Results of your search :

Citations available:

Citations displayed:

*Go to ...* Help |
Logoff
*Query for Holdings at...* Purdue-West Lafayette

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.

[Click a holdings site listed above and a new browser window will open.]

**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.