Four-body corrected first Born approximation for single-electron capture into arbitrary states of energetic projectiles

Mančev, Ivan; Milojević, Nenad; Belkić, Dževad

doi:10.1103/physreva.86.022704

Cited by 27 publications

(16 citation statements)

References 75 publications

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“…Such a derivation of the closed form for the integral D l provides a reduction of the original nine-dimensional integral of the prior CB1-4B transition amplitude [35] to a one-dimensional quadrature. Finally, a closed form can likewise be derived for the integral C l from Eq.…”

Section: Appendix Amentioning

confidence: 99%

“…The solid curve represents the prior total cross sections in the prior BCIS-4B method (present computation). The dashed curve represents the results from the prior form of the prior CB1-4B method [35]. The initial ground state of He(1s 2 ) is described by means of the two-parameter wave function of Silverman et al [44].…”

Section: B Total Cross Sectionsmentioning

confidence: 99%

“…This is a second-order theory which provides a fully adequate description of the fact that, in an intermediate stage of collision, the captured electron moves in a Coulomb field rather than propagating freely according to a plane-wave formalism in the JacksonSchiff first Born (JSB1-4B) approximation [2,6] with incorrect boundary conditions. The four-body boundary-corrected first Born (CB1-4B) method for single-electron capture [35,36], which also obeys the asymptotic convergence criteria for Coulomb potentials [1,5,34] can be obtained as a further simplification of the BCIS-4B method, if the invoked electron Coulomb wave from the latter method is replaced by its long-range logarithmic phase factor for the relative motion of heavy nuclei and, as such, redefined in terms of the corresponding interaggregate separation R.…”

Section: Introductionmentioning

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: Appendix Amentioning

confidence: 99%

Section: B Total Cross Sectionsmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Experiments: squares, Schryber [61]; circles, Welsh et al [65]; triangles, Williams [64]. [77]. However, at energies below 2 MeV the ratio increases to reach a value of 1.90 at 50 keV.…”

Section: High Energy Collision (E > 100 Kev/u)mentioning

confidence: 99%

Charge transfer in proton–helium collisions from low to high energy

Loreau

Ryabchenko

Vaeck

2014

J. Phys. B: At. Mol. Opt. Phys.

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The cross section for charge transfer in proton-helium collisions has been computed in the energy range from 10 eV/u up to 10 MeV/u. Four different methods (full quantal time-independent and time-dependent methods, molecular and atomic basis set semi-classical approaches) valid in different energy regimes have been used to calculate the partial and total cross section for single-electron capture. The results are compared with previous theoretical calculations and experimental measurements and the different theoretical methods used are shown to be complementary for describing the charge transfer reaction. A fit of the cross section, valid for collision energies from 10 eV/u up to 10 MeV/u is presented based on these results.

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“…These computations [20][21][22][23][24] have been performed for the ground-to-ground-state capture. In a recent paper [25], we have carried out an extension of the CB1-4B model in its prior version to encompass electron capture into arbitrary final states of the projectile. A number of quantum-mechanical four-body methods have been proposed to study one-and two-electron transitions for nonrelativistic fast ion-atom collisions with two actively participating electrons, as reviewed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Electron correlations in single-electron capture into any state of fast projectiles from heliumlike atomic systems

2013

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State-selective and total single-electron capture cross sections in fast collisions of a bare projectile with a heliumlike target are examined in the four-body formalism. A special emphasis is given to a proper inclusion of dynamic electron-electron correlation effects. For this purpose, the post form of the four-body boundary-corrected first Born approximation (CB1-4B) is utilized. With regard to our related previous study, where the prior version has been considered, in the present work an extensive analytical study of the post-transition amplitude for electron capture into the arbitrary final states n f l f m f of the projectile is carried out. The post-transition amplitude for single charge exchange encompassing symmetric and asymmetric collisions is derived in terms of five-dimensional integrals over real variables. The dielectronic interaction V 12 = 1/r 12 ≡ 1/| r 1 − r 2 | explicitly appears in the perturbation potential V f of the post-transition probability amplitude T + if , such that the CB1-4B method can provide information about the relative significance of the dynamic interelectron correlation in the collisions under study. An illustrative computation is performed involving state-selective and total single capture cross sections for the p-He collisions at intermediate and high impact energies. The so-called post-prior discrepancy, which plagues almost all the existing distorted wave approximations, is presently shown to be practically nonexistent in the CB1-4B method. The validity of our findings is critically assessed in comparisons with the available experimental data for both state-selective and total cross sections summed over all the discrete energy levels of the hydrogenlike atom formed with the projectile. Overall, excellent performance of the CB1-4B method is recorded, thus robustly establishing this formalism as the leading first-order description of high-energy single charge exchange, which is a collision of paramount theoretical and practical importance across interdisciplinary fields ranging from astrophysics to medicine.

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Four-body corrected first Born approximation for single-electron capture into arbitrary states of energetic projectiles

Cited by 27 publications

References 75 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

Charge transfer in proton–helium collisions from low to high energy

Electron correlations in single-electron capture into any state of fast projectiles from heliumlike atomic systems

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