Record 1 of 40
Author(s): Sergeev AV; Kais S
Title: Critical nuclear charges for N-electron atoms
Source: INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 1999, Vol 75, Iss 4-5, pp 533-542
Addresses: Kais S, Purdue Univ, Dept Chem, 1393 Brown Bldg, W Lafayette, IN 47907 USA.
Purdue Univ, Dept Chem, W Lafayette, IN 47907 USA.
Author Keywords: critical nuclear charges; N-electron atoms; stability of atomic dianions
KeywordsPlus: STRUCTURE CRITICAL PARAMETERS; STATE CORRELATION ENERGIES; LARGE-DIMENSION LIMIT; GROUND-STATE; NEGATIVE-IONS; BOUND-STATES; RENORMALIZATION; EQUATION
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(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 less than or equal to Z(c) less than or equal to N - 1. We show that in the presence of a strong magnetic field many atomic dianions become stable. (C) 1999 John Wiley & Sons, Inc.
Times Cited: 0
Source item page count: 10
Publication Date: NOV-DEC
IDS No.: 254ME
29-char source abbrev: INT J QUANTUM CHEM



Record 2 of 40
Author(s): Sergeev AV; Kais S
Title: Variational principle for critical parameters of quantum systems
Source: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 1999, Vol 32, Iss 39, pp 6891-6896
Addresses: Sergeev AV, Purdue Univ, Dept Chem, 1393 Brown Bldg, W Lafayette, IN 47907 USA.
Purdue Univ, Dept Chem, W Lafayette, IN 47907 USA.
KeywordsPlus: MAGNETIC-FIELD; CONVERGENCE; RADIUS; STATES; HELIUM; ATOM
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.
Times Cited: 0
Source item page count: 6
Publication Date: OCT 1
IDS No.: 245VG
29-char source abbrev: J PHYS-A-MATH GEN



Record 3 of 40
Author(s): Goodson DZ; Sergeev AV
Title: On the use of algebraic approximants to sum divergent series for Fermi resonances in vibrational spectroscopy
Source: JOURNAL OF CHEMICAL PHYSICS 1999, Vol 110, Iss 16, pp 8205-8206
Addresses: Goodson DZ, So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
KeywordsPlus: DIMENSIONAL PERTURBATION-THEORY; ANHARMONIC-OSCILLATORS
Times Cited: 0
Source item page count: 2
Publication Date: APR 22
IDS No.: 186QC
29-char source abbrev: J CHEM PHYS



Record 4 of 40
Author(s): Elout MO; Goodson DZ; Elliston CD; Huang SW; Sergeev AV; Watson DK
Title: Improving the convergence and estimating the accuracy of summation approximants of 1/D expansions for Coulombic systems
Source: JOURNAL OF MATHEMATICAL PHYSICS 1998, Vol 39, Iss 10, pp 5112-5122
Addresses: Elout MO, So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
Univ Oklahoma, Dept Phys & Astron, Norman, OK 73019 USA.
SI Vavilov State Opt Inst, St Petersburg 199034, Russia.
KeywordsPlus: LARGE-DIMENSION LIMIT; PERTURBATION-THEORY; ELECTRONIC-STRUCTURE; 2-ELECTRON ATOMS; SCHRODINGER-EQUATION; QUANTUM-MECHANICS; MAGNETIC-FIELD; EXCITED-STATES; HYDROGEN-ATOM; HELIUM
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 Pade'-Borel approximants with modifications that 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(j)E(j)'/ j!, where E-j' are the the expansion coefficients of the energy with singularity structure removed at d51, farther from the origin and thereby accelerate summation convergence. The ground-state energies of He and H-2(+) are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using F-m(delta) = Sigma(j)E(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. (C) 1998 American Institute of Physics. [S0022-2488(98)04210-8].
Times Cited: 0
Source item page count: 11
Publication Date: OCT
IDS No.: 124NC
29-char source abbrev: J MATH PHYS-NY



Record 5 of 40
Author(s): Popov VS; Sergeev AV
Title: Ionization of atoms in weak fields and the asymptotic behavior of higher-order perturbation theory
Source: JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS 1998, Vol 86, Iss 6, pp 1122-1126
Addresses: Popov VS, Inst Theoret & Expt Phys, Moscow 117218, Russia.
Inst Theoret & Expt Phys, Moscow 117218, Russia.
So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
KeywordsPlus: ANHARMONIC-OSCILLATOR; PADE APPROXIMANTS; MAGNETIC-FIELD; GROUND-STATE; HYDROGEN; 1/N-EXPANSION; COULOMB
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 < gamma(c)) to having a variable sign (for gamma > gamma(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(c) depends on the angle theta between the electric and magnetic fields. (C) 1998 American Institute of Physics.
Times Cited: 0
Source item page count: 5
Publication Date: JUN
IDS No.: 107XT
29-char source abbrev: J EXP THEOR PHYS



Record 6 of 40
Author(s): Sergeev AV; Goodson DZ
Title: Semiclassical self-consistent field perturbation theory for the hydrogen atom in a magnetic field
Source: INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 1998, Vol 69, Iss 2, pp 183-192
Addresses: Goodson DZ, So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
SI Vavilov State Opt Inst, St Petersburg 199034, Russia.
Author Keywords: self-consistent field theory; semiclassical perturbation theory; dimensional perturbation theory; adiabatic approximations; hydrogen atom in magnetic field
KeywordsPlus: LARGE-DIMENSION LIMIT; SCHRODINGER-EQUATION; QUANTUM-MECHANICS; ENERGY-LEVELS; 2-ELECTRON ATOMS; EXCITED-STATES; 1/N EXPANSION; HARTREE-FOCK; SYSTEMS; EIGENVALUES
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. (C) 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 183-192, 1998.
Times Cited: 0
Source item page count: 10
Publication Date: AUG 5
IDS No.: 102WJ
29-char source abbrev: INT J QUANTUM CHEM



Record 7 of 40
Author(s): Sergeev AV; Goodson DZ
Title: Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators
Source: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 1998, Vol 31, Iss 18, pp 4301-4317
Addresses: Sergeev AV, So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
SI Vavilov State Opt Inst, St Petersburg 199034, Russia.
KeywordsPlus: GROUND-STATE ENERGY; SCHRODINGER PERTURBATION-THEORY; SERIES ANALYSIS; EXCHANGE
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.
Times Cited: 5
Source item page count: 17
Publication Date: MAY 8
IDS No.: ZP034
29-char source abbrev: J PHYS-A-MATH GEN



Record 8 of 40
Author(s): Sergeev AV; Goodson DZ
Title: Self-consistent field perturbation theory of molecular vibrations
Source: MOLECULAR PHYSICS 1998, Vol 93, Iss 3, pp 477-484
Addresses: Sergeev AV, So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
So Methodist Univ, Dept Chem, Dallas, TX 75275 USA.
SI Vavilov State Opt Inst, St Petersburg 199034, Russia.
KeywordsPlus: COMPLEX ENERGY EIGENVALUES; WAVE-FUNCTIONS; BOUND-STATES; SYSTEM; SPECTROSCOPY; DYNAMICS; SERIES; ORDER; MODEL
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.
Times Cited: 0
Source item page count: 8
Publication Date: FEB 20
IDS No.: YY054
29-char source abbrev: MOL PHYS



Record 9 of 40
Author(s): Mur VD; Popov VS; Sergeev AV
Title: Coulomb corrections to scattering lengths and effective ranges for l not equal 0
Source: PHYSICS OF ATOMIC NUCLEI 1996, Vol 59, Iss 11, pp 1888-1894
Addresses: INST THEORET & EXPT PHYS, STATE RES CTR, MOSCOW 117259, RUSSIA.
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.
Times Cited: 0
Source item page count: 7
Publication Date: NOV
IDS No.: VU620
29-char source abbrev: PHYS ATOM NUCL-ENGL TR



Record 10 of 40
Author(s): Popov VS; Sergeev AV
Title: Effect of a magnetic field on the ionization of atoms
Source: JETP LETTERS 1996, Vol 63, Iss 6, pp 417-422
Addresses: Popov VS, INST THEORET & EXPTL PHYS, MOSCOW 117259, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG 199034, RUSSIA.
KeywordsPlus: PERTURBATION-THEORY; LARGE-ORDER
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. (C) 1996 American Institute of Physics.
Times Cited: 8
Source item page count: 6
Publication Date: MAR 25
IDS No.: UM315
29-char source abbrev: JETP LETT-ENGL TR



Record 11 of 40
Author(s): Mur VD; Popov VS; Sergeev AV
Title: Coulomb corrections to nuclear scattering lengths and effective ranges for weakly bound systems
Source: PHYSICS OF ATOMIC NUCLEI 1996, Vol 59, Iss 1, pp 62-71
Addresses: STATE RES CTR, INST THEORET & EXPTL PHYS, MOSCOW 117259, RUSSIA.
KeywordsPlus: 1/N EXPANSION; EIGENVALUES; POTENTIALS; LEVEL
Abstract: A procedure is considered for extracting the purely nuclear scattering length a(s) and effective range r(s) (which correspond to a strong-interaction potential V-s with disregarded Coulomb interaction) from the experimentally determined nuclear quantities a(cs) and r(cs), which are modified by Coulomb interaction. The Coulomb renormalization of a(s) and r(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-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(s) is found for potentials with a barrier.
Times Cited: 0
Source item page count: 10
Publication Date: JAN
IDS No.: TT600
29-char source abbrev: PHYS ATOM NUCL-ENGL TR



Record 12 of 40
Author(s): SERGEEV AV
Title: SUMMATION OF THE EIGENVALUE PERTURBATION-SERIES BY MULTIVALUED PADE APPROXIMANTS - APPLICATION TO RESONANCE PROBLEMS AND DOUBLE WELLS
Source: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 1995, Vol 28, Iss 14, pp 4157-4162
Addresses: SERGEEV AV, SI VAVILOV STATE OPT INST, TUCHKOV PEREULOK 1, ST PETERSBURG 199034, RUSSIA.
KeywordsPlus: ANHARMONIC-OSCILLATOR; ORDER; REAL
Abstract: Quadratic Pade approximants are used to obtain energy levels both for the anharmonic oscillator x(2)/2-lambda x(4) and for the double well -x(2)/2 + lambda x(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 sheer, 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.
Times Cited: 3
Source item page count: 6
Publication Date: JUL 21
IDS No.: RM213
29-char source abbrev: J PHYS-A-MATH GEN



Record 13 of 40
Author(s): POPOV VS; MUR VD; SERGEEV AV
Title: THEORY OF STARK-EFFECT IN THE STRONG-FIELD - CRITICAL FIELDS, ABOVE-BARRIER RESONANCES, DEPENDENCE ON DIMENSIONAL SCALING
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1994, Vol 106, Iss 4, pp 1001-1030
Addresses: POPOV VS, INT PHYS INST, MOSCOW 125040, RUSSIA.
MOSCOW THEORET & EXPTL PHYS INST, MOSCOW 117259, RUSSIA.
MOSCOW ENGN PHYS INST, MOSCOW 115409, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG 199034, RUSSIA.
KeywordsPlus: QUASI-STATIONARY STATES; UNIFORM ELECTRIC-FIELD; HYDROGEN-ATOM; PERTURBATION-THEORY; INTERFERENCE PHENOMENA; TUNNELING IONIZATION; RYDBERG ATOMS; LASER FIELD; HIGH ORDERS; 1/N-EXPANSION
Times Cited: 0
Source item page count: 30
Publication Date: OCT
IDS No.: PQ455
29-char source abbrev: ZH EKSP TEOR FIZ



Record 14 of 40
Author(s): POPOV VS; MUR VD; SERGEEV AV
Title: CRITICAL ELECTRIC-FIELDS AND STARK RESONANCES IN THE HYDROGEN-ATOM
Source: PHYSICS LETTERS A 1994, Vol 193, Iss 2, pp 159-164
Addresses: POPOV VS, INST THEORET & EXPTL PHYS, MOSCOW 117259, RUSSIA.
INT INST PHYS, MOSCOW 125040, RUSSIA.
MOSCOW PHYS ENGN INST, MOSCOW 115409, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG 199034, RUSSIA.
KeywordsPlus: TUNNELING IONIZATION; QUANTIZATION RULES; LASER FIELD; PHOTOIONIZATION; 1/N-EXPANSION; STATES
Abstract: The exact values of critical electric fields E(c) for different states of a hydrogen atom, including its ground state, as well as the widths Gamma(n) of the Stark resonances at E = E(c), are calculated (at E=E(c)(n(1), n(2), m) the potential barrier for an electron in the (n(1), n(2), m) state disappears). Using the modified quantization condition with barrier penetrability included, we explain the dependence of Gamma(n) on the principal quantum number n.
Times Cited: 4
Source item page count: 6
Publication Date: SEP 26
IDS No.: PH692
29-char source abbrev: PHYS LETT A



Record 15 of 40
Author(s): POPOV VS; SERGEEV AV
Title: LARGE ORDERS OF 1/N-EXPANSION FOR MULTIDIMENSIONAL PROBLEMS
Source: PHYSICS LETTERS A 1994, Vol 193, Iss 2, pp 165-172
Addresses: POPOV VS, INST THEORET & EXPTL PHYS, MOSCOW 117259, RUSSIA.
INT INST PHYS, MOSCOW 125040, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG 199034, RUSSIA.
KeywordsPlus: PERTURBATION-THEORY; QUANTUM-MECHANICS; STRONG-FIELD
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-2(+)), 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.
Times Cited: 11
Source item page count: 8
Publication Date: SEP 26
IDS No.: PH692
29-char source abbrev: PHYS LETT A



Record 16 of 40
Author(s): POPOV VS; MUR VD; SERGEEV AV
Title: CRITICAL FIELDS AND ABOVE-BARRIER STARK RESONANCES
Source: JETP LETTERS 1994, Vol 59, Iss 3, pp 158-162
Addresses: POPOV VS, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW 117259, RUSSIA.
MOSCOW ENGN PHYS INST, MOSCOW 115409, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG 199034, RUSSIA.
KeywordsPlus: QUANTIZATION RULES; 1/N-EXPANSION
Abstract: Exact values of the critical field E(c) are calculated for a hydrogen atom, including the case of the ground state. The widths GAMMA(n) of Stark resonances at E = E(c) are also calculated. In the above-barrier region (E > E(c)) the widths GAMMA(n)(E) are essentially linear functions of the electric field strength.
Times Cited: 4
Source item page count: 5
Publication Date: FEB 10
IDS No.: NC978
29-char source abbrev: JETP LETT-ENGL TR



Record 17 of 40
Author(s): POPOV VS; SERGEEV AV; MUR VD; SHCHEBLYKIN AV
Title: ON THE ASYMPTOTICS OF HIGH-ORDER TERMS OF THE 1/N EXPANSION
Source: PHYSICS OF ATOMIC NUCLEI 1994, Vol 57, Iss 6, pp 1057-1065
Addresses: POPOV VS, INST THEORET & EXPTL PHYS, MOSCOW, RUSSIA.
KeywordsPlus: PERTURBATION-THEORY; QUANTUM-MECHANICS; STRONG-FIELD; 1/N-EXPANSION; HYDROGEN
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.
Times Cited: 0
Source item page count: 9
Publication Date: JUN
IDS No.: NW247
29-char source abbrev: PHYS ATOM NUCL-ENGL TR



Record 18 of 40
Author(s): POPOV VS; SERGEEV AV
Title: ASYMPTOTICS OF THE HIGHEST ORDERS OF 1-N-DECOMPOSITION FOR MULTIDIMENSIONAL PROBLEMS
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1994, Vol 105, Iss 3, pp 568-591
Addresses: POPOV VS, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW 117259, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG 199164, RUSSIA.
KeywordsPlus: EXPONENTIALLY SMALL TERMS; PERTURBATION-THEORY; QUANTUM-MECHANICS; HYDROGEN-ATOM; 1/R EXPANSION; STRONG-FIELD; 1/N-EXPANSION; H2+
Times Cited: 1
Source item page count: 24
Publication Date: MAR
IDS No.: NE470
29-char source abbrev: ZH EKSP TEOR FIZ



Record 19 of 40
Author(s): POPOV VS; SERGEEV AV
Title: ASYMPTOTIC FORM OF HIGHER ORDERS OF THE 1/N EXPANSION
Source: JETP LETTERS 1993, Vol 57, Iss 5, pp 281-285
Addresses: POPOV VS, RUSSIAN ACAD SCI, INST THEORET & EXPTL PHYS, MOSCOW 117259, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG 199164, RUSSIA.
KeywordsPlus: PERTURBATION-THEORY; HYDROGEN-ATOM; STRONG-FIELD; 1/N-EXPANSION
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.
Times Cited: 0
Source item page count: 5
Publication Date: MAR 10
IDS No.: LA291
29-char source abbrev: JETP LETT-ENGL TR



Record 20 of 40
Author(s): POPOV VS; SERGEEV AV; SHCHEBLYKIN AV
Title: ON THE STRUCTURE OF LARGE ORDERS IN 1/N-EXPANSION
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1992, Vol 102, Iss 5, pp 1453-1468
Addresses: POPOV VS, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, RUSSIA.
SI VAVILOV STATE OPT INST, ST PETERSBURG, RUSSIA.
KeywordsPlus: LARGE-N EXPANSIONS; BENDER-WU FORMULA; PERTURBATION-THEORY; QUANTUM-MECHANICS; HYDROGEN-ATOM; STRONG-FIELD
Abstract: The asymptotic behaviour of large orders in 1/n-expansion is found for the problems of quantum mechanics. The coefficients of 1/n-expansion epsilon(k) are shown to increase as a factorial k! a(k) at k-->infinity. The a-parameter vs coupling constant dependence is studied. The analytic formulas obtained agree with the numerical calculations. The structure of 1/n-expansion is considered in detail for the Yukawa, Hulten and funnel potentials, as well as for the Stark effect in hydrogen and for the molecular ion H.
Times Cited: 9
Source item page count: 16
Publication Date: NOV
IDS No.: KC951
29-char source abbrev: ZH EKSP TEOR FIZ



Record 21 of 40
Author(s): POPOV VS; SERGEEV AV
Title: LARGE ORDERS OF THE 1/N EXPANSION IN QUANTUM-MECHANICS
Source: PHYSICS LETTERS A 1993, Vol 172, Iss 4, pp 193-198
Addresses: POPOV VS, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW 117259, RUSSIA.
KeywordsPlus: BENDER-WU FORMULA; PERTURBATION-THEORY; STRONG-FIELD; HYDROGEN; 1/N-EXPANSION
Abstract: The asymptotics of large orders of the 1/n expansion in quantum mechanics has been found. It is shown that the coefficients epsilon(k) grow as k!a(k) With k-->infinity, and the dependence of the parameter a on the coupling constant is investigated.
Times Cited: 12
Source item page count: 6
Publication Date: JAN 4
IDS No.: KG309
29-char source abbrev: PHYS LETT A



Record 22 of 40
Author(s): SERGEEV AV
Title: POSITRON NUCLEUS RESONANCES IN ELECTRIC AND MAGNETIC-FIELDS
Source: SOVIET JOURNAL OF NUCLEAR PHYSICS-USSR 1991, Vol 54, Iss 5, pp 744-747
Addresses: SERGEEV AV, STATE OPT INST, MOSCOW, USSR.
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.
Times Cited: 0
Source item page count: 4
Publication Date: NOV
IDS No.: HL314
29-char source abbrev: SOV J NUCL PHYS-ENGL TR



Record 23 of 40
Author(s): MUR VD; POPOV VS; SERGEEV AV
Title: GENERALIZATION OF THE GAMOW FORMULA TO THE MULTIDIMENSIONAL CASE
Source: SOVIET JOURNAL OF NUCLEAR PHYSICS-USSR 1991, Vol 54, Iss 4, pp 575-581
Addresses: MUR VD, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
KeywordsPlus: COUPLED ANHARMONIC OSCILLATORS; ELECTRIC-FIELD; RYDBERG ATOMS; STARK; 1/N-EXPANSION; RESONANCES; HYDROGEN
Abstract: A generalization of the Gamow formula for the width GAMMA of a quasistationary level (with energy E = E(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.
Times Cited: 0
Source item page count: 7
Publication Date: OCT
IDS No.: HG786
29-char source abbrev: SOV J NUCL PHYS-ENGL TR



Record 24 of 40
Author(s): POPOV VS; MUR VD; SERGEEV AV
Title: QUANTIZATION RULES WITH ALLOWANCE FOR BARRIER PENETRATION
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1991, Vol 100, Iss 1, pp 20-44
Addresses: POPOV VS, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
MOSCOW ENGN PHYS INST, MOSCOW, USSR.
SI VAVILOV STATE OPT INST, LENINGRAD, USSR.
KeywordsPlus: COUPLED ANHARMONIC OSCILLATORS; UNIFORM ELECTRIC-FIELD; HYDROGEN-ATOM; INTERFERENCE PHENOMENA; VACUUM POLARIZATION; PERTURBATION-THEORY; WKB APPROXIMATION; RYDBERG ATOMS; RESONANCES; STATES
Abstract: A correction to the quasiclassical quantization rules is found which is connected with the taking into account of the barrier penetration. The equation derived defines both the position E(r) and width GAMMA of the quasistationary level. The results are compared with numerical solutions of the Schrodinger equation and with the exactly soluble models. A generalization of the Gamov formula for systems with separated variables is obtained. The possibility of extending the results to the relativistic case is discussed.
Times Cited: 4
Source item page count: 25
Publication Date: JUL
IDS No.: GC903
29-char source abbrev: ZH EKSP TEOR FIZ



Record 25 of 40
Author(s): POPOV VS; MUR VD; SERGEEV AV
Title: QUANTIZATION RULES FOR QUASI-STATIONARY STATES
Source: PHYSICS LETTERS A 1991, Vol 157, Iss 4-5, pp 185-191
Addresses: POPOV VS, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
KeywordsPlus: STRONG ELECTRIC-FIELD; HYDROGEN-ATOM; 1/N-EXPANSION
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(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.
Times Cited: 11
Source item page count: 7
Publication Date: JUL 29
IDS No.: GA879
29-char source abbrev: PHYS LETT A



Record 26 of 40
Author(s): POPOV VS; MUR VD; SERGEV AV
Title: GENERALIZATION OF THE GAMOW FORMULA TO THE MULTIDIMENSIONAL CASE
Source: JETP LETTERS 1991, Vol 53, Iss 9, pp 455-458
Addresses: POPOV VS, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW 117259, USSR.
MOSCOW ENGN PHYS INST, MOSCOW 115409, USSR.
SI VAVILOV STATE OPT INST, LENINGRAD 199034, USSR.
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.
Times Cited: 0
Source item page count: 4
Publication Date: MAY 10
IDS No.: GA007
29-char source abbrev: JETP LETT-ENGL TR



Record 27 of 40
Author(s): VAINBERG VM; POPOV VS; SERGEYEV AV
Title: 1/N-EXPANSION FOR THE HYDROGEN-ATOM IN AN EXTERNAL-FIELD
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1990, Vol 98, Iss 3, pp 847-860
Addresses: VAINBERG VM, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
KeywordsPlus: MAGNETIC-FIELD; PERTURBATION-THEORY; STARK; STATES
Times Cited: 6
Source item page count: 14
Publication Date: SEP
IDS No.: EJ551
29-char source abbrev: ZH EKSP TEOR FIZ



Record 28 of 40
Author(s): POPOV VS; MUR VD; SERGEEV AV; WEINBERG VM
Title: STRONG-FIELD STARK-EFFECT - PERTURBATION-THEORY AND 1/N-EXPANSION
Source: PHYSICS LETTERS A 1990, Vol 149, Iss 9, pp 418-424
Addresses: POPOV VS, INT CTR THEORET PHYS, I-34100 TRIESTE, ITALY.
MOSCOW THEORET & EXPTL PHYS INST, MOSCOW 117259, USSR.
Times Cited: 39
Source item page count: 7
Publication Date: OCT 15
IDS No.: EE852
29-char source abbrev: PHYS LETT A



Record 29 of 40
Author(s): POPOV VS; MUR VD; SERGEEV AV
Title: 1/N-EXPANSION AND SCALING FOR THE STARK-EFFECT IN RYDBERG ATOMS
Source: PHYSICS LETTERS A 1990, Vol 149, Iss 9, pp 425-430
Addresses: POPOV VS, INT CTR THEORET PHYS, I-34100 TRIESTE, ITALY.
MOSCOW THEORET & EXPTL PHYS INST, MOSCOW 117259, USSR.
Times Cited: 31
Source item page count: 6
Publication Date: OCT 15
IDS No.: EE852
29-char source abbrev: PHYS LETT A



Record 30 of 40
Author(s): SERGEEV AV
Title: 1/N EXPANSION FOR THE 3-BODY PROBLEM
Source: SOVIET JOURNAL OF NUCLEAR PHYSICS-USSR 1989, Vol 50, Iss 4, pp 589-592
Addresses: SERGEEV AV, SI VAVILOV STATE OPT INST, LENINGRAD, USSR.
Times Cited: 2
Source item page count: 4
Publication Date: OCT
IDS No.: CY908
29-char source abbrev: SOV J NUCL PHYS-ENGL TR



Record 31 of 40
Author(s): MUR VD; POPOV VS; SERGEYEV AV
Title: THE 1/N-EXPANSION IN QUANTUM-MECHANICS
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1990, Vol 97, Iss 1, pp 32-46
Addresses: MUR VD, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
MOSCOW ENGN PHYS INST, MOSCOW, USSR.
Times Cited: 24
Source item page count: 15
Publication Date: JAN
IDS No.: CR130
29-char source abbrev: ZH EKSP TEOR FIZ



Record 32 of 40
Author(s): KREPOSTNOV PI; SERGEEV AV; UTKIN AB
Title: STUDY OF OPTICAL-PROPERTIES OF A DENSE XENON PLASMA IN FLASH TUBES
Source: OPTIKA I SPEKTROSKOPIYA 1989, Vol 67, Iss 3, pp 538-541
Times Cited: 1
Source item page count: 4
Publication Date: SEP
IDS No.: AU833
29-char source abbrev: OPT SPEKTROSK



Record 33 of 40
Author(s): MUR VD; POPOV VS; SERGEEV AV; SHCHEBLYKIN AV
Title: STARK RESONANCES AND SCALING IN RYDBERG ATOMS
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1989, Vol 96, Iss 1, pp 91-106
Addresses: MUR VD, MOSCOW ENGN PHYS INST, MOSCOW, USSR.
MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
Times Cited: 4
Source item page count: 16
Publication Date: JUL
IDS No.: AJ918
29-char source abbrev: ZH EKSP TEOR FIZ



Record 34 of 40
Author(s): VAINBERG VM; MUR VD; POPOV VS; SERGEEV AV; SHCHEBLYKIN AV
Title: THE 1/N EXPANSION IN QUANTUM-MECHANICS
Source: THEORETICAL AND MATHEMATICAL PHYSICS 1988, Vol 74, Iss 3, pp 269-278
Times Cited: 10
Source item page count: 10
Publication Date: MAR
IDS No.: U1727
29-char source abbrev: THEOR MATH PHYS-ENGL TR



Record 35 of 40
Author(s): VAINBERG VM; MUR VD; POPOV VS; SERGEEV AV
Title: STARK-EFFECT FOR THE RYDBERG STATES OF THE HYDROGEN-ATOM
Source: JETP LETTERS 1987, Vol 46, Iss 5, pp 225-230
Addresses: VAINBERG VM, MOSCOW ENGN PHYS INST, INST THEORET & EXPTL PHYS, MOSCOW, USSR.
Times Cited: 6
Source item page count: 6
Publication Date: SEP 10
IDS No.: L9987
29-char source abbrev: JETP LETT-ENGL TR



Record 36 of 40
Author(s): WEINBERG VM; MUR VD; POPOV VS; SERGEEV AV
Title: HYDROGEN-ATOM IN A STRONG ELECTRIC-FIELD
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1987, Vol 93, Iss 2, pp 450-462
Addresses: WEINBERG VM, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
Times Cited: 6
Source item page count: 13
Publication Date: AUG
IDS No.: J7763
29-char source abbrev: ZH EKSP TEOR FIZ



Record 37 of 40
Author(s): SERGEYEV AV
Title: A RECURSIVE ALGORITHM FOR PADE-HERMITE APPROXIMATIONS
Source: USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 1986, Vol 26, Iss 2, pp 17-22
Times Cited: 2
Source item page count: 6
IDS No.: J4963
29-char source abbrev: USSR COMPUT MATH MATH-ENGL TR



Record 38 of 40
Author(s): VAINBERG VM; MUR VD; POPOV VS; SERGEEV AV
Title: STRONG-FIELD STARK-EFFECT
Source: JETP LETTERS 1986, Vol 44, Iss 1, pp 9-13
Addresses: VAINBERG VM, MOSCOW THEORET & EXPTL PHYS INST, MOSCOW, USSR.
Times Cited: 31
Source item page count: 5
Publication Date: JUL 10
IDS No.: F1167
29-char source abbrev: JETP LETT-ENGL TR



Record 39 of 40
Author(s): SERGEEV AV; SHERSTYUK AI
Title: HIGHER-ORDER PERTURBATION-THEORY FOR THE BOUND-STATES OF THE DIRAC-EQUATION WITH A YUKAWA-TYPE POTENTIAL
Source: SOVIET JOURNAL OF NUCLEAR PHYSICS-USSR 1984, Vol 39, Iss 5, pp 731-734
Addresses: SERGEEV AV, SI VAVILOV STATE OPT INST, LENINGRAD, USSR.
Times Cited: 7
Source item page count: 4
IDS No.: TY964
29-char source abbrev: SOV J NUCL PHYS-ENGL TR



Record 40 of 40
Author(s): SERGEEV AV; SHERSTYOUK AI
Title: HIGHER ORDERS AND STRUCTURE OF PERTURBATION-THEORY SERIES FOR SCREENED COULOMB POTENTIAL
Source: ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI 1982, Vol 82, Iss 4, pp 1070-1078
Times Cited: 6
Source item page count: 9
IDS No.: NM751
29-char source abbrev: ZH EKSP TEOR FIZ