Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., USSR.
Title
The hydrogen atom in a strong electric field.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.93, no.2, Aug. 1987,
pp.450-62. USSR.
Country of Publication
USSR.
Translated Source
Soviet Physics - JETP (USA), vol.66, no.2, Aug. 1987, pp.258-64. CODEN:
SPHJAR. ISSN: 0038-5646.
Abstract
A calculation is reported of Stark shifts and widths of the ground and first excited states of the hydrogen atom in a strong electric field E up to values of E comparable with the field strength on an atomic orbit. Two independent methods are used, namely, summation of divergent perturbation-theory series and the 1/n expansion. The two methods have a wide region of overlap (in the parameters n/sub 1/, n/sub 2/, m, and E). The calculations are confirmed by considering the Rydberg limit as n to infinity . (28 References).
Abstract Number
A88102574
Subject Headings
Atomic excited states
Atomic spectral line breadth
Hydrogen neutral atoms
Perturbation theory
Spectral line shift
Stark effect
Key Phrase Identifiers
spectral line widths; ground state; first excited state; divergent
perturbation-theory series summation; Stark shifts; 1/n expansion; H.
Classification Codes
Excited states of atoms and molecules [A3150]; Stark effect in atoms
[A3260S]; Atomic line shapes, widths, and shifts [A3270J].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
0038-5646/87/080258-07$04.00.
Publication Type
Journal Paper.
Update Code
198800.

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Citation 6
Accession Number
003337778
Author
Vainberg VM. Mur VD. Popov VS. Sergeev AV. Shcheblykin AV.
Institution
Inst. of Theor. & Exp. Phys., USSR.
Title
The 1/n expansion in quantum mechanics.
Source
Teoreticheskaya i Matematicheskaya Fizika, vol.74, no.3, March 1988,
pp.399-411. USSR.
Country of Publication
USSR.
Translated Source
Theoretical and Mathematical Physics (USA), vol.74, no.3, March 1988,
pp.269-78. CODEN: TMPHAH. ISSN: 0040-5779.
Abstract
The classical approximation (l=n-1 to infinity ) for the energy in /sup (0)/ and the semiclassical expansion in quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order to in /sup (0)/, this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the possibility of a more general choice of the parameter of the semiclassical expansion are considered. The method is illustrated by the example of the Yukawa and 'funnel' potentials and for the Stark effect in the hydrogen atom. These examples demonstrate the rapid convergence of the 1/n expansion even for small quantum numbers. (25 References).
Abstract Number
A89039261
Subject Headings
Convergence
Hydrogen neutral atoms
Quantum theory
Stark effect
Key Phrase Identifiers
Yukawa potential; funnel potential; bound states; 1/n expansion; quantum
mechanics; classical approximation; semiclassical expansion; recursive
method; quantum corrections; quasistationary states; Stark effect;
convergence; H atom.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G]; General
mathematical and computational developments for atoms and molecules [A3115];
Stark effect in atoms [A3260S]; Semiclassical theories and applications in
quantum theory [A0365S].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
TMFZAL
Language
English.
ISSN
0564-6162.
U.S. Copyright Clearance Center Code
0040-5779/88/7403-0269$12.50.
Publication Type
Journal Paper.
Update Code
198900.

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Citation 7
Accession Number
003576302
Author
Mur VD. Popov VS. Sergeev AV. Shcheblykin AV.
Institution
Inst. of Theor. & Exp. Phys., USSR.
Title
Stark resonances and scaling in Rydberg atoms.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.96, no.1, July 1989,
pp.91-106. USSR.
Country of Publication
USSR.
Translated Source
Soviet Physics - JETP (USA), vol.69, no.1, July 1989, pp.49-57. CODEN:
SPHJAR. ISSN: 0038-5646.
Abstract
The Stark shifts and the widths of highly excited states are calculated in a strong electric field (n/sup 4/E approximately 1, n[right angle bracket][right angle bracket]1) for an arbitrary atom (the difference between the atomic field and the Coulomb field is taken into account by introducing quantum defects in a parabolic basis). A correction to the Bohr-Sommerfeld quantization rule, necessitated by the finite barrier penetration factor, is introduced. The possibility of analytic continuation into the above-barrier region is discussed. Scaling relations are obtained via a 1/n-expansion for the near-threshold Stark resonances with quantum numbers n/sub 1/[right angle bracket][right angle bracket]1, n/sub 2/, and m approximately 1. The theoretical results are compared with the experimental data on the photoionization of atoms in the presence of a constant electric field E. (32 References).
Abstract Number
A90039013
Subject Headings
Atomic excited states
Stark effect
Key Phrase Identifiers
Stark shifts; highly excited states; strong electric field; quantum defects;
Bohr-Sommerfeld quantization rule; finite barrier penetration factor;
near-threshold Stark resonances; photoionization.
Classification Codes
Stark effect in atoms [A3260S]; Excited states of atoms and molecules
[A3150].
Treatment
Theoretical or mathematical.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
0038-5646/89/070049-09$04.00.
Publication Type
Journal Paper.
Update Code
199000.

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Citation 8
Accession Number
003683874
Author
Sergeev AV.
Institution
S.I. Vavilov State Opt. Inst., USSR.
Title
1/N expansion for the three-body problem.
Source
Yadernaya Fizika, vol.50, no.4, Oct. 1989, pp.945-50. USSR.
Country of Publication
USSR.
Translated Source
Soviet Journal of Nuclear Physics (USA), vol.50, no.4, Oct. 1989, pp.589-92.
CODEN: SJNCAS. ISSN: 0038-5506.
Abstract
An expansion in powers of 1/N, where N is the dimension of space, is used for the calculation of the energy of a quantum-mechanical three-body system. It is proved that the limit N to infinity corresponds to the classical motion of a rigid configuration of particles in four-dimensional space. The results of the summation of the series in 1/N are discussed in the case of an anharmonic oscillator the mu mu alpha muonic atom, and screened helium. (14 References).
Abstract Number
A90103720
Subject Headings
Harmonic oscillators
Helium neutral atoms
Many-body problems
Muonic atoms
Nuclear screening
Key Phrase Identifiers
muon-muon-alpha; 1/N expansion; three-body problem; energy;
quantum-mechanical three-body system; classical motion; anharmonic
oscillator; screened He.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G];
Positronium, muonium, muonic atoms and molecules [A3610D].
Treatment
Theoretical or mathematical.
Chemicals
He/el.
CODEN
IDFZA7
Language
English.
ISSN
0044-0027.
U.S. Copyright Clearance Center Code
0038-5506/89/100589-04$03.80.
Publication Type
Journal Paper.
Update Code
199000.

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Citation 9
Accession Number
003705597
Author
Mur VD. Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Experimental Phys., Moscow Eng.-Phys. Inst., USSR.
Title
The 1/N expansion in quantum mechanics.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.97, no.1, Jan. 1990,
pp.32-46. USSR.
Country of Publication
USSR.
Translated Source
Soviet Physics - JETP (USA), vol.70, no.1, Jan. 1990, pp.16-24. CODEN:
SPHJAR. ISSN: 0038-5646.
Abstract
The authors consider the application of the 1/N expansion to the calculation of energies (of both discrete levels and quasi-stationary states) and wave functions, as well as to the problem of two Coulomb centers and the three-body problem. They show that in many cases (for example, for the cc charmonium states) the method yields high accuracy even for low quantum numbers, including the ground state. The relation of these results to the properties of minimizing-uncertainty coherent states is discussed. (33 References).
Abstract Number
A90114669
Subject Headings
Quantum theory
Wave functions
Key Phrase Identifiers
1/N expansion; quantum mechanics; discrete levels; quasi-stationary states;
wave functions; Coulomb centers; three-body problem; charmonium states;
ground state; minimizing-uncertainty coherent states.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G].
Treatment
Theoretical or mathematical.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
0038-5646/90/010016-09$03.00.
Publication Type
Journal Paper.
Update Code
199000.

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Citation 10
Accession Number
003728319
Author
Krepostnov PI. Sergeev AV. Utkin AB.
Title
Optical properties of a dense xenon plasma in flashlamps.
Source
Optika i Spektroskopiya, vol.67, no.3, Sept. 1989, pp.538-41. USSR.
Country of Publication
USSR.
Translated Source
Optics and Spectroscopy (USA), vol.67, no.3, Sept. 1989, pp.315-17. CODEN:
OPSUA3. ISSN: 0030-400X.
Abstract
Theoretical calculations of the continuous and line absorption coefficients of a xenon flashlamp at T=8000-20000 K are carried out. The results are compared to experimental data and possible causes of the discrepancy between calculations and these data are discussed. (20 References).
Abstract Number
A90131741
Subject Headings
Flash lamps
Laser accessories
Light sources
Plasma diagnostics
Xenon
Key Phrase Identifiers
continuous absorption coefficient; laser pump source; flashlamps; line
absorption coefficients; 8000 to 20000 K; Xe plasma.
Classification Codes
Optical (ultraviolet, visible, infrared) plasma diagnostic techniques
[A5270K]; Optical sources and standards [A4272]; Emission, absorption, and
scattering of radiation in plasma [A5225P]; Laser optical systems: design and
operation [A4260].
Treatment
Theoretical or mathematical.
Chemicals
Xe/el.
Numeric Data
Temperature 8.0E+03 to 2.0E+04 K
CODEN
OSFMA3
Language
English.
ISSN
0030-4034.
U.S. Copyright Clearance Center Code
0030-400X/89/090315-03$05.00.
Publication Type
Journal Paper.
Update Code
199000.

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Citation 11
Accession Number
003796907
Author
Popov VS. Mur VD. Sergeev AV. Weinberg VM.
Institution
Int. Centre for Theor. Phys., Trieste, Italy.
Title
Strong-field Stark effect: perturbation theory and 1/n expansion.
Source
Physics Letters A, vol.149, no.9, 15 Oct. 1990, pp.418-24. Netherlands.
Country of Publication
Netherlands.
Abstract
The Stark shifts and the widths of the ground and excited states of a hydrogen atom are calculated. Two independent calculation methods are used: a summation of divergent perturbation theory series and 1/n expansion. The results of the calculations for the Rydberg (n[right angle bracket][right angle bracket]1) states are in agreement with the experiment. (19 References).
Abstract Number
A91015513
Subject Headings
Atomic excited states
Atomic spectral line breadth
Hydrogen neutral atoms
Perturbation theory
Spectral line shift
Stark effect
Key Phrase Identifiers
ground state; Stark widths; Rydberg states; perturbation theory; 1/n
expansion; Stark shifts; excited states; H.
Classification Codes
Stark effect in atoms [A3260S]; Excited states of atoms and molecules
[A3150]; Atomic line shapes, widths, and shifts [A3270J].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
PYLAAG
Language
English.
ISSN
0375-9601.
U.S. Copyright Clearance Center Code
0375-9601/90/$03.50.
Publication Type
Journal Paper.
Update Code
199100.

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Citation 12
Accession Number
003796908
Author
Popov VS. Mur VD. Sergeev AV.
Institution
Inst. Centre for Theor. Phys., Trieste, Italy.
Title
1/n-expansion and scaling for the Stark effect in Rydberg atoms.
Source
Physics Letters A, vol.149, no.9, 15 Oct. 1990, pp.425-30. Netherlands.
Country of Publication
Netherlands.
Abstract
The Stark shifts and widths of atomic states in an intense electric field are calculated with the help of the 1/n-expansion. A previous theory is generalized to highly excited states of an arbitrary atom. The scaling relations for near-threshold (E approximately=0) resonances are obtained which are in good agreement with experiment. The modification of the Bohr-Sommerfeld quantization rule due to the finite barrier penetrability is also considered. (12 References).
Abstract Number
A91015514
Subject Headings
Atomic excited states
Spectral line shift
Stark effect
Key Phrase Identifiers
Stark widths; near-threshold resonances; scaling; Rydberg atoms; Stark
shifts; intense electric field; 1/n-expansion; scaling relations;
Bohr-Sommerfeld quantization rule; finite barrier penetrability.
Classification Codes
Stark effect in atoms [A3260S]; Excited states of atoms and molecules
[A3150]; Atomic line shapes, widths, and shifts [A3270J].
Treatment
Theoretical or mathematical.
CODEN
PYLAAG
Language
English.
ISSN
0375-9601.
U.S. Copyright Clearance Center Code
0375-9601/90/$03.50.
Publication Type
Journal Paper.
Update Code
199100.

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Citation 13
Accession Number
003872737
Author
Popov VS. Mur VD. Sergeev AV.
Institution
Inst. of Theor. & Exper. Phys., Moscow, USSR.
Title
Quantization rules with barrier penetrability.
Source
Journal of the Moscow Physical Society, vol.1, no.1, Feb. 1991, pp.15-31.
UK.
Country of Publication
UK.
Abstract
A correction to the quasiclassical quantization rules that allows for the presence of a barrier factor is found. The equation obtained in the process determines both the position of the quasistationary level E/sub r/ and the level width Gamma . The results are compared with numerical solutions of the Schrodinger equation and with those obtained from an exactly solvable model. Finally, a generalization of the Gamow formula for systems with separable variables is derived. (21 References).
Abstract Number
A91057782
Subject Headings
Quantisation
Quantum theory
Key Phrase Identifiers
quasiclassical quantization rules; barrier factor; quasistationary level;
level width; Schrodinger equation; exactly solvable model; Gamow formula.
Classification Codes
Semiclassical theories and applications in quantum theory [A0365S].
Treatment
Theoretical or mathematical.
CODEN
JMPSEC
Language
English.
ISSN
0960-0175.
U.S. Copyright Clearance Center Code
0960-0175/91/010015+17$03.50.
Publication Type
Journal Paper.
Update Code
199100.

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Citation 14
Accession Number
003874290
Author
Vainberg VM. Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., USSR.
Title
The 1/n expansion for a hydrogen atom in an external field.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.98, no.3, Sept. 1990,
pp.847-60. USSR.
Country of Publication
USSR.
Translated Source
Soviet Physics - JETP (USA), vol.71, no.3, Sept. 1990, pp.470-7. CODEN:
SPHJAR. ISSN: 0038-5646.
Abstract
The authors construct a 1/n expansion for a hydrogen atom in constant electric and magnetic fields. The summation of the 1/n expansion enables them with a large degree of accuracy to find the position and the width of atomic levels in a strong field. The method is generalized to resonances in a repulsive Coulomb center and to two-electron atoms. (22 References).
Abstract Number
A91059095
Subject Headings
Atomic excited states
Atomic resonant states
Atomic spectral line breadth
Hydrogen neutral atoms
Key Phrase Identifiers
electric fields; Rydberg states; external field; 1/n expansion; magnetic
fields; width; atomic levels; strong field; resonances; repulsive Coulomb
center; two-electron atoms; H atom.
Classification Codes
Excited states of atoms and molecules [A3150]; Atomic line shapes, widths,
and shifts [A3270J].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
0038-5646/90/090470-08$03.00.
Publication Type
Journal Paper.
Update Code
199100.

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Citation 15
Accession Number
003993209
Author
Popov VS. Mur VD. Sergev AV.
Institution
Inst. of Theoret. & Exp. Phys., Moscow, USSR.
Title
Generalization of the Gamow formula to the multidimensional case.
Source
Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.53, no.9, May
1991, pp.433-6. USSR.
Country of Publication
USSR.
Translated Source
JETP Letters (USA), vol.53, no.9, May 1991, pp.455-8. CODEN: JTPLA2. ISSN:
0021-3640.
Abstract
The Gamow formula for a level width is generalized to the case of multidimensional systems with separable variables. A condition for the applicability of this approximation is found. (6 References).
Abstract Number
A91133134
Subject Headings
Hydrogen neutral atoms
Stark effect
Key Phrase Identifiers
Stark effect; Gamow formula; multidimensional case; level width; H atom.
Classification Codes
Stark effect in atoms [A3260S].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
PZETAB
Language
English.
ISSN
0370-274X.
U.S. Copyright Clearance Center Code
0021-3640/91/090455-04$01.00.
Publication Type
Journal Paper.
Update Code
199100.

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Citation 16
Accession Number
003996451
Author
Popov VS. Mur VD. Sergeev AV.
Institution
Inst. of Theor. & Experimental Phys., Moscow, USSR.
Title
Quantization rules for quasistationary states.
Source
Physics Letters A, vol.157, no.4-5, 29 July 1991, pp.185-91. Netherlands.
Country of Publication
Netherlands.
Abstract
The modification of the Bohr-Sommerfeld quantization rules, which is due to the barrier penetrability, is found. The equation obtained is valid for an arbitrary analytical potential U(x), obeying the quasiclassical conditions. It determines both the position E/sub r/ and the width Gamma of the quasistationary state. A generalization of the Gamow formula for multidimensional systems with separable coordinates is derived. A comparison with exactly solvable models as well as with numerical solutions of the Schrodinger equation for the Stark problem is performed. (15 References).
Abstract Number
A91131584
Subject Headings
Quantisation
Schrodinger equation
Stark effect
Tunnelling
Key Phrase Identifiers
Bohr-Sommerfeld quantization rules; barrier penetrability; arbitrary
analytical potential; quasiclassical conditions; position; width;
quasistationary state; Gamow formula; multidimensional systems; separable
coordinates; exactly solvable models; numerical solutions; Schrodinger
equation; Stark problem.
Classification Codes
Foundations, theory of quantum measurement, miscellaneous quantum theories
[A0365B]; Solutions of wave equations: bound state in quantum theory
[A0365G]; Stark effect in atoms [A3260S].
Treatment
Theoretical or mathematical.
CODEN
PYLAAG
Language
English.
ISSN
0375-9601.
U.S. Copyright Clearance Center Code
0375-9601/91/$03.50.
Publication Type
Journal Paper.
Update Code
199100.

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Citation 17
Accession Number
004049528
Author
Popov VS. Mur VD. Sergeev AV.
Institution
Moscow Eng. Phys. Inst., USSR.
Title
Quantization rules with allowance for barrier penetration.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.100, no.1, July 1991,
pp.20-44. USSR.
Country of Publication
USSR.
Translated Source
Soviet Physics - JETP (USA), vol.73, no.1, July 1991, pp.9-22. CODEN: SPHJAR.
ISSN: 0038-5646.
Abstract
The semiclassical quantization rules are corrected with allowance for barrier penetration. The resulting equation determines both the position E/sub r/ and the width Gamma of the quasistationary level. A comparison is made with numerical solutions of the Schrodinger equation and with exactly solvable models. The generalization of the Gamov formula for systems with separating variables is found. The possibility of generalizing the results obtained to the relativistic case is discussed. (39 References).
Abstract Number
A9202-0365-067
Subject Headings
Quantisation
Schrodinger equation
Tunnelling
Wave functions
Key Phrase Identifiers
barrier penetration; semiclassical quantization rules; quasistationary level;
numerical solutions; Schrodinger equation; exactly solvable models; Gamov
formula.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G].
Treatment
Theoretical or mathematical.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
0038-5646/91/070009-14$03.00.
Publication Type
Journal Paper.
Update Code
199200.

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Citation 18
Accession Number
004136369
Author
Mur VD. Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Generalization of the Gamow formula to the multidimensional case.
Source
Yadernaya Fizika, vol.54, no.4, Oct. 1991, pp.950-61. USSR.
Country of Publication
USSR.
Translated Source
Soviet Journal of Nuclear Physics (USA), vol.54, no.4, Oct. 1991, pp.575-81.
CODEN: SJNCAS. ISSN: 0038-5506.
Abstract
A generalization of the Gamow formula for the width Gamma of a quasistationary level (with energy E=E/sub r/-i Gamma /2) is given for the case of multidimensional systems with separable variables. The condition for applicability of this approximation is obtained, and some examples are considered. (30 References).
Abstract Number
A9211-2430-004
Subject Headings
Nuclear resonances
Nuclear structure theory
Key Phrase Identifiers
Gamow formula; quasistationary level; multidimensional systems.
Classification Codes
Resonance nuclear reactions and scattering [A2430]; Nuclear-structure models
and methods [A2160].
Treatment
Theoretical or mathematical.
CODEN
IDFZA7
Language
English.
ISSN
0044-0027.
U.S. Copyright Clearance Center Code
0038-5506/91/100575-07$03.00.
Publication Type
Journal Paper.
Update Code
199200.

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Citation 19
Accession Number
004159755
Author
Sergeev AV.
Institution
State Opt. Inst., Russia.
Title
Positron-nucleus resonances in electric and magnetic fields.
Source
Yadernaya Fizika, vol.54, no.5, Nov. 1991, pp.1225-31. Russia.
Country of Publication
Russia.
Translated Source
Soviet Journal of Nuclear Physics (USA), vol.54, no.5, Nov. 1991, pp.744-7.
CODEN: SJNCAS. ISSN: 0038-5506.
Abstract
Resonance states of a positron in the Coulomb field of a nucleus and in parallel homogeneous electric and magnetic fields are studied. In the classical description, the positron undergoes oscillatory motion along the symmetry axis, being reflecting consecutively from the nucleus and the anode. The magnetic field does not permit the positron to go around the nucleus and move to the cathode, stabilizing the resonances. The nucleus is regarded as infinitely heavy, and the problem reduces to a one-particle Schrodinger equation. The energies and widths of the resonances are determined by means of versions of perturbation theory in weak electric and strong magnetic fields, the 1/n expansion, and the quasiclassical approximation. Different methods are in good agreement with one another. (4 References).
Abstract Number
A9213-2530-003
Subject Headings
Electron-nucleus reactions
Nuclear resonance reactions and scattering
Perturbation theory
Schrodinger equation
Key Phrase Identifiers
positron-nucleus resonances; electric fields; Coulomb field; magnetic fields;
oscillatory motion; symmetry axis; anode; cathode; one-particle Schrodinger
equation; perturbation theory; 1/n expansion; quasiclassical approximation.
Classification Codes
Electron and positron reactions and scattering [A2530C]; Resonance nuclear
reactions and scattering [A2430]; Solutions of wave equations: bound state in
quantum theory [A0365G].
Treatment
Theoretical or mathematical.
CODEN
IDFZA7
Language
English.
ISSN
0044-0027.
U.S. Copyright Clearance Center Code
0038-5506/91/110744-04$03.00.
Publication Type
Journal Paper.
Update Code
199200.

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Citation 20
Accession Number
004351784
Author
Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Large orders of the 1/n expansion in quantum mechanics.
Source
Physics Letters A, vol.172, no.4, 4 Jan. 1993, pp.193-8. Netherlands.
Country of Publication
Netherlands.
Abstract
The asymptotics of large orders of the 1/n expansion in quantum mechanics has been found. It is shown that the coefficients epsilon /sup (k)/ grow as k]a/sup k/ with k to infinity , and the dependence of the parameter a on the coupling constant is investigated. (20 References).
Abstract Number
A9307-0365-036
Subject Headings
Quantum theory
Key Phrase Identifiers
1/n expansion; quantum mechanics; coupling constant.
Classification Codes
Foundations, theory of quantum measurement, miscellaneous quantum theories
[A0365B].
Treatment
Theoretical or mathematical.
CODEN
PYLAAG
Language
English.
ISSN
0375-9601.
U.S. Copyright Clearance Center Code
0375-9601/93/$06.00.
Publication Type
Journal Paper.
Update Code
199300.

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Citation 21
Accession Number
004352533
Author
Popov VS. Sergeev AV. Shcheblykin AV.
Institution
Inst. of Theor. & Exp. Phys., Russia.
Title
Structure of higher orders of the 1/n expansion.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.102, no.5, Nov. 1992,
pp.1453-68. Russia.
Country of Publication
Russia.
Translated Source
Soviet Physics - JETP (USA), vol.75, no.5, Nov. 1992, pp.787-95. CODEN:
SPHJAR. ISSN: 0038-5646.
Abstract
The asymptote of higher orders of the 1/n expansion in quantum mechanical problems is found. It is shown that the coefficients epsilon /sup (k)/ of the 1/n expansion grow factorially like k] a/sup k/ as k to infinity . The parameter a as a function of the coupling constant is studied. The derived analytic expressions agree with numerical calculations. As examples, the Yukawa, Hulthen and V funnel potentials are considered, as well as the Stark effect in the hydrogen atom and the molecular ion H/sub 2//sup +/. (33 References).
Abstract Number
A9307-3260S-001
Subject Headings
Hydrogen ions
Hydrogen neutral atoms
Positive ions
Potential energy functions
Quantum theory
Stark effect
Key Phrase Identifiers
Yukawa potentials; Hulthen potentials; 1/n expansion; quantum mechanical
problems; funnel potentials; Stark effect; H/sub 2//sup +/; H.
Classification Codes
Stark effect in atoms [A3260S]; Intramolecular energy transfer;
intramolecular dynamics; dynamics of van der Waals molecules [A3425]; Quantum
theory; quantum mechanics [A0365]; Zeeman and Stark effects in molecules
[A3345B]; Interatomic and intermolecular potentials and forces [A3420].
Treatment
Theoretical or mathematical.
Chemicals
H/el; H2/el; H/el.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
0038-5646/92/110787-09$05.00.
Publication Type
Journal Paper.
Update Code
199300.

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Citation 22
Accession Number
004435191
Author
Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Russian Acad. of Sci., Moscow, Russia.
Title
Asymptotic form of higher orders of the 1/n expansion.
Source
Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.57, no.5, 10
March 1993, pp.273-6. Russia.
Country of Publication
Russia.
Translated Source
JETP Letters (USA), vol.57, no.5, 10 March 1993, pp.281-5. CODEN: JTPLA2.
ISSN: 0021-3640.
Abstract
The asymptotic form of higher orders of the 1/n expansion in quantum mechanics is factorial. The Yukawa potential and the hydrogen atom in electric and magnetic fields are discussed. (10 References).
Abstract Number
A9315-0365-028
Subject Headings
Hydrogen neutral atoms
Nuclear forces
Quantum theory
Series (mathematics)
Key Phrase Identifiers
electric fields; higher orders; asymptotic form; 1/n expansion; quantum
mechanics; Yukawa potential; magnetic fields; H atom.
Classification Codes
Formalism in quantum theory [A0365C]; Solutions of wave equations: bound
state in quantum theory [A0365G]; Nuclear forces [A2130].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
PZETAB
Language
English.
ISSN
0370-274X.
U.S. Copyright Clearance Center Code
0021-3640/93/000281-05$10.00.
Publication Type
Journal Paper.
Update Code
199300.

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Citation 23
Accession Number
004444854
Author
Mur VD. Popov VS. Sergeev AV.
Institution
Moscow Eng. Phys. Inst., Russia.
Title
The 1/n-expansion in quantum mechanics and quasi-stationary states.
Source
Journal of the Moscow Physical Society, vol.2, no.3, Aug. 1992, pp.189-217.
UK.
Country of Publication
UK.
Abstract
Applications of the 1/n-expansion to energy and wavefunction calculations, especially for quasi-stationary states are considered. As an illustration the authors have examined the funnel and Yukawa potentials, the Stark effect in a strong field and a hydrogen atom in electric and magnetic fields. They have found that in many cases the method ensures high accuracy, even for small quantum number, n approximately 1. The connection between these results and the properties of coherent states is briefly discussed. Finally, the behaviour of the large-order terms in the 1/n-expansion is investigated. (41 References).
Abstract Number
A9316-0365-041
Subject Headings
Hydrogen neutral atoms
Quantum theory
Stark effect
Wave functions
Key Phrase Identifiers
funnel potential; applied magnetic field; applied electric field;
1/n-expansion; quantum mechanics; quasi-stationary states; energy;
wavefunction calculations; Yukawa potentials; Stark effect; strong field;
coherent states; large-order terms; H atom.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G]; Zeeman
effect in atoms [A3260V].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
JMPSEC
Language
English.
ISSN
0960-0175.
U.S. Copyright Clearance Center Code
0960-0175/92/030189+29$07.50.
Publication Type
Journal Paper.
Update Code
199300.

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Citation 24
Accession Number
004667621
Author
Popov VS. Mur VD. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Critical fields and above-barrier Stark resonances.
Source
Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.59, no.3, 10
Feb. 1994, pp.150-3. Russia.
Country of Publication
Russia.
Translated Source
JETP Letters (USA), vol.59, no.3, 10 Feb. 1994, pp.158-62. CODEN: JTPLA2.
ISSN: 0021-3640.
Abstract
Exact values of the critical field C/sub c/ are calculated for a hydrogen atom, including the case of the ground state. The widths Gamma /sub n/ of Stark resonances at C=C/sub c/, are also calculated. In the above-barrier region (C[right angle bracket]C/sub c/ the widths Gamma /sub n/(C) are essentially linear functions of the electric field strength. (12 References).
Abstract Number
A9412-3260S-001
Subject Headings
Hydrogen neutral atoms
Stark effect
Key Phrase Identifiers
above-barrier Stark resonances; critical field; H atom; ground state;
above-barrier region; linear functions; electric field strength; H.
Classification Codes
Stark effect in atoms [A3260S].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
PZETAB
Language
English.
ISSN
0370-274X.
U.S. Copyright Clearance Center Code
0021-3640/94/030158-05$10.00.
Publication Type
Journal Paper.
Update Code
199400.

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Citation 25
Accession Number
004678291
Author
Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Asymptotic form of higher orders of the 1/n expansion for multidimensional
problems.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.105, no.3, March 1994,
pp.568-91. Russia.
Country of Publication
Russia.
Translated Source
Journal of Experimental and Theoretical Physics (USA), vol.78, no.3, March
1994, pp.303-14. CODEN: JTPHES. ISSN: 1063-7761.
Abstract
The asymptotic form of higher orders of the 1/n expansion is analyzed for multidimensional problems of quantum mechanics and atomic physics. Problems in which variables can and cannot be separated are discussed. Examples of the former are the molecular hydrogen atom and the Stark effect; an example of the latter is the hydrogen atom in electric and magnetic fields. The asymptotic form is always factorial. Its parameters can be calculated through a calculation of electron tunneling trajectories by the "imaginary time" method. Possible types of singularities of the asymptotic parameter alpha at the collision point of the classical solutions are determined. (36 References).
Abstract Number
A9413-0365-031
Subject Headings
Hydrogen neutral atoms
Hydrogen neutral molecules
Molecular energy level calculations
Quantum theory
Stark effect
Key Phrase Identifiers
asymptotic form; higher orders; 1/n expansion; multidimensional problems;
quantum mechanics; atomic physics; molecular H atom; Stark effect; atomic H;
electric fields; magnetic fields; electron tunneling trajectories; imaginary
time method; singularities; collision point; classical solutions; H; H/sub
2/.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G];
Foundations, theory of quantum measurement, miscellaneous quantum theories
[A0365B]; Zeeman and Stark effects in molecules [A3345B]; Specific
calculations and results for atoms and molecules [A3120].
Treatment
Theoretical or mathematical.
Chemicals
H/el; H2/el; H/el.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
1063-7761/94/030303-12$10.00.
Publication Type
Journal Paper.
Update Code
199400.

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Citation 26
Accession Number
004732543
Author
Popov VS. Sergeev AV. Mur VD. Shcheblykin AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
On the asymptotics of high-order terms of the 1/n expansion.
Source
Yadernaya Fizika, vol.57, no.6, June 1994, pp.1119-28. Russia.
Country of Publication
Russia.
Translated Source
Physics of Atomic Nuclei (Russia), vol.57, no.6, June 1994, pp.1057-65.
CODEN: PANUEO. ISSN: 1063-7788.
Abstract
Analytic and numerical methods for determining the asymptotics of high-order terms of the 1/n expansion in quantum-mechanical problems are developed. It is shown that this asymptotics is always of the factorial type. The dependence of parameters of the asymptotics on the form of the potential and on the coupling constant is especially analyzed in the vicinity of the point of collision of classical solutions. (23 References).
Abstract Number
A9418-0365-090
Subject Headings
Elementary particle coupling constants
Numerical analysis
Quantum theory
Key Phrase Identifiers
asymptotics; high-order terms; 1/n expansion; analytic methods; numerical
methods; quantum-mechanical problems; factorial type; coupling constant;
potential; classical solutions.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G];
Numerical approximation and analysis [A0260]; Quantum field theory [A1110].
Treatment
Theoretical or mathematical.
CODEN
IDFZA7
Language
English.
ISSN
0044-0027.
U.S. Copyright Clearance Center Code
1063-7788/94/5706-1057$10.00.
Publication Type
Journal Paper.
Update Code
199400.

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Citation 27
Accession Number
004788405
Author
Popov VS. Mur VD. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Critical electric fields and Stark resonances in the hydrogen atom.
Source
Physics Letters A, vol.193, no.2, 26 Sept. 1994, pp.159-64. Netherlands.
Country of Publication
Netherlands.
Abstract
The exact values of critical electric fields E/sub c/ for different states of a hydrogen atom, including its ground state, as well as the widths Gamma /sub n/ of the Stark resonances at E=E/sub c/, are calculated (at E=E/sub c/ (n/sub 1/, n/sub 2/, m) the potential barrier for an electron in the (n/sub 1/, n/sub 2/, m) state disappears). Using the modified quantization condition with barrier penetrability included, we explain the dependence of Gamma /sub n/ on the principal quantum number n. (17 References).
Abstract Number
A9422-3260S-003
Subject Headings
Atomic spectral line breadth
Hydrogen neutral atoms
Quantisation
Stark effect
Key Phrase Identifiers
critical electric fields; Stark resonances; H atom; ground state; level
widths; potential barrier; quantization condition; barrier penetrability;
principal quantum number; H.
Classification Codes
Stark effect in atoms [A3260S]; Atomic line shapes, widths, and shifts
[A3270J].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
PYLAAG
Language
English.
ISSN
0375-9601.
U.S. Copyright Clearance Center Code
0375-9601/94/$07.00.
Publication Type
Journal Paper.
Update Code
199400.

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Citation 28
Accession Number
004788406
Author
Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Large orders of 1/n-expansion for multidimensional problems.
Source
Physics Letters A, vol.193, no.2, 26 Sept. 1994, pp.165-72. Netherlands.
Country of Publication
Netherlands.
Abstract
The asymptotics of large orders of the 1/n-expansion is investigated for multidimensional problems of quantum mechanics and atomic physics, including those with separable variables (the hydrogen molecular ion H/sub 2//sup +/), and those where separation of variables is impossible (a hydrogen atom in electric and magnetic fields). It is shown that the parameters of the asymptotics can be found by means of calculating sub-barrier trajectories with the help of the "imaginary time" method, as well as by solution of the eikonal equation. (17 References).
Abstract Number
A9422-0365-056
Subject Headings
Atomic structure
Hydrogen ions
Hydrogen neutral atoms
Molecular electronic states
Quantum theory
Key Phrase Identifiers
1/n-expansion; multidimensional problems; large orders asymptotics; quantum
mechanics; atomic physics; separable variables; H molecular ion; H atom;
electric fields; magnetic fields; subbarrier trajectories; imaginary time;
eikonal equation; H/sub 2//sup +/; H/sub 2/; H.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G]; General
theory of structure, transitions and chemical binding in atoms and molecules
[A3110]; General mathematical and computational developments for atoms and
molecules [A3115].
Treatment
Theoretical or mathematical.
Chemicals
H2/el; H/el; H/el.
CODEN
PYLAAG
Language
English.
ISSN
0375-9601.
U.S. Copyright Clearance Center Code
0375-9601/94/$07.00.
Publication Type
Journal Paper.
Update Code
199400.

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Citation 29
Accession Number
004835651
Author
Popov VS. Mur VD. Sergeev AV.
Institution
Int. Inst. of Phys., Moscow, Russia.
Title
Theory of the Stark effect in a strong field: critical fields, above-barrier
resonances, dependence on dimensionality.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.106, no.4, Oct. 1994,
pp.1001-30. Russia.
Country of Publication
Russia.
Translated Source
Journal of Experimental and Theoretical Physics (USA), vol.79, no.4, Oct.
1994, pp.547-60. CODEN: JTPHES. ISSN: 1063-7761.
Abstract
We have calculated accurate values of the critical fields E/sub c/ for various states (n/sub 1/, n/sub 2/, m) of a hydrogen atom, including the ground state. Using modified quantization rules that take into account the finite permeability of the barrier, we determine how the widths Gamma /sub n/ of the Stark resonances depend on n for E=E/sub c/. Using the 1/n expansion, along with several model problems as examples, we show that in the above-barrier (E[right angle bracket]E/sub c/) region the Stark widths Gamma /sub n/(E) depend almost linearly on the electric field. We determine the dependence of the ground-state Stark shift of a d-dimensional "hydrogen atom" on the dimensionality D of the space. (45 References).
Abstract Number
A9502-3260S-001
Subject Headings
Stark effect
Key Phrase Identifiers
Stark effect; strong field; critical fields; above-barrier resonances;
dimensionality; ground state; finite permeability; Stark resonances.
Classification Codes
Stark effect in atoms [A3260S]; Spin-orbit coupling, Zeeman, Stark and strain
splitting (condensed matter) [A7170E].
Treatment
Theoretical or mathematical.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
1063-7761/94/100547-14$10.00.
Publication Type
Journal Paper.
Update Code
199400.

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Citation 30
Accession Number
005029796
Author
Sergeev AV.
Institution
S.I. Vavilov State Optical Inst., St. Petersburg, Russia.
Title
Summation of the eigenvalue perturbation series by multi-valued Pade
approximants: application to resonance problems and double wells.
Source
Journal of Physics A-Mathematical & General, vol.28, no.14, 21 July 1995,
pp.4157-62. UK.
Country of Publication
UK.
Abstract
Quadratic Pade approximants are used to obtain energy levels both for the anharmonic oscillator x/sup 2//2- lambda x/sup 4/ and for the double well -x/sup 2//2+ lambda x/sup 4/. In the first case, the complex-valued energy of the resonances is reproduced by summation of the real terms of the perturbation series. The second case is treated formally as an anharmonic oscillator with a purely imaginary frequency. We use the expansion around the central maximum of the potential to obtain a complex perturbation series on the unphysical sheet of the energy function. Then, we perform an analytical continuation of this solution to the neighbouring physical sheet taking into account the supplementary branch of quadratic approximants. In this way we can reconstruct the real energy by summation of the complex series. Such an unusual approach eliminates the double degeneracy of states that makes ordinary perturbation theory (around the minima of the double well potential) incorrect. (18 References).
Abstract Number
A9518-0365-020
Subject Headings
Bound states
Eigenvalues and eigenfunctions
Harmonic oscillators
Perturbation theory
Quantum theory
Key Phrase Identifiers
quadratic Pade approximants; eigenvalue perturbation series; resonance;
double wells; energy levels; anharmonic oscillator; degeneracy.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G];
Algebraic methods in quantum theory [A0365F].
Treatment
Theoretical or mathematical.
CODEN
JPHAC5
Language
English.
ISSN
0305-4470.
U.S. Copyright Clearance Center Code
0305-4470/95/144157+06$19.50.
Publication Type
Journal Paper.
Update Code
199500.
Copyright
Copyright 1995, IEE.

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Citation 31
Accession Number
005195998
Author
Mur VD. Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Coulomb corrections to nuclear scattering lengths and effective ranges for
weakly bound systems.
Source
Yadernaya Fizika, vol.59, no.1, Jan. 1996, pp.68-77. Publisher: MAIK
Nauka/Interperiodica Publishing, Russia.
Country of Publication
Russia.
Translated Source
Physics of Atomic Nuclei (Russia), vol.59, no.1, Jan. 1996, pp.62-71. CODEN:
PANUEO. ISSN: 1063-7788.
Abstract
A procedure is considered for extracting the purely nuclear scattering length a/sub s/ and effective range r/sub s/ (which correspond to a strong-interaction potential V/sub s/ with disregarded Coulomb interaction) from the experimentally determined nuclear quantities a/sub cs/ and r/sub cs/ which are modified by Coulomb interaction. The Coulomb renormalization of a/sub s/ and r/sub s/ is especially strong if the system under study involves a level with energy close to zero (on the nuclear scale). This applies to formulas that determine the Coulomb renormalization of the low energy parameters of s scattering (l=0). Detailed numerical calculations are performed for coefficients appearing in the equations that determine Coulomb corrections for various models of the potential V/sub s/(r). This makes it possible to draw qualitative conclusions about the dependence of Coulomb corrections on the form of the strong-interaction potential and, in particular, on its small-distance behavior. A considerable enhancement of Coulomb corrections to the effective range r/sub s/ is found for potentials with a barrier. (32 References).
Abstract Number
A9607-2410-001
Subject Headings
Nuclear reaction theory
Key Phrase Identifiers
nuclear scattering lengths; Coulomb corrections; effective ranges; weakly
bound systems; effective range; strong-interaction potential; Coulomb
interaction; Coulomb renormalization; low energy parameters; small-distance
behavior.
Classification Codes
Nuclear reaction and scattering models and methods [A2410].
Treatment
Theoretical or mathematical.
CODEN
IDFZA7
Language
English.
ISSN
0044-0027.
U.S. Copyright Clearance Center Code
1063-7788/96/5901-0062$10.00.
Publication Type
Journal Paper.
SICI
0044-0027(199601)59:1L.68;1-Z
1063-7788(199601)59:1L.62:CCNS;1-7
Update Code
199600.
Copyright
Copyright 1996, IEE.

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Citation 32
Accession Number
005294672
Author
Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Effect of a magnetic field on the ionization of atoms.
Source
Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.63, no.6, 25
March 1996, pp.398-402. Publisher: AIP, Russia.
Country of Publication
Russia.
Translated Source
JETP Letters (USA), vol.63, no.6, 25 March 1996, pp.417-22. CODEN: JTPLA2.
ISSN: 0021-3640.
Abstract
The ionization probability of an atomic s state under the action of static electric and magnetic fields is calculated taking into account the Coulomb interaction between the escaping electron and the atomic core. The structure of the perturbation series for the energy of the level is investigated and the asymptotic behavior of the higher orders of the perturbation theory is found. (14 References).
Abstract Number
A9614-3450H-011
Subject Headings
Ionisation
Perturbation theory
Key Phrase Identifiers
atom ionization probability; static magnetic field; static electric fields;
Coulomb interaction; escaping electron; perturbation series; energy level.
Classification Codes
Electronic excitation and ionization (atoms and molecules) [A3450H].
Treatment
Theoretical or mathematical.
CODEN
PZETAB
Language
English.
ISSN
0370-274X.
U.S. Copyright Clearance Center Code
0021-3640/96/060417-06$10.00.
Publication Type
Journal Paper.
SICI
0370-274X(19960325)63:6L.398;1-B
0021-3640(19960325)63:6L.417:EMFI;1-L
Update Code
199600.
Copyright
Copyright 1996, IEE.

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Citation 33
Accession Number
005458366
Author
Mur VD. Popov VS. Sergeev AV.
Institution
Eng. Phys. Inst., Acad. of Sci., Moscow, Russia.
Title
Coulomb corrections to scattering lengths and effective ranges for l not=0.
Source
Yadernaya Fizika, vol.59, no.11, Nov. 1996, pp.1958-65. Publisher: MAIK
Nauka/Interperiodica Publishing, Russia.
Country of Publication
Russia.
Translated Source
Physics of Atomic Nuclei (Russia), vol.59, no.11, Nov. 1996, pp.1888-94.
CODEN: PANUEO. ISSN: 1063-7788.
Abstract
Coulomb corrections to the low-energy scattering parameters (scattering lengths and effective ranges) of states with nonzero orbital angular momentum are studied. The greatest attention is paid to the case of the p wave. Resonance scattering is considered for a system with a shallow nuclear bound or quasistationary (resonance) p level. Coulomb corrections are calculated numerically, and their dependence on the shape of the strong-interaction potential-in particular, on its short-distance behavior-is studied in detail. (17 References).
Abstract Number
A9703-2410-001
Subject Headings
Nuclear reaction theory
Nuclear resonance scattering
Key Phrase Identifiers
scattering lengths; Coulomb corrections; effective ranges; p wave; resonance
scattering; quasistationary p level; strong-interaction potential;
short-distance behavior; nuclear scattering.
Classification Codes
Nuclear reaction and scattering models and methods [A2410]; Resonance nuclear
reactions and scattering [A2430].
Treatment
Theoretical or mathematical.
CODEN
IDFZA7
Language
English.
ISSN
0044-0027.
U.S. Copyright Clearance Center Code
1063-7788/96/5911-1888$10.00.
Publication Type
Journal Paper.
SICI
0044-0027(199611)59:11L.1958;1-E
1063-7788(199611)59:11L.1888:CCSL;1-U
Update Code
199700.
Copyright
Copyright 1997, IEE.

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Citation 34
Accession Number
005892522
Author
Sergeev AV. Goodson DZ.
Institution
Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.
Title
Self-consistent field perturbation theory of molecular vibrations.
Source
Molecular Physics, vol.93, no.3, 20 Feb. 1998, pp.477-84. Publisher: Taylor &
Francis, UK.
Country of Publication
UK.
Abstract
Perturbation theory is used to perform non-iterative calculations of energy eigenvalues of the coupled ordinary differential equations that result from imposing separability assumptions in terms of normal coordinates on vibrational wavefunctions. Various model Hamiltonians with 2 or 3 coupled normal modes are studied and the increase of computational cost with the number of degrees of freedom is analysed. Quadratic Pade approximants of the perturbation expansions are rapidly convergent, and directly yield complex numbers for resonance eigenvalues. For a 3-mode system, results are obtained within partial separability assumptions, with a pair of modes left coupled. Large-order perturbation theory with partial separability is suggested as an alternative to low-order exact perturbation theory. (35 References).
Abstract Number
A9810-3310-020
Subject Headings
Differential equations
Eigenvalues and eigenfunctions
Perturbation theory
SCF calculations
Vibrational states
Wave functions
Key Phrase Identifiers
self-consistent field perturbation theory; molecular vibrations; noniterative
calculations; energy eigenvalues; coupled ordinary differential equations;
normal coordinates; vibrational wavefunctions; model Hamiltonians; coupled
normal modes; quadratic Pade approximants; perturbation expansions; resonance
eigenvalues; partial separability assumptions; large-order perturbation
theory; low-order exact perturbation theory.
Classification Codes
Vibrational analysis (molecular spectra) [A3310G]; Numerical approximation
and analysis [A0260]; Algebra, set theory, and graph theory [A0210]; Specific
calculations and results for atoms and molecules [A3120].
Treatment
Theoretical or mathematical.
CODEN
MOPHAM
Language
English.
ISSN
0026-8976.
U.S. Copyright Clearance Center Code
0026-8976/98/$12.00.
Publication Type
Journal Paper.
SICI
0026-8976(19980220)93:3L.477:SCFP;1-8
Update Code
199800.
Copyright
Copyright 1998, IEE.

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Citation 35
Accession Number
005929646
Author
Sergeev AV. Goodson DZ.
Institution
Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.
Title
Summation of asymptotic expansions of multiple-valued functions using
algebraic approximants: application to anharmonic oscillators.
Source
Journal of Physics A-Mathematical & General, vol.31, no.18, 8 May 1998,
pp.4301-17. Publisher: IOP Publishing, UK.
Country of Publication
UK.
Abstract
The divergent Rayleigh-Schrodinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pade approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence of the diagonal staircase approximant sequence increases with the degree. Different branches of the approximants converge to different branches of the function. The success of the high-degree approximants is attributed to their ability to model the function on multiple sheets of the Riemann surface and to reproduce the correct singularity structure in the limit of large perturbation parameter. An efficient recursive algorithm for computing the diagonal approximant sequence is presented. (56 References).
Abstract Number
A9813-0365-048
Subject Headings
Algebra
Approximation theory
Convergence
Eigenvalues and eigenfunctions
Functions
Harmonic oscillators
Perturbation techniques
Key Phrase Identifiers
asymptotic expansions; multiple-valued functions; algebraic approximants;
anharmonic oscillators; divergent Rayleigh-Schrodinger perturbation
expansions; energy eigenvalues; cubic oscillators; quartic oscillators;
sextic oscillators; octic oscillators; generalized Pade approximants;
diagonal staircase approximant sequence; convergence; high-degree
approximants; singularity structure; Riemann surface; efficient recursive
algorithm; diagonal approximant sequence.
Classification Codes
Solutions of wave equations: bound state in quantum theory [A0365G]; Function
theory, analysis [A0230]; Algebra, set theory, and graph theory [A0210].
Treatment
Theoretical or mathematical.
CODEN
JPHAC5
Language
English.
ISSN
0305-4470.
U.S. Copyright Clearance Center Code
0305-4470/98/184301+17$19.50.
Document Number
S0305-4470(98)87859-1.
Publication Type
Journal Paper.
SICI
0305-4470(19980508)31:18L.4301:SAEM;1-X
Update Code
199800.
Copyright
Copyright 1998, IEE.

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Citation 36
Accession Number
005979869
Author
Popov VS. Sergeev AV.
Institution
Inst. of Theor. & Exp. Phys., Moscow, Russia.
Title
Ionization of atoms in weak fields and the asymptotic behavior of
higher-order perturbation theory.
Source
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.113, no.6, June 1998,
pp.2047-55. Publisher: AIP, Russia.
Country of Publication
Russia.
Translated Source
Journal of Experimental and Theoretical Physics (USA), vol.86, no.6, June
1998, pp.1122-6. CODEN: JTPHES. ISSN: 1063-7761.
Abstract
Using the imaginary time method, we study the structure of the perturbation series for the hydrogen atom in electric E and magnetic H fields. It is shown that there is a "critical" value of the ratio gamma =H/E at which the perturbation series for the ground state changes from having a fixed sign (for gamma [left angle bracket] gamma /sub c/) to having a variable sign (for gamma [right angle bracket] gamma /sub c/). This conclusion is confirmed by direct higher-order perturbation calculations. The change in the asymptotic regime is explained by competition among the contributions of the various complex trajectories that describe the subbarrier motion of the electrons. Here the parameter gamma /sub c/ depends on the angle theta between the electric and magnetic fields. (41 References).
Abstract Number
A9817-3450H-001
Subject Headings
Field ionisation
Ground states
Perturbation theory
Key Phrase Identifiers
weak fields; asymptotic behavior; higher order perturbation theory; imaginary
time method; perturbation theory series; ground state; complex trajectories;
atomic ionisation.
Classification Codes
Electronic excitation and ionization (atoms and molecules) [A3450H].
Treatment
Theoretical or mathematical.
CODEN
ZETFA7
Language
English.
ISSN
0044-4510.
U.S. Copyright Clearance Center Code
1063-7761/98/061122-5$15.00.
Document Number
S1063-7761(98)01006-3.
Publication Type
Journal Paper.
SICI
0044-4510(199806)113:6L.2047;1-B
1063-7761(199806)86:6L.1122:IAWF;1-L
Update Code
199800.
Copyright
Copyright 1998, IEE.

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Citation 37
Accession Number
006050968
Author
Elout MO. Goodson DZ. Elliston CD. Shi-Wei Huang. Sergeev AV. Watson DK.
Institution
Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.
Title
Improving the convergence and estimating the accuracy of summation
approximants of 1/D expansions for Coulombic systems.
Source
Journal of Mathematical Physics, vol.39, no.10, Oct. 1998, pp.5112-22.
Publisher: AIP, USA.
Country of Publication
USA.
Abstract
The convergence of large-order expansions in delta =1/D, where D is the dimensionality of coordinate space, for energies E( delta ) of Coulomb systems is strongly affected by singularities at delta =1 and delta =0. Pade-Borel approximants with modifications that completely remove the singularities at delta =1 and remove the dominant singularity at delta =0 are demonstrated. A renormalization of the interelectron repulsion is found to move the dominant singularity of the Borel function F( delta )= Sigma jE/sub j/'/j], where E/sub j//sup '/ are the the expansion coefficients of the energy with singularity structure removed at delta =1, farther from the origin and thereby accelerate summation convergence. The ground-state energies of He and H/sub 2//sup +/ are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using F/sub m/( delta )= Sigma jE/sub j/'/ Gamma (j+1-m) is considered. The standard deviation of results calculated with different values of the shift parameter m is proposed as a measure of summation accuracy. (47 References).
Abstract Number
A9822-3115-003
Subject Headings
Atomic structure
Convergence
Ground states
Helium neutral atoms
Hydrogen ions
Molecular electronic states
Perturbation theory
Positive ions
Key Phrase Identifiers
convergence; large-order expansions; Coulomb systems; singularities;
Pade-Borel approximants; renormalization; interelectron repulsion; Borel
function; summation convergence; ground-state energies; He; H/sub 2//sup +/;
shifted Borel summation; 1/D expansions; H.
Classification Codes
General mathematical and computational developments for atoms and molecules
[A3115].
Treatment
Theoretical or mathematical.
Chemicals
He/el; H/el.
CODEN
JMAPAQ
Language
English.
ISSN
0022-2488.
U.S. Copyright Clearance Center Code
0022-2488/98/39(10)/5112(11)/$15.00.
Document Number
S0022-2488(98)04210-8.
Publication Type
Journal Paper.
SICI
0022-2488(199810)39:10L.5112:ICEA;1-S
Update Code
199800.
Copyright
Copyright 1998, IEE.

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Citation 38
Accession Number
006093699
Author
Sergeev AV. Goodson DZ.
Institution
Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.
Title
Semiclassical self-consistent field perturbation theory for the hydrogen atom
in a magnetic field.
Source
International Journal of Quantum Chemistry, vol.69, no.2, 5 Aug. 1998,
pp.183-92. Publisher: Wiley, USA.
Country of Publication
USA.
Abstract
A recently developed perturbation theory for solving self-consistent field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent field approximation varies according to field strength and quantum state but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis. (45 References).
Abstract Number
A9901-3120B-001
Subject Headings
Hydrogen neutral atoms
Magnetic field effects
Perturbation theory
SCF calculations
Key Phrase Identifiers
semiclassical self-consistent field perturbation theory; H atom; magnetic
field; self-consistent field equations; summable large-order expansions;
field strength; quantum state; adiabatic approximations; adiabatic
hypothesis; H.
Classification Codes
SCF and HF calculations (atoms and molecules) [A3120B].
Treatment
Theoretical or mathematical.
Chemicals
H/el.
CODEN
IJQCB2
Language
English.
ISSN
0020-7608.
U.S. Copyright Clearance Center Code
0020-7608/98/020183-10.
Publication Type
Journal Paper.
SICI
0020-7608(19980805)69:2L.183:SSCF;1-A
Update Code
199800.
Copyright
Copyright 1998, IEE.

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Citation 39
Accession Number
006255458
Author
Goodson DZ. Sergeev AV.
Institution
Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.
Title
On the use of algebraic approximants to sum divergent series for Fermi
resonances in vibrational spectroscopy.
Source
Journal of Chemical Physics, vol.110, no.16, 22 April 1999, pp.8205-6.
Publisher: AIP, USA.
Country of Publication
USA.
Abstract
Pade summation of large-order perturbation theory can often yield highly accurate energy eigenvalues for molecular vibrations. However, for eigenstates involved in Fermi resonances the convergence of the Pade approximants can be very slow. This is because the energy is a multivalued function of the perturbation parameter while Pade approximants are single valued, and Fermi resonances occur when a branch point lies close to the physical value of the parameter. Algebraic approximants are multivalued generalizations of Pade approximants. Using the (200) state of H/sub 2/S and the (400) state of H/sub 2/O as examples of Fermi resonances, it is demonstrated here that algebraic approximants greatly improve the summation convergence. (10 References).
Abstract Number
A1999-13-3310-003
Subject Headings
Eigenvalues and eigenfunctions
Fermi resonance
Perturbation theory
Spectroscopy
Vibrational states
Key Phrase Identifiers
algebraic approximants; sum divergent series; Fermi resonances; vibrational
spectroscopy; eigenstates; perturbation theory; wave functions; strong
mixing; unperturbed harmonic eigenfunctions; resonant states; branch points;
eigenvalues; Riemann sheet; harmonic energies; branch point; convergence;
Pade approximants; rational functions; multiple-valued nature; algebraic
summation approximants.
Classification Codes
Vibrational analysis (molecular spectra) [A3310G]; Algebra, set theory, and
graph theory [A0210]; Molecular rotation, vibration, and vibration-rotation
constants [A3520P]; Specific calculations and results for atoms and molecules
[A3120].
Treatment
Theoretical or mathematical.
CODEN
JCPSA6
Language
English.
ISSN
0021-9606.
U.S. Copyright Clearance Center Code
0021-9606/99/110(16)/8205(2)/$15.00.
Document Number
S0021-9606(99)01216-7.
Publication Type
Journal Paper.
SICI
0021-9606(19990422)110:16L.8205:AADS;1-N
Update Code
199921.
Copyright
Copyright 1999, IEE.

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Citation 40
Accession Number
006406930
Author
Sergeev AV. Kais S.
Institution
Dept. of Chem., Purdue Univ., West Lafayette, IN, USA.
Title
Variational principle for critical parameters of quantum systems.
Source
Journal of Physics A-Mathematical & General, vol.32, no.39, 1 Oct. 1999,
pp.6891-6. Publisher: IOP Publishing, UK.
Country of Publication
UK.
Abstract
The variational principle for eigenvalue problems with a nonidentity weight operator is used to establish upper or lower bounds on critical parameters of quantum systems. Three problems from atomic physics are considered as examples. Critical screening parameters for the exponentially screened Coulomb potential are found using a trial function with one nonlinear variational parameter. The critical charge for the helium isoelectronic series is found using a Hylleraas-type trial function. Finally, critical charges for the same system subjected to a magnetic field are found using a product of two hydrogen-like basis sets. (21 References).
Abstract Number
A1999-24-3115-005
Subject Headings
Critical phenomena
Isoelectronic series
Nuclear screening
Potential energy functions
Quantum theory
Variational techniques
Key Phrase Identifiers
variational principle; eigenvalue problems; nonidentity weight operator;
upper bounds; lower bounds; critical parameters; quantum systems; atomic
physics; critical screening parameters; exponentially screened Coulomb
potential; nonlinear variational parameter; critical charge; He isoelectronic
series; Hylleraas-type trial function; magnetic field; hydrogen-like basis
sets.
Classification Codes
General mathematical and computational developments for atoms and molecules
[A3115]; Electronic structure of atoms and molecules, corrections and effects
of interactions [A3130]; Interatomic and intermolecular potentials and forces
[A3420]; Foundations, theory of quantum measurement, miscellaneous quantum
theories [A0365B].
Treatment
Theoretical or mathematical.
CODEN
JPHAC5
Language
English.
ISSN
0305-4470.
U.S. Copyright Clearance Center Code
0305-4470/99/396891+06$30.00.
Document Number
S0305-4470(99)04438-8.
Publication Type
Journal Paper.
SICI
0305-4470(19991001)32:39L.6891:VPCP;1-C
Update Code
199945.
Copyright
Copyright 1999, IEE.

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Citation 41
Accession Number
006479310
Author
Sergeev AV. Kais S.
Institution
Dept. of Chem., Purdue Univ., West Lafayette, IN, USA.
Title
Critical nuclear charges for N-electron atoms.
Source
Wiley. International Journal of Quantum Chemistry, vol.75, no.4-5, 15 Nov.-5
Dec. 1999, pp.533-42. USA.
Country of Publication
USA.
Conference Information
International Symposium on Atomic, Molecular, and Condensed Matter Theory. St
Augustine, FL, USA. 27 Feb.-5 March 1999.
Abstract
One-particle model with a spherically-symmetric screened Coulomb potential is proposed to describe the motion of a loosely bound electron in a multielectron atom when the nuclear charge, which is treated as a continuous parameter, approaches its critical value. The critical nuclear charge, Z/sub c/, is the minimum charge necessary to bind N electrons. Parameters of the model are chosen to meet known binding energies of the neutral atom and the isoelectronic negative ion. This model correctly describes the asymptotic behavior of the binding energy in the vicinity of the critical charge, gives accurate estimation of the critical charges in comparison with ab initio calculations for small atoms, and is in full agreement with the prediction of the statistical theory of large atoms. Our results rule out the stability of doubly charged atomic negative ions in the gas phase. Moreover, the critical charge obeys the proposed inequality, N-2[left angle bracket]or=Z/sub c/[left angle bracket]or=N-1. We show that in the presence of a strong magnetic field many atomic dianions become stable. (41 References).
Abstract Number
A2000-05-3120A-006
Subject Headings
Ab initio calculations
Binding energy
Negative ions
Potential energy functions
Statistical analysis
Key Phrase Identifiers
critical nuclear charges; N-electron atoms; one-particle model;
spherically-symmetric screened Coulomb potential; loosely bound electron;
multielectron atom; nuclear charge; continuous parameter; negative ions;
critical nuclear charge; parameters; binding energies; neutral atom;
isoelectronic negative ion; asymptotic behavior; critical charges;
statistical theory; doubly charged atomic negative ions; strong magnetic
field; atomic dianions.
Classification Codes
Ab initio calculations (atoms and molecules) [A3120A]; Atomic ionization
potentials, electron affinities [A3510H]; Probability theory, stochastic
processes, and statistics [A0250].
Treatment
Theoretical or mathematical.
CODEN
IJQCB2
Language
English.
ISSN
0020-7608.
U.S. Copyright Clearance Center Code
0020-7608/99/040533-10.
Publication Type
Conference Paper.
SICI
0020-7608(19991115/1205)75:4/5L.533:CNCE;1-K
Update Code
200004.
Copyright
Copyright 2000, IEE.

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Citation 42
Accession Number
006960904
Author
Sergeev AV. Kais S.
Institution
Dept. of Chem., Purdue Univ., West Lafayette, IN, USA.
Title
Resonance states of atomic anions.
Source
International Journal of Quantum Chemistry, vol.82, no.5, 20 April 2001,
pp.255-61. Publisher: Wiley, USA.
Country of Publication
USA.
Abstract
We study destabilization of an atom in its ground state with decrease of its nuclear charge. By analytic continuation from bound to resonance states, we obtain complex energies of unstable atomic anions with nuclear charge that is less than the minimum "critical" charge necessary to bind N electrons. We use an extrapolating scheme with a simple model potential for the electron, which is loosely bound outside the atomic core. Results for O/sup 2-/ and S/sup 2-/ are in good agreement with earlier estimates. Alternatively, we use the Hylleraas basis variational technique with three complex nonlinear parameters to find accurately the energy of two-electron atoms as the nuclear charge decreases. Results are used to check the less accurate one-electron model. (0 References).
Abstract Number
A2001-15-3150-002
Subject Headings
Bound states
Extrapolation
Ground states
Negative ions
Nuclear charge
Oxygen
Resonant states
Sulphur
Variational techniques
Key Phrase Identifiers
atomic anions; resonance state; destabilization; atom; ground state; nuclear
charge; analytic continuation; bound states; resonance states; complex
energies; unstable atomic anions; minimum critical charge; extrapolating
scheme; simple model potential; atomic core; S/sup 2-/; O/sup 2-/; Hylleraas
basis variational technique; complex nonlinear parameters; two-electron
atoms; one-electron model; S; O.
Classification Codes
Excited states of atoms and molecules [A3150]; Function theory, analysis
[A0230]; Specific calculations and results for atoms and molecules [A3120];
Numerical approximation and analysis [A0260].
Treatment
Theoretical or mathematical.
Chemicals
S/el; O/el.
CODEN
IJQCB2
Language
English.
ISSN
0020-7608.
Publication Type
Journal Paper.
SICI
0020-7608(20010420)82:5L.255:RSAA;1-N
Update Code
200125.
Copyright
Copyright 2001, IEE.