Correlated wavefunctions for helium-like atomic systems

Tweed, R J

doi:10.1088/0022-3700/5/4/015

Cited by 50 publications

(34 citation statements)

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“…Despite the present numerical computations being restricted to the four wave functions, it should be noted that the presented CB1-4B method can also be extended and adapted for using multiparameter highly correlated wave functions, such those of Byron and Joachain [56], Joachain and Vanderpoorten [57], or Tweed [58], which include a number of CI terms ranging from 12 to 108. These orbitals [56][57][58] are capable of including most radial and angular correlations, despite the fact that they do not explicitly contain the interelectronic coordinate r 12 .…”

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confidence: 99%

“…These orbitals [56][57][58] are capable of including most radial and angular correlations, despite the fact that they do not explicitly contain the interelectronic coordinate r 12 . Such wave functions [56][57][58] are convenient for analytical calculations due to their separable form ϕ i ( r 1 , r 2 ) = k,l ϕ k ( r 1 )ϕ l ( r 2 ), where ϕ k,l ( r 1,2 ) are unnormalized Slater-type orbitals. [62], together with the partial differential procedure, yields the following expressions:…”

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Electron correlations in single-electron capture from helium by fast protons andαparticles

Mančev

Milojević

2010

Phys. Rev. A

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Single-electron capture from heliumlike atomic systems by bare projectiles is investigated by means of the four-body boundary-corrected first Born approximation (CB1-4B). The effect of the dynamic electron correlation is explicitly taken into account through the complete perturbation potential. The quantum-mechanical post and prior transition amplitudes for single charge exchange encompassing symmetric and/or asymmetric collisions are derived in terms of two-dimensional real integrals in the case of the prior form and five-dimensional quadratures for the post form. An illustrative computation is performed for single-electron capture from helium by protons and α particles at intermediate and high impact energies. The role of dynamic correlations is examined as a function of increased projectile energy. The validity and utility of the proposed CB1-4B method is critically assessed in comparison with the existing experimental data for total cross sections, and excellent agreement is obtained.

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Electron correlations in single-electron capture from helium by fast protons andαparticles

Mančev

Milojević

2010

Phys. Rev. A

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“…In the case of two-electron systems, this is a multiparametric Hylleraas-type wave function [123], and, in the case of Be atom, this is, as a rule, a Hartree-Fock wave function obtained in the multiconfiguration approximation [114][115][116]. In our papers we used the Tweed [124] wave function as well, see [14] for details. The system of equations in the ICCNR method has the following form:…”

Section: Formalism Of the Methodsmentioning

confidence: 99%

The Method of Interacting Configurations in Complex Number Representations: From Helium to the Complex Atoms

Simulik¹,

Tymchyk²,

Zajac³

2017

ujpa

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The transition from the He atom to the complex atoms description in the method of interacting configurations in the complex number representation has been presented. As a first step the problem of ionization of H − and Li + ions is considered. The spectroscopic characteristics of the Be, Mg and Ca atoms in the problem of the electron-impact ionization of these atoms are investigated. Few results in the photoionization problem on the 1 P autoionizing states above the n=2 threshold of helium-like Be ++ ion are presented. The energies and the widths of the lowest 1 S, 1 P, 1 D, and 1 F autoionizing states of the Be, Mg atoms, and the lowest ( 1 P ) autoionizing states of Ca atom, are calculated. We consider briefly both a review of our previous results (together with results of other authors) and new calculations of our group. A brief review of the methods of the quasi-stationary states calculation is given.

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“…Nevertheless, method 2 has its own merits because it can be extended to the excited states and highly correlated con6guration interaction (CI) orbitals [62,63] in a much easier manner than in the case of method 1. In the present work, method 2 will serve as an independent check of the numerical results obtained by means of method 1.…”

Section: Theorymentioning

confidence: 99%

Intermediate ionization continua for double charge exchange at high impact energies

Belkić¹

1993

Phys. Rev. A

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We investigate the problem of two-electron capture from heliumlike atomic systems by bare nuclei Zp +(ZT' e "e2); -+ ( Zp, e &, e2 )f +ZT at high incident energies, using the four-body formalism of the first-and second-order theories. Our goal is to establish the relative importance of the intermediate ionization continua of the two electrons in comparison with the usual direct path of the double electron transfer. For this purpose we presently introduce the boundary-corrected continuum-intermediate-state (BCIS) approximation, which preserves all the features of two-electron capture as a genuine four-body problem. The proposed second-order theory provides a fully adequate description of the fact that, in an intermediate stage of collision, both electrons move in the field of the two Coulomb centers. The previously devised boundary-corrected first Born (CB1) approximation can be obtained as a further simplification of the BCIS model if the invoked two-electron Coulomb waves are replaced by their longrange logarithmic phase factors defined in terms of the corresponding interaggregate separation R. The BCIS method is implemented on the symmetric resonant double charge exchange in collisions between a particles and He( ls ) at impact energies E~900 keV. The obtained results for the differential and total cross sections are compared with the available experimental data and satisfactory agreement is recorded.As the incident energy increases, a dramatic improvement is obtained in going from the CB1 to the BCIS approximation, since the latter closely follows the measurement, whereas the former overestimates the observed total cross sections by two orders of magnitude.PACS number(s): 34.70. +e, 82.30.Fi

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Correlated wavefunctions for helium-like atomic systems

Cited by 50 publications

References 6 publications

Electron correlations in single-electron capture from helium by fast protons andαparticles

Electron correlations in single-electron capture from helium by fast protons andαparticles

The Method of Interacting Configurations in Complex Number Representations: From Helium to the Complex Atoms

Intermediate ionization continua for double charge exchange at high impact energies

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