Extensions of the complex-coordinate method to the study of resonances in many-electron systems

Rescigno, T. N.; McCurdy, C. W.; Orel, A. E.

doi:10.1103/physreva.17.1931

Cited by 124 publications

(58 citation statements)

References 26 publications

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“…[15,14] showed that cross sections for the elastic and excitation channels could be calculated at energies above the ionization threshold by including positive-energy pseudostates in the expansion. This work was extended in the 1980's by Oza and Callaway [23,22]. However, these calculations were marred by the presence of "pseudo-resonances" that prevented accurate calculations at certain energies.…”

Section: The Expansion Functions In Close-coupling Methods Are Obtainmentioning

confidence: 99%

“…In practice, the eigenvalues may depend strongly on the rotation angle for basis sets that are not carefully optimized and modifications of the method, which need not concern us here, are needed to make the method practical for marry-electron systems [23]. We refer the interested reader to several reviews for further details [5,6,24].…”

Section: Il Complex Scalingmentioning

confidence: 99%

“…The inner-core orbitals in a heavy atom become highly oscillatory under uniform complex scaling which causes severe convergence problems. Whh complex basis function methods, one can use real basis functions to expand the core orbitals and complex functions ordy for the outer orbitals [23]. The method is then no longer the same as uniform complex scrding and may well not correspond to an easily derived variable scaling of the Harniltonian operator.…”

Section: Iilcomplex Scaling Vscomplex Basismentioning

confidence: 99%

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Electron-impact ionization of atomic hydrogen

Baertschy

2001

Phys. Rev. A

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131

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. DISCLAIMER DISCLAIMERPortions of this document may be illegible in electronic image products. Images are produced from the best avaiiabie original document.,-. LBNL-4521O Electron-Impact Ionization of Atomic Hydrogen 2000_-------.---.... . . . . . . . . . . . . . . . 72 6.4.2 SDCSfor 17.6,20,25, and30eV . . . . . . . . . . . . . . . . 73 6.5 Integral Ionization Cross Sections . . . . . . . . . . . . . . . . . . . . 74 7 The Three-Body Electron-Impact In the early 1970's Burke and Mitchell [15, 14] showed that cross sections for the elastic and excitation channels could be calculated at energies above the ionization threshold by including positive-energy pseudostates in the expansion. This work was extended in the 1980's by Oza and Callaway [23,22] (Fl, 72) Electron-Impact Ionization of Atomic Hydrogen List of Tables Nature of Ionization Electron-impact ionization is the process in which a target atom or molecule is ionized by a collision with an electron. Scattering theory calculations have progressed to the point of being able to accurately treat non-breakup processes for an electron scattering from relatively complicated target molecules. However, ionization represents a fundamentally different class of problems characterized by a final state in which three particles that interact via long-range by rearranging the Schrodinger equation (Equation 2.1).Since lli~ (?'l, 72) represents the scattered part of the wave function at large distances it must be an outgoing wave in rl and r2. Thus, we define W; (71, 72) Exterior Complex Scaling Application to long-range potentials Finite Difference Implementation ECS on a grid Under ECS, the scattered wave @& (z(rI), Z(T2)) is a continuous function but has discontinuous first derivatives along the lines rl or r2 equal to&.There is no problem representing the wave function on a two-dimensional grid in rl and r2, but in order to correctly approximate its derivatives on each grid point we will require that~be one of the grid points. The scattered wave will be calculated directly on to the ECS contour by solving Equation 3.5 on the two-dimensional, complex-scaled grid. Functions whose analytic forms are known, such as the right-hand side of Equation 3.5 and the potentials in the Hamiltonian, are mapped on to the ECS contour by simply evaluating them on the contour z(r) for both rl and r2. The non-analytic two-electron potential $ is scaled in this way by noting that it is piece-wise analytic and scaling the rl < r2 and rl > r2 regions separately. The potential is unchanged on the real part of the grid and, as will be demonstratedlater in this chapter, the potentials beyond~have very little effect on the wave function in the interior region. Finite difference approximations to derivatives Dimension of the problem Properties of the Calculated Wave FunctionsThe figure on the left shows the absolute value of #~P (rl, Tz) ..................................................j .......................... Total Cross Section Differential Cross ...

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Section: The Expansion Functions In Close-coupling Methods Are Obtainmentioning

confidence: 99%

Section: Il Complex Scalingmentioning

confidence: 99%

Section: Iilcomplex Scaling Vscomplex Basismentioning

confidence: 99%

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Electron-impact ionization of atomic hydrogen

Baertschy

2001

Phys. Rev. A

Self Cite

131

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“…47,49,50 The latter approach is implemented in the present work, SCF and CI calculations are performed by using the complex scaled Gaussian basis functions. Only the basis functions are scaled and all calculations are carried out on the real axis, which is computationally efficient.…”

Section: Theoretical Methodsmentioning

confidence: 99%

Complex multireference configuration interaction calculations for the K-vacancy Auger states of N q+ (q = 2-5) ions

Peng

Zhu

et al. 2016

The Journal of Chemical Physics

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Ab initio multireference configuration-interaction theoretical study on the low-lying spin states in binuclear transition-metal complex: Magnetic exchange of [ ( NH 3 ) K-vacancy Auger states of N q+ (q = 2-5) ions are studied by using the complex multireference single-and double-excitation configuration interaction (CMRD-CI) method. The calculated resonance parameters are in good agreement with the available experimental and theoretical data. It shows that the resonance positions and widths converge quickly with the increase of the atomic basis sets in the CMRD-CI calculations; the standard atomic basis set can be employed to describe the atomic K-vacancy Auger states well. The strong correlations between the valence and core electrons play important roles in accurately determining those resonance parameters, Rydberg electrons contribute negligibly in the calculations. Note that it is the first time that the complex scaling method has been successfully applied for the B-like nitrogen. CMRD-CI is readily extended to treat the resonance states of molecules in the near future. C 2016 AIP Publishing LLC. [http://dx

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“…By using a complex scaled hamiltonian (Ho, 1983) or a set of complex basis functions (Rescigno et al, 1978;Rescigno and McCurdy, 1985), the problem of Þnding resonance states is reduced to the solution of a complex eigenvalue problem, where the technique of bound-state conÞguration interaction can be used. Recently, the complex-rotation method has also been applied to the study of doubly excited resonances in the presence of an external electric or magnetic Þeld (Fang and Ho, 1999).…”

Section: B-spline Based Complex-rotation (Bscr) Methodsmentioning

confidence: 99%

Multiple excitation in photoionization using B-splines

Chang

Fang

2004

Radiation Physics and Chemistry

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We present a review of a few recent applications of three B-spline based methods to atomic photoionization dominated by multiple excitation for both single and multiple ionization channels. The emphases are given to physical interpretation of atomic processes based on the energy variation of effective one-particle orbital functions and their corresponding scattering phase shifts or eigenphase shifts extracted from the state wavefunctions. A number of general features which characterize the photoionization resonance spectra and a few exceptions due to interference between overlapping autoionization series are given.

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Extensions of the complex-coordinate method to the study of resonances in many-electron systems

Cited by 124 publications

References 26 publications

Electron-impact ionization of atomic hydrogen

Electron-impact ionization of atomic hydrogen

Complex multireference configuration interaction calculations for the K-vacancy Auger states of N q+ (q = 2-5) ions

Multiple excitation in photoionization using B-splines

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