N. Elander - Academia.edu (original) (raw)

Papers by N. Elander

Chemical Physics, 2015

Abstract In this paper it is demonstrated that the split-potential driven Schrodinger approach to... more Abstract 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 Σ g + electronic states of the H 2 molecule. The obtained cross sections are in good agreement with other methods applied to the same model.

Physical Review A, 1982

A recently proposed complex stabilization method is examined from the viewpoint of the necessity ... more A recently proposed complex stabilization method is examined from the viewpoint of the necessity for an explicit construction of the coordinate-rotated Hamiltonian. It is demonstrated and proved that the argument for using unrotated Hamiltonians in resonance-structure determinations must be taken in a restricted sense. With the use of square-integrable basis functions, it is shown that complex rotation is necessary to directly calculate complex resonance poles. We illustrate our conclusion by a numerical model calculation.

The boundary conditions for the Schroedinger operator with the ‐ 0 -interaction are discussed. A ... more The boundary conditions for the Schroedinger operator with the ‐ 0 -interaction are discussed. A new class of selfadjoint extensions is investigated. This note is devoted to the Schroedinger operator with ‐ 0 -potential

An approach based on splitting the reaction potential into a finite range part and a long range t... more 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 Schr\"odinger 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 Schr\"odinger 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.

arXiv: Atomic Physics, 2020

The multi-channel Coulomb scattering problem in the adiabatic representation is considered. The n... more The multi-channel Coulomb scattering problem in the adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-zero asymptotic behavior at large internuclear separations. The asymptotic solutions at large inter-nuclear distances are {therefore} constructed. The asymptotic boundary conditions with S-matrix and K-matrix for the scattering problem are formulated on the basis of constructed asymptotic solutions.

Physical Review Letters, 1993

Long lived (0.8 ms, 6 ms, and >3.8 s) states i... more Long lived (0.8 ms, 6 ms, and >3.8 s) states in CO2+ have been observed for the first time by monitoring beams of 75-300 keV ions in the ion storage ring ASTRID. It is the first experimental evidence that a doubly charged molecule can be stable on a time scale of seconds. The results are theoretically interpreted by means of

The matrix elements of the multi-channel Jost matrices are written in such a way that their depen... more The matrix elements of the multi-channel Jost matrices are written in such a way that their dependencies on all possible odd powers of channel momenta are factorized explicitly. As a result the branching of the Riemann energy surface at all the channel thresholds is represented in them via exact analytic expressions. The remaining single-valued functions of the energy are expanded in the Taylor series near an arbitrary point on the real axis. Using the thus obtained Jost matrices, the S-matrix is constructed and then the scattering cross section is calculated, which therefore depends on the Taylor expansion coefficients. These coefficients are considered as the adjustable parameters that are optimized to fit a given set of experimental data. After finding the coefficients, the resonances are located as zeros of the Jost matrix determinant at complex energies. Within this approach the S-matrix has proper analytic structure. This enables us not only to locate multi-channel resonances ...

Use of an electron-beam phase-shift apparatus to obtain the radiative lifetimes for vibrational l... more Use of an electron-beam phase-shift apparatus to obtain the radiative lifetimes for vibrational levels of the SiO E 1 Sigma (+) state. It is found that the radiative lifetimes for the vibrational transitions of the E-X band are independent of the vibrational upper state. The measured phase shifts yield cascade free lifetimes of 10.5 plus or minus 1.1 nsec for v' from 1 to 7. Spectroscopic data from Elander and Lagerqvist (1971) were used to calculate potential curves by the Klein-Dunham procedure, and Franck-Condon factors and r-centroids for the transition were computed.

The phase-shift method was used to obtain radiative lifetimes for the SiO E/sup 1/ SIGMA /sup +/ ... more The phase-shift method was used to obtain radiative lifetimes for the SiO E/sup 1/ SIGMA /sup +/ state. Electron-beam excitation was used. The lifetimes are essentially constant at 10.5 plus or minus 1.1 ns for v' = 1-7. KleinDunham potential curves and Franck-- Condon factors were computed, the dipole transition moment variation with vibrational quantum number (internuclear distance) was derived, band f-values. are given. The lines of SiO which should be observable in the interstellar medium through this transition are indicated, along with their absorption f-values. (auth)

Journal of Physics A: Mathematical and Theoretical, 2011

Similarly to the standard effective range expansion that is done near the threshold energy, we ob... more Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jostmatrix 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 dependencies 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 Smatrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.

In order to describe few-body scattering in the case of the Coulomb interaction, an approach base... more In order to describe few-body scattering in the case of the Coulomb interaction, an approach based on splitting the reaction potential into a finite range part and a long range tail part is presented. The solution to the Schrodinger equation for the long range tail is used as an incoming wave in an inhomogeneous Schrodinger equation with the finite range potential. The resulting equation with asymptotic outgoing waves is then solved with the exterior complex scaling. The potential splitting approach is illustrated with calculations of scattering processes in the H${}^+$ -- H${}^+_2$ system considered as the three-body system with one-state electronic potential surface.

International Journal of Modern Physics E

Within the proposed method, a set of experimental data points are fitted using a multi-channel S-... more 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 correspon...

Journal of Physics B: Atomic, Molecular and Optical Physics

Journal of Physics B: Atomic and Molecular Physics

We have computed the cross section for charge transfer from atomic hydrogen to the excited 3s lev... more We have computed the cross section for charge transfer from atomic hydrogen to the excited 3s level of doubly charged nitrogen, triply charged nitrogen and atomic hydrogen at very low relative collision energies (mcv). A rich resonance structure is found and interpreted in terms of quasi-bound states associated with the classical phenomenon of orbiting. Possible experimental verification of the resonance structure is discussed.

AIP Conference Proceedings

The three-body Coulomb Green’s function asymptotic structure is studied by the stationary phase m... more The three-body Coulomb Green’s function asymptotic structure is studied by the stationary phase method for the convolution integral for the case of two charged particles. The stationary phase points are roots of the third degree polinomial with the coefficients depending on the position in configuration space.

Journal of Physics B: Atomic, Molecular and Optical Physics, 2015

The study of scattering processes in few body systems is a difficult problem especially if long r... more 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 Schrödinger 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.

Chemical Physics, 2015

Abstract In this paper it is demonstrated that the split-potential driven Schrodinger approach to... more Abstract 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 Σ g + electronic states of the H 2 molecule. The obtained cross sections are in good agreement with other methods applied to the same model.

Physical Review A, 1982

A recently proposed complex stabilization method is examined from the viewpoint of the necessity ... more A recently proposed complex stabilization method is examined from the viewpoint of the necessity for an explicit construction of the coordinate-rotated Hamiltonian. It is demonstrated and proved that the argument for using unrotated Hamiltonians in resonance-structure determinations must be taken in a restricted sense. With the use of square-integrable basis functions, it is shown that complex rotation is necessary to directly calculate complex resonance poles. We illustrate our conclusion by a numerical model calculation.

The boundary conditions for the Schroedinger operator with the ‐ 0 -interaction are discussed. A ... more The boundary conditions for the Schroedinger operator with the ‐ 0 -interaction are discussed. A new class of selfadjoint extensions is investigated. This note is devoted to the Schroedinger operator with ‐ 0 -potential

An approach based on splitting the reaction potential into a finite range part and a long range t... more 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 Schr\"odinger 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 Schr\"odinger 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.

arXiv: Atomic Physics, 2020

The multi-channel Coulomb scattering problem in the adiabatic representation is considered. The n... more The multi-channel Coulomb scattering problem in the adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-zero asymptotic behavior at large internuclear separations. The asymptotic solutions at large inter-nuclear distances are {therefore} constructed. The asymptotic boundary conditions with S-matrix and K-matrix for the scattering problem are formulated on the basis of constructed asymptotic solutions.

Physical Review Letters, 1993

Long lived (0.8 ms, 6 ms, and >3.8 s) states i... more Long lived (0.8 ms, 6 ms, and >3.8 s) states in CO2+ have been observed for the first time by monitoring beams of 75-300 keV ions in the ion storage ring ASTRID. It is the first experimental evidence that a doubly charged molecule can be stable on a time scale of seconds. The results are theoretically interpreted by means of

The matrix elements of the multi-channel Jost matrices are written in such a way that their depen... more The matrix elements of the multi-channel Jost matrices are written in such a way that their dependencies on all possible odd powers of channel momenta are factorized explicitly. As a result the branching of the Riemann energy surface at all the channel thresholds is represented in them via exact analytic expressions. The remaining single-valued functions of the energy are expanded in the Taylor series near an arbitrary point on the real axis. Using the thus obtained Jost matrices, the S-matrix is constructed and then the scattering cross section is calculated, which therefore depends on the Taylor expansion coefficients. These coefficients are considered as the adjustable parameters that are optimized to fit a given set of experimental data. After finding the coefficients, the resonances are located as zeros of the Jost matrix determinant at complex energies. Within this approach the S-matrix has proper analytic structure. This enables us not only to locate multi-channel resonances ...

Use of an electron-beam phase-shift apparatus to obtain the radiative lifetimes for vibrational l... more Use of an electron-beam phase-shift apparatus to obtain the radiative lifetimes for vibrational levels of the SiO E 1 Sigma (+) state. It is found that the radiative lifetimes for the vibrational transitions of the E-X band are independent of the vibrational upper state. The measured phase shifts yield cascade free lifetimes of 10.5 plus or minus 1.1 nsec for v' from 1 to 7. Spectroscopic data from Elander and Lagerqvist (1971) were used to calculate potential curves by the Klein-Dunham procedure, and Franck-Condon factors and r-centroids for the transition were computed.

The phase-shift method was used to obtain radiative lifetimes for the SiO E/sup 1/ SIGMA /sup +/ ... more The phase-shift method was used to obtain radiative lifetimes for the SiO E/sup 1/ SIGMA /sup +/ state. Electron-beam excitation was used. The lifetimes are essentially constant at 10.5 plus or minus 1.1 ns for v' = 1-7. KleinDunham potential curves and Franck-- Condon factors were computed, the dipole transition moment variation with vibrational quantum number (internuclear distance) was derived, band f-values. are given. The lines of SiO which should be observable in the interstellar medium through this transition are indicated, along with their absorption f-values. (auth)

Journal of Physics A: Mathematical and Theoretical, 2011

Similarly to the standard effective range expansion that is done near the threshold energy, we ob... more Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jostmatrix 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 dependencies 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 Smatrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.

In order to describe few-body scattering in the case of the Coulomb interaction, an approach base... more In order to describe few-body scattering in the case of the Coulomb interaction, an approach based on splitting the reaction potential into a finite range part and a long range tail part is presented. The solution to the Schrodinger equation for the long range tail is used as an incoming wave in an inhomogeneous Schrodinger equation with the finite range potential. The resulting equation with asymptotic outgoing waves is then solved with the exterior complex scaling. The potential splitting approach is illustrated with calculations of scattering processes in the H${}^+$ -- H${}^+_2$ system considered as the three-body system with one-state electronic potential surface.

International Journal of Modern Physics E

Within the proposed method, a set of experimental data points are fitted using a multi-channel S-... more 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 correspon...

Journal of Physics B: Atomic, Molecular and Optical Physics

Journal of Physics B: Atomic and Molecular Physics

We have computed the cross section for charge transfer from atomic hydrogen to the excited 3s lev... more We have computed the cross section for charge transfer from atomic hydrogen to the excited 3s level of doubly charged nitrogen, triply charged nitrogen and atomic hydrogen at very low relative collision energies (mcv). A rich resonance structure is found and interpreted in terms of quasi-bound states associated with the classical phenomenon of orbiting. Possible experimental verification of the resonance structure is discussed.

AIP Conference Proceedings

The three-body Coulomb Green’s function asymptotic structure is studied by the stationary phase m... more The three-body Coulomb Green’s function asymptotic structure is studied by the stationary phase method for the convolution integral for the case of two charged particles. The stationary phase points are roots of the third degree polinomial with the coefficients depending on the position in configuration space.

Journal of Physics B: Atomic, Molecular and Optical Physics, 2015

The study of scattering processes in few body systems is a difficult problem especially if long r... more 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 Schrödinger 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.