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  • 1. Albeverio, Sergio
    et al.
    Elander, NilsStockholm University, Faculty of Science, Department of Physics.
    Operator methods in ordinary and partial differential equations: proceedings of the Sonja Kovalevsky symposium held in the University of Stockholm, June 16-22, 20002002Conference proceedings (editor) (Refereed)
  • 2.
    Elander, Nils
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Levin, Sergey B.
    Yarevsky, Evgeny
    Convergence and Quantum Number Assignment Studies of Rovibrational Eigenstates in a Model of Predissociating NeICI van der Waals Complex2009In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 109, no 3, p. 459-468Article in journal (Refereed)
    Abstract [en]

    This report details extensions and further analysis of the results presented in an earlier study (Elander et al., Phys Rev A 2001, 64, 012505). Rovibrational resonances in a model of the triatomic van der Waals complex NeICI were studied with a full quantum mechanical, smooth exterior dilation technique realized in a three-dimensional finite element code. Both exact and approximate results, where Coriolis effects are neglected, are presented, and their structures are discussed. Although the helicity is a good quantum number in a one-equation approximation, it is here demonstrated that this is not in the case when including Coriolis coupling, that is, couplings to other helicity components. The behavior of the resonance widths and the positions together with the structure of the resonance wave functions and their dependence on the total angular momentum and its projection have been studied. The dependence of the width of a given resonance oil the total angular momentum was found to be weak while the dependence on the helicity is stronger. 

  • 3.
    Elander, Nils O
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Rakityansky, Sergei
    Univ Pretoria, Dept Phys, ZA-002 Pretoria, South Africa .
    Resonances and Their Relations to Spectral Densities and Scattering Cross Sections in the Schrodinger Formulation2013In: Few-body systems, ISSN 0177-7963, E-ISSN 1432-5411, Vol. 54, no 5-6, p. 685-695Article in journal (Refereed)
    Abstract [en]

    The concept of resonances for a two-body single and many channel Schrodinger problem is discussed with respect to the Titchmarsh-Weyl theory. It is argued that the contributions from the entire set of resonances together with the free particle spectral density build the entire spectrum. The implication of this statement on the influence of resonances on a two-body scattering cross section is discussed. It is described how the residues of the S-matrix at a complex resonance energy, i.e. two complex numbers, is used to define its contribution to the cross section. The limitations of the Breit-Wigner approximation is discussed.

  • 4.
    Elander, Nils
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Shilyaeva, Ksenia
    Stockholm University, Faculty of Science, Department of Physics.
    Ostrovsky, Valentin
    V. Fock Institute of Physics, St. Petersburg State University.
    Yarevsky, Evgeny
    St. Petersburg State University.
    Rakityanski, Sergey
    University of South Africa.
    Tools for assigning resonance structures in collisions of few body quantum systems2006In: Few-body systems, ISSN 0177-7963, E-ISSN 1432-5411, Vol. 38, no 2-4, p. 109-114Article in journal (Refereed)
  • 5.
    Elander, Nils
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Volkov, Mikhail
    Stockholm University, Faculty of Science, Department of Physics.
    Larsson, Åsa
    Stockholm University, Faculty of Science, Department of Physics.
    Stenrup, Michael
    Stockholm University, Faculty of Science, Department of Physics.
    Mezei, J. Zsolt
    Stockholm University, Faculty of Science, Department of Physics.
    Yarevsky, Evgeny
    Yakolev, Sergey
    Quantum Scattering with the Driven Schrödinger Approachand Complex Scaling2009In: Few-body systems, ISSN 0177-7963, E-ISSN 1432-5411, Vol. 45, no 2-4, p. 197-201Article in journal (Refereed)
    Abstract [en]

    Quantum scattering calculations of two and three-body systems with Coulomb interaction using thedriven Schrödinger equation combined with exterior complex scaling are discussed. A rigorous formulationfor two-body scattering is reported, and its generalization to three-body scattering is considered.

  • 6. Gagin, Anton
    et al.
    Yarevsky, Evgeny
    Salci, Moses
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Eigen Energies and the Statistical Distributions of the Rovibrational Levels of the Bosonic van der Waals Argon Trimer2009In: Journal of Physical Chemistry A, ISSN 1089-5639, E-ISSN 1520-5215, Vol. 113, no 52, p. 14979-14986Article in journal (Refereed)
    Abstract [en]

    The eigen energies and the statistical distributions of the rovibrational levels (J = 0-2) of the bosonic van der Waals argon trimer were calculated using a full angular momentum three-dimensional finite element method. The influence of interatomic potentials on the vibrational levels and statistical properties of the trimer was discussed.

  • 7.
    Kapshai, Valery
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Alferova, Tatjana
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Integral equations and complex resonance energies for analytical potentials2007In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 107, no 5, p. 1029-1039Article in journal (Refereed)
    Abstract [en]

    It is shown that the Volterra integral equation in combination with complex scaling gives a formalism capable to solve Schrodinger-type problems concerning bound states and resonances. The regular solution of the Schrodinger equation presented at the Volterra integral equation allows us to define the explicit form of the Jost function analytically continued into the lower half complex momentum plane. The resulting formalism is used to develop a numerical method for finding resonances defined as zeros of the Jost function. The numerical method is tested on several analytical potentials; it gives good results for arbitrary orbital momentum l.

  • 8.
    Kapshai, Valery
    et al.
    Gomel State University.
    Shilyaeva, Ksenia
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Integral equations for different wavefunctions and their use in finding resonances2009In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 42, no 4, p. 044001-Article in journal (Refereed)
  • 9.
    Kapshai, Valery
    et al.
    Gomel State University.
    Shilyaeva, Ksenia
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Integral equations for the Jost solutions and decaying resonance states2006In: Proceedings of the Gomel State University, 2006, Vol. 6, p. 3-8Conference paper (Refereed)
  • 10.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Complex scaling and selfadjoint dilations1993In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 46, no 3, p. 415-418Article in journal (Refereed)
    Abstract [en]

    Complex scaling of the Schrödinger equation on the halfaxis with a nontrivial boundary condition at the origin is investigated. A self-adjoint dilation of the corresponding dissipative operator is constructed. The relations between the scattering problems for the operator and it's dilation are clarified

  • 11.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Pavlov, Boris
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Resonances and irreversibility for Schroedinger evolution1993In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 46, no 3, p. 401-413Article in journal (Refereed)
    Abstract [en]

    The relations between the Schrödinger and wave evolutions are investigated. A generalization of the Lax-Phillips scattering theory for the case of the Schrödinger equation is constructed. An analog of the wave decay operator is obtained. The general ideas are illustrated by an explicitly solvable model of multichannel scattering on the halfaxis. A Lax-Phillips scattering theory is developed for the model operator obtained by a self-adjoint perturbation of the background operator

  • 12.
    Mezei, J. Z.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Roos, Johanna Brinne
    Stockholm University, Faculty of Science, Department of Physics.
    Shilyaeva, K.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Larson, Åsa
    Stockholm University, Faculty of Science, Department of Physics.
    Mutual neutralization in low-energy H(+) + F(-) collisions2011In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 84, no 1, p. 012703-Article in journal (Refereed)
    Abstract [en]

    The cross section for mutual neutralization in collisions between H(+) and F(-) ions at low energies ( E <= 10 eV) is calculated using a molecular close-coupling approach. Two different representations of the quasidiabatic potentials and couplings of HF are used. The effect of autoionization on the cross section is investigated. The coupled Schrodinger equation for the nuclear motion is solved using a numerical integration of the corresponding matrix Riccati equation and the cross section for mutual neutralization is computed from the asymptotic value of the logarithmic derivative of the radial wave function. The magnitude of the cross section for mutual neutralization in this reaction is small compared to other systems. This can be understood by the lack of avoided crossings at large internuclear distances. Resonant structures are found in the cross section and these are assigned with dominant angular momentum quantum number. The cross section for mutual neutralization in collisions of D(+) and F(-) ions is also calculated.

  • 13.
    Mezei, Zsolt
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Stenrup, Michael
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Larson, Åsa
    Stockholm University, Faculty of Science, Department of Physics.
    Double charge transfer in low-energy H+ + H- collisions2010In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 82, no 1, p. 14701-Article in journal (Refereed)
    Abstract [en]

    The cross section for double charge transfer between H+ and H- at low collision energies (E <= 90 eV) is calculated using a many-state molecular close-coupling model. The wave function is expanded in a diabatic representation of the seven lowest (1)Sigma(+)(g) and the six lowest (1)Sigma(+)(u) states of the hydrogen molecule. The calculated cross section shows clear oscillations as a function of the collision energy, similar to those observed experimentally. However, the magnitude of the calculated cross section is larger than found in experiments. Also, the cross section for double charge transfer in collisions between D+ and H- is calculated.

  • 14.
    Nkambule, Sifiso M.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Larson, Åsa
    Stockholm University, Faculty of Science, Department of Physics.
    Lecointre, Julien
    Urbain, Xavier
    Differential and total cross sections of mutual neutralization in low-energy collisions of isotopes of H+ + H-2016In: Physical Review A, ISSN 2469-9926, Vol. 93, no 3, article id 032701Article in journal (Refereed)
    Abstract [en]

    Mutual neutralization in the collisions of H+ and H- is studied both theoretically and experimentally. The quantum-mechanical ab initio model includes covalent states associated with the H(1)+H(n <= 3) limits and the collision energy ranges from 1 meV to 100 eV. The reaction is theoretically studied for collisions between different isotopes of the hydrogen ions. From the partial wave scattering amplitude, the differential and total cross sections are computed. The differential cross section is analyzed in terms of forward- and backward-scattering events, showing a dominance of backward scattering which can be understood by examining the phase of the scattering amplitudes for the gerade and ungerade set of states. The isotope dependence of the total cross section is compared with the one obtained using a semiclassical multistate Landau-Zener model. The final state distribution analysis emphasizes the dominance of the n = 3 channel for collisions below 10 eV, while at higher collision energies, the n = 2 channel starts to become important. For collisions of ions forming a molecular system with a larger reduced mass, the n = 2 channel starts to dominate at lower energies. Using a merged ion-beam apparatus, the branching ratios for mutual neutralization in H+ and H- collisions in the energy range from 11 to 185 eV are measured with position- and time-sensitive particle detectors. The measured and calculated branching ratios satisfactorily agree with respect to state contributions.

  • 15.
    Rakityansky, S. A.
    et al.
    Univ Pretoria, Dept Phys, Pretoria, South Africa.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Analytic structure and power series expansion of the Jost function for the two-dimensional problem2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 13, p. 135209-Article in journal (Refereed)
    Abstract [en]

    For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots.

  • 16. Rakityansky, S. A.
    et al.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Multi-channel analog of the effective-range expansion2011In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, no 11, p. 115303-Article in journal (Refereed)
    Abstract [en]

    Similar to the standard effective-range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jost-matrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependences at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power series near an arbitrary point in the domain of the complex energy plane where it is analytic. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This means that near an arbitrary point in the domain of physically interesting complex energies it is possible to obtain a semi-analytic expression for the Jost-matrix (and therefore for the S-matrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.

  • 17. Rakityansky, S. A.
    et al.
    Elander, Nils O.
    Stockholm University, Faculty of Science, Department of Physics.
    A METHOD FOR EXTRACTING THE RESONANCE PARAMETERS FROM EXPERIMENTAL CROSS-SECTIONS2013In: International Journal of Modern Physics E, ISSN 0218-3013, Vol. 22, no 5, p. UNSP 1350032-Article in journal (Refereed)
    Abstract [en]

    Within the proposed method, a set of experimental data points are fitted using a multi-channel S-matrix. Then the resonance parameters are located as its poles on an appropriate sheet of the Riemann surface of the energy. The main advantage of the method is that the S-matrix is constructed in such a way that it has proper analytic structure, i.e. for any number of two-body channels, the branching at all the channel thresholds is represented via exact analytic expressions in terms of the channel momenta. The way the S-matrix is constructed makes it possible not only to locate multi-channel resonances but also to extract their partial widths as well as to obtain the scattering cross-section in the channels for which no data are available. The efficiency of the method is demonstrated by two model examples of a single-channel and a two-channel problems, where known resonance parameters are rather accurately reproduced by fitting the pseudo-data artificially generated using the corresponding potentials.

  • 18.
    Rakityansky, S. A.
    et al.
    Univ Pretoria, Dept Phys, Pretoria, South Africa.
    Elander, Nils O.
    Stockholm University, Faculty of Science, Department of Physics.
    Analytic Structure and Power-Series Expansion of the Jost Matrix2013In: Few-body systems, ISSN 0177-7963, E-ISSN 1432-5411, Vol. 54, no 5-6, p. 673-683Article in journal (Refereed)
    Abstract [en]

    For the Jost-matrix that describes the multi-channel scattering, the momentum dependencies at all the branching points on the Riemann surface are factorized analytically. The remaining single-valued matrix functions of the energy are expanded in the power-series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain an analytic expression for the Jost-matrix (and therefore for the S-matrix) near an arbitrary point on the Riemann surface (within the domain of its analyticity) and thus to locate the resonant states as the S-matrix poles. This approach generalizes the standard effective-range expansion that now can be done not only near the threshold, but practically near an arbitrary point on the Riemann surface of the energy. Alternatively, The semi-analytic (power-series) expression of the Jost matrix can be used for extracting the resonance parameters from experimental data. In doing this, the expansion coefficients can be treated as fitting parameters to reproduce experimental data on the real axis (near a chosen center of expansion E (0)) and then the resulting semi-analytic matrix S(E) can be used at the nearby complex energies for locating the resonances. Similarly to the expansion procedure in the three-dimensional space, we obtain the expansion for the Jost function describing a quantum system in the space of two dimensions (motion on a plane), where the logarithmic branching point is present.

  • 19.
    Rakityansky, S. A.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils O
    Stockholm University, Faculty of Science, Department of Physics.
    Generalized effective-range expansion2009In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 42, no 22, p. 225302-Article in journal (Refereed)
    Abstract [en]

    A systematic and accurate procedure has been developed for calculating the coefficients phi((in/out))(ln) of the series expansion f(l)((in/out))(k) = Sigma(infinity)(n=0)(k-k(0))(n) phi((in/out))(ln) of the Jost functions in the vicinity of an arbitrary point k(0) in the complex momentum plane. This makes it possible to obtain an analytic expression for the S-matrix s(l)(k) = f(l)((out))(k)/f(l)((in))(k) around k(0) and locate its possible poles. In the particular case of l = 0 and k(0) = 0, any number of the parameters of the standard effective-range expansion k cot delta(0) = -1/a + r(0)k(2)/2 - ... are easily obtained using the corresponding coefficients phi((in/out))(ln). Numerical examples demonstrate the stability and accuracy of the proposed method.

  • 20.
    Salci, Moses
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Evgeny, Yarevsky
    Stockholm University, Faculty of Science, Department of Physics.
    Levin, Sergey B.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Finite element investigation of the ground states of the helium trimers 4He3 and 4He23He2007In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 107, no 7, p. 464-468Article in journal (Refereed)
    Abstract [en]

    A three-dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers 4He3 and 4He23He. Three different He–He interaction potentials of hard-core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated.

  • 21.
    Shilyaeva, Ksenia
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander , Nils
    Yarevsky, Evgeny
    Role of resonances in building cross sections: A comparison between the Mittag-Leffler and the Lippman Schwiger approaches2007In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 107, no 6, p. 1301-1315Article in journal (Refereed)
  • 22.
    Shilyaeva, Ksenia
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Yarevsky, Evgeny
    St. Petersburg State University.
    The role of resonances in building cross sections: The Mittag-Leffler expansion in a two channel scattering2009In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 109, no 3, p. 414-424Article in journal (Refereed)
  • 23.
    Shilyaeva, Ksenia
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Yarevsky, Evgeny
    St. Petersburg State University.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Identifying resonance structures in a scattering cross section using the N3+ + H -> NH3+ -> N2+ + H+ reaction as an example2009In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 42, no 4, p. 044011-Article in journal (Refereed)
  • 24.
    Stenrup, Michael
    et al.
    Kungliga tekniska högskolan (KTH), Skolan för bioteknologi, Teoretisk kemi.
    Larson, Åsa
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Mutual neutralization in low-energy H+ + H- collisions: A quantum ab initio study2009In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 79, no 1, p. 012713-Article in journal (Refereed)
    Abstract [en]

    The mutual neutralization of H+ and H at low collision energies is studied by means of a molecular close-coupling approach. All degrees of freedom are treated at the full quantum level also taking into account the identity of the nuclei. The relevant 1Σg+ and 1Σu+ electronic states as well as the associated nonadiabatic radial couplings are calculated for internuclear distances between 0.5 and 50a0. Following a transformation into a strictly diabatic basis, these quantities enter into a set of coupled equations for the motion of the nuclei. Numerical solution of these equations allows the cross sections for neutralization into the H(1)+H(n), n=1,2,3 final states to be calculated. In the present paper, results are reported for the collision energy region 0.001–100 eV, with special emphasis on the important energy region below 10 eV. The low temperature rate coefficient is obtained from a parametrization of the calculated cross section and is estimated to be valid over the range 10–10 000 K.

  • 25. Volkov, M. V.
    et al.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Yakovlev, S. L.
    Yarevsky, E. A.
    Investigation of scattering processes in quantum few-body systems involving long-range interaction by the complex-rotation method2013In: Physics of Atomic Nuclei, ISSN 1063-7788, E-ISSN 1562-692X, Vol. 76, no 2, p. 188-195Article in journal (Refereed)
    Abstract [en]

    The complex-rotation method adapted to solving the multichannel scattering problem in the two-body system where the interaction potential contains the long-range Coulomb components is described. The scattering problem is reformulated as the problem of solving a nonhomogeneous Schrodinger equation in which the nonhomogeneous term involves a Coulomb potential cut off at large distances. The incident wave appearing in the nonhomogeneous term is a solution of the Schrodinger equation with longrange Coulomb interaction. This formulation is free from approximations associated with a direct cutoff of Coulomb interaction at large distances. The efficiency of this formalism is demonstrated by considering the example of solving scattering problems in the alpha-alpha and p-p systems.

  • 26.
    Volkov, Mikhail V.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Yakovlev, S. L.
    Yarevsky, E. A.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Potential splitting approach to multichannel Coulomb scattering: The driven Schrodinger equation formulation2011In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 83, no 3, p. 032722-Article in journal (Refereed)
    Abstract [en]

    In this paper we suggest an approach for the multichannel Coulomb scattering problem. The Schrodinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The boundary conditions at infinity for this set of equations have been proven to be purely outgoing waves. The formulation presented here is based on splitting the interaction potential into a finite-range core part and a long-range tail part. The conventional matching procedure coupled with the integral Lippmann-Schwinger equations technique is used in the formal theoretical basis of this approach. The reformulated scattering problem is suitable for application in the exterior complex scaling technique: the practical advantage is that after complex scaling, the problem is reduced to a boundary problem with zero boundary conditions. The Coulomb wave functions are used only at a single point; if this point is chosen to be at a sufficiently large distance, on using the asymptotic expansion of Coulomb functions, one may completely avoid the Coulomb functions in the calculations. The theoretical results are illustrated with numerical calculations for two models.

  • 27.
    Volkov, Mikhail V.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Yarevsky, E.
    Yakovlev, S. L.
    Solving the Coulomb scattering problem using the complex-scaling method2009In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 85, no 3, p. 30001-Article in journal (Refereed)
    Abstract [en]

    We present a rigorous formalism for solving the scattering problem for long-rangeinteractions without using exact asymptotic boundary conditions. The long-range interaction maycontain both Coulomb and short-range potentials. The exterior complex-scaling method, appliedto a specially constructed inhomogeneous Schr¨odinger equation, transforms the scattering probleminto a boundary problem with zero boundary conditions. The local and integral representations forthe scattering amplitudes have been derived. The formalism is illustrated with numerical examples.

  • 28.
    Volkov, Mikhail V.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Yakovlev, S. L.
    Yarevsky, E.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Potential splitting approach to multichannel Coulomb scattering: the driven Schrödinger equation formulationArticle in journal (Refereed)
    Abstract [en]

    In this paper we suggest a new approach for the multichannel Coulomb scattering problem. TheSchr¨odinger equation for the problem is reformulated in the form of a set of inhomogeneous equationswith a finite-range driving term. The boundary conditions at infinity for this set of equations havebeen proven to be purely outgoing waves. The formulation presented here is based on splittingthe interaction potential into a finite range core part and a long range tail part. The conventionalmatching procedure coupled with the integral Lippmann-Schwinger equations technique are usedin the formal theoretical basis of this approach. The reformulated scattering problem is suitablefor application in the exterior complex scaling technique: the practical advantage is that after thecomplex scaling the problem is reduced to a boundary problem with zero boundary conditions. TheCoulomb wave functions are used only at a single point: if this point is chosen to be at a sufficientlylarge distance, on using the asymptotic expansion of Coulomb functions, one may completely avoidthe Coulomb functions in the calculations. The theoretical results are illustrated with numericalcalculations for two models.

  • 29.
    Volkov, Mikhail Vladimirovich
    et al.
    Stockholm University, Faculty of Science, Department of Physics. St Petersburg State University, Russia.
    Yakovlev, S. L.
    Yarevsky, E. A.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Adiabatic versus diabatic approach to multichannel Coulomb scattering for mutual neutralisation reaction H+ + H- -> H*(2) -> H(1) + H(n)2015In: Chemical Physics, ISSN 0301-0104, E-ISSN 1873-4421, Vol. 462, p. 57-64Article in journal (Refereed)
    Abstract [en]

    In this paper it is demonstrated that the split-potential driven Schrodinger approach to two-body Coulomb multichannel quantum scattering in a diabatic framework presented by us in a previous paper (Volkov et al., 2011) also can be formulated within an adiabatic framework. The new formulation of the theory is numerically realised using finite element discrete variable representation. The method is applied to a realistic model of the fundamental mutual neutralisation reaction H+ + H- -> H*(2) -> H(1) + H(n) described in terms of the seven lowest (1)Sigma(+)(g) electronic states of the H-2 molecule. The obtained cross sections are in good agreement with other methods applied to the same model.

  • 30.
    Volkov, Mikhail
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Yakovlev, S. L.
    Yarevsky, E.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    A Potential-splitting approach to multichannel Coulomb scattering: the driven Schrödinger equation formulation II. Comparing an Adiabatic versus a Diabaticrepresentation. Application to the fundamental low-energy mutual neutralisationreaction H+ + H− ! H2 ! H(1) + H(n)Manuscript (preprint) (Other academic)
    Abstract [en]

    In this paper it is demonstrated that the split-potential driven Schrödinger approach to two-body Coulomb multichannel quantum scattering in a diabatic framework presented by us in a previouspaper [XXXXX] also can be formulated within an adiabatic framework. The new formulation of thetheory is numerically realised using finite element discrete variable representation. The method isapplied to a realistic model of the fundamental mutual neutralisation reaction H+ + H−! H2 !H(1) + H(n) described in terms of the seven lowest 1+g electronic states of the H2 molecule. Theobtained cross sections are in good agreement with other methods applied to the same model.

  • 31. Yakovlev, S. L.
    et al.
    Volkov, Mikhail V.
    Stockholm University, Faculty of Science, Department of Physics.
    Yarevsky, E.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    The impact of sharp screening on the Coulomb scattering problem in three dimensions2010In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 43, no 24, p. 245302-Article in journal (Refereed)
    Abstract [en]

    The scattering problem for two particles interacting via theCoulomb potential isexamined for the case where the potential has a sharp cut-off at some distance.The problem is solved for two complementary situations, firstly, when theinterior part of the Coulomb potential is left in the Hamiltonian and, secondly,when the long-range tail is considered as the potential. The partial wave resultsare summed up to obtain the wavefunction in three dimensions. It is shownthat in the domains where the wavefunction is expected to be proportionalto the known solutions, the proportionality is given by an operator actingon the angular part of the wavefunction. The explicit representation for thisoperator is obtained in the basis of Legendre polynomials. We proposed adriven Schr¨odinger equation including an inhomogeneous term of the finiterange with purely outgoing asymptotics for its solution in the case of thethree-dimensional scattering problem with long-range potentials.

  • 32. Yakovlev, S. L.
    et al.
    Yarevsky, E. A.
    Elander, Nils O.
    Stockholm University, Faculty of Science, Department of Physics.
    Belyaev, A. K.
    Asymptotic Solution of A Multichannel Scattering Problem with A Nonadiabatic Coupling2018In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 195, no 3, p. 874-885Article in journal (Refereed)
    Abstract [en]

    We consider a multichannel scattering problem in an adiabatic representation. We assume that the nonadiabatic coupling matrix has a nontrivial value at large internuclear separations, and we construct asymptotic solutions at large internuclear distances. We show that these solutions up to the first order of the perturbation theory are identical to the asymptotic solutions of the reprojection approach, which was previously proposed as a means for solving the electron translation problem in the context of the Born-Oppenheimer method.

  • 33. Yarevsky, E.
    et al.
    Yakovlev, S. L.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Potential splitting approach to e-H and e-He+ scattering2017In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 50, no 5, article id 055001Article in journal (Refereed)
    Abstract [en]

    An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schrodinger equation for the long range tail of the reaction potential is used as an incoming wave. This reformulation of the scattering problem into an inhomogeneous Schrodinger equation with asymptotic outgoing waves makes it suitable for solving with the exterior complex scaling technique. The validity of the approach is analyzed from a formal point of view and demonstrated numerically, where the calculations are performed with the finite element method. The method of splitting the potential in this way is illustrated with calculations of the electron scattering on the hydrogen atom and the positive helium ion in energy regions where resonances appear.

  • 34. Yarevsky, E.
    et al.
    Yakovlev, S. L.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Volkov, M. V.
    On the Scattering of the Electron off the Hydrogen Atom and the Helium Ion Below and Above the Ionization Threshold: Temkin-Poet Model2014In: Few-body systems, ISSN 0177-7963, E-ISSN 1432-5411, Vol. 55, no 8-10, p. 1057-1058Article in journal (Refereed)
    Abstract [en]

    We generalize here the splitting approach to the long range (Coulomb) interaction for the three body scattering problem. With this approach, the exterior complex rotation technique can be applied for systems with asymptotic Coulomb interaction. We illustrate the method with calculations of the electron scattering on the hydrogen atom and positive helium ion in the frame of the Temkin-Poet model.

  • 35. Yarevsky, E.
    et al.
    Yakovlev, S. L.
    Larson, Åsa
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Potential-splitting approach applied to the Temkin-Poet model for electron scattering off the hydrogen atom and the helium ion2015In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 48, no 11Article in journal (Refereed)
    Abstract [en]

    The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three-body systems. This approach is based on splitting the reaction potential into a finite range core part and a long range tail part. The solution to the Schrodinger equation for the long range tail Hamiltonian is found analytically, and used as an incoming wave in the three body scattering problem. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling technique in the sense that the problem after the complex dilation is reduced to a boundary value problem with zero boundary conditions. We illustrate the method with calculations on the electron scattering off the hydrogen atom and the positive helium ion in the frame of the Temkin-Poet model.

1 - 35 of 35
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