Configuration-interaction wave functions for two-electron systems

Joachain, Charles; Vanderpoorten, R

doi:10.1016/0031-8914(70)90009-1

Cited by 46 publications

(15 citation statements)

References 34 publications

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“…For L = 3, b 1 = b 2 , k max = 6 and with 109 parameters in the CI wave function (14), the binding energy is found to be i = −2.902 67 [38]. This estimate, which remarkably accounts for 97% of the correlation energy, is in excellent agreement with the corresponding value i = −2.903 724 377 0 obtained by Drake [39] using (13) with K = 8 and 269 parameters.…”

Section: E Heliumlike Bound-state Wave Functionssupporting

confidence: 72%

“…The practical utility of the CI wave functions for multielectron atomic systems is that they facilitate analytical or semianalytical calculations of bound-free form factors, much in the same fashion as in the case of single charge exchange in purely three-body collisions involving only the hydrogenlike wave functions of one-electron atomic systems. This has been illustrated by Belkić [3,40,41] for single ionization in the H + − H − (1s 2 ) collision using the highly correlated CI wave function of H − with some 61 variational parameters [38] in the four-body modified Coulomb-Born (MCB-4B), or equivalently, the four-body continuum distorted wave and eikonal initial state (CDW-EIS-4B) method.…”

Section: E Heliumlike Bound-state Wave Functionsmentioning

confidence: 99%

“…Another alternative is to employ the concept of configuration interactions (CIs). These involve a linear combination of the products of one-electron radial orbitals dependent only on x 1 and x 2 multiplied altogether by the Legendre polynomial P l (cos θ 12 ) ≡ P l ( cos ( x 1 · x 2 )) as a function of the angle θ 12 between x 1 and x 2 [38]:…”

Section: E Heliumlike Bound-state Wave Functionsmentioning

confidence: 99%

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Boundary-corrected four-body continuum-intermediate-state method: Single-electron capture from heliumlike atomic systems by fast nuclei

2015

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Single charge exchange in collisions between bare projectiles and heliumlike atomic systems at intermediate and high incident energies is examined by using the four-body formalism of the first-and second-order theories. The main purpose of the present study is to investigate the relative importance of the intermediate ionization continua of the captured electron compared to the usual direct path of the single electron transfer from a target to a projectile. In order to achieve this goal, comprehensive comparisons are made between the four-body boundary-corrected continuum-intermediate-states (BCIS-4B) method and the four-body boundary-corrected first Born (CB1-4B) method. The perturbation potential is the same in the CB1-4B and BCIS-4B methods. Both methods satisfy the correct boundary conditions in the entrance and exit channels. However, unlike the CB1-4B method, the second-order BCIS-4B method takes into account the electronic Coulomb continuum-intermediate states in either the entrance or the exit channel depending on whether the post or the prior version of the transition amplitude is used. Hence, by comparing the results from these two theories, the relative importance of the intermediate ionization electronic continua can be assessed within the four-body formalism of scattering theory. The BCIS-4B method predicts the usual second-order effect through double scattering of the captured electron on two nuclei as a quantum-mechanical counterpart of the Thomas classical two-step, billiard-type collision. The physical mechanism for this effect in the BCIS-4B method is also comprised of two steps such that ionization occurs first. This is followed by capture of the electron by the projectile with both processes taking place on the energy shell. Moreover, the role of the second, noncaptured electron in a heliumlike target is revisited. To this end, the BCIS-4B method describes the effect of capture of one electron by the interaction of the projectile nucleus with the other electron via the static electron-electron correlations in the target. This effect yields a novelty seen as the second Thomas peak. As an illustration, detailed computations were carried out involving both the differential and total cross sections for one-electron capture in the p − He collisions at intermediate and high impact energies. The results obtained in the BCIS-4B method are compared with those from the CB1-4B method and with the available experimental data. The overall usefulness of the BCIS-4B method is assessed in predicting experimental data for four-body single charge exchange both qualitatively (shapes of cross sections) and quantitatively (numerical values from measurements).

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Section: E Heliumlike Bound-state Wave Functionssupporting

confidence: 72%

Section: E Heliumlike Bound-state Wave Functionsmentioning

confidence: 99%

Section: E Heliumlike Bound-state Wave Functionsmentioning

confidence: 99%

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Boundary-corrected four-body continuum-intermediate-state method: Single-electron capture from heliumlike atomic systems by fast nuclei

2015

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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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“…In this case the calculation is simplified because the logarithmic term E(R) in (3a, b) vanishes. For describing the electronic ground state a configuration-interaction wave function of Joachim et al [18] • ei~m4~+,~,h,m,(rrO q~h+k,h,,,~(rr2).…”

Section: Theorymentioning

confidence: 99%

Resonant double electron capture by fast He2+ from helium: the first-order Born approximation with correct boundary condition

Gulyás

Szabó

1994

Z Phys D - Atoms, Molecules and Clusters

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Configuration-interaction wave functions for two-electron systems

Cited by 46 publications

References 34 publications

Boundary-corrected four-body continuum-intermediate-state method: Single-electron capture from heliumlike atomic systems by fast nuclei

Boundary-corrected four-body continuum-intermediate-state method: Single-electron capture from heliumlike atomic systems by fast nuclei

Intermediate ionization continua for double charge exchange at high impact energies

Resonant double electron capture by fast He2+ from helium: the first-order Born approximation with correct boundary condition

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