Fonction d'onde approchée à un paramètre pour l'état fondamental des atomes à deux électrons

Pluvinage, P.

doi:10.1051/anphys/195012050145

Cited by 87 publications

(60 citation statements)

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“…Only the ground and first S Helium states energies have been calculated in the previous original paper concerned with our method [24]. We show here that, as in molecular works quoted above, several energy levels can be deduced with monoconfigurational calculations or with small diagonalization.…”

Section: Introductionmentioning

confidence: 53%

“…During the past few years we have shown [23] how to build an approximate solution for the twoelectron problem using the Pluvinage method [24]. Basically, this method provides an approximate solution of the Schr6dinger equation written as a product of two functions: one of them, the correlation term, depends explicitly on the interelectronic distance.…”

Section: Introductionmentioning

confidence: 99%

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Description of interelectronic correlation with the Pluvinage method

Dulieu¹,

Sech²

1989

Z Phys D - Atoms, Molecules and Clusters

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A correlated wave function method, already used for two-electron molecular systems is extended here to the case of two-electron atomic systems. A careful investigation of some exact properties of the wave function is performed (Kato's conditions, Fock's development, fulfilment of the virial theorem), showing its good behaviour at small interelectronic distances or in strongly correlated states. The application to Helium and Hdoubly-excited states is developed as a preliminary case of a more general study concerned with alkali-negative ions featuring in the second paper of this series. Energies and some autoionizing widths of He and H -are calculated. Given the simplicity of our model, close agreement is found in all cases with experimental and other theoretical works. This provides a confirmation of the large application field of this method to general correlated two-electron systems.

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Section: Introductionmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Description of interelectronic correlation with the Pluvinage method

Dulieu¹,

Sech²

1989

Z Phys D - Atoms, Molecules and Clusters

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“…Le Sech and co-workers [15,16] suggested that the original Pluvinage ground state [13] could be improved by introducing the screening of the interelectron interaction by the nucleus. This can be implemented by changing the effective strength of the Coulomb interaction to = q͑2k͒ −1 where q Ͻ 1.…”

Section: ͒ ͑3͒mentioning

confidence: 99%

Convergent calculations of double ionization of helium: From(γ,2e)to(e,3e
Kheifets
¹
,
Bray
²

2004
Phys. Rev. A
39
1
23
0
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The first absolute ͑e ,3e͒ measurements, by Lahmam-Bennani et al. [Phys. Rev. A 59, 3548 (1999) When attempting calculations of complex collision processes we have found it important to utilize a formalism where convergence of the results can be tested by substantial variation of as many of the input parameters as possible. The goal is to develop a predictive theory whose outcomes can be relied upon on scientific merit irrespective of agreement with experiment or other theory. The convergent close-coupling (CCC) method [1] was developed with this idea in mind. The total wave function is expanded utilizing a complete Laguerre basis and so greater accuracy is ensured with increasing basis size. In the Coulomb three-body problems, such as e-H scattering, once convergence is reached there is no freedom left to alter the results. Hence, when there is disagreement with experiment as discussed in Ref. Whereas in e-H calculations convergence considerations relate primarily to the usage of the Laguerre basis, in ͑␥ ,2e͒ calculations there is additional consideration of convergence with respect to the description of the initial state. In the more complicated Coulomb four-body problem that is electronimpact double ionization of helium ͑e ,3e͒ there are further considerations of convergence with respect to the Born approximation order used to treat the case of a fast projectile. It is these issues that are of interest to us presently.The physics of the He ͑e ,3e͒ reaction in the very fast projectile mode where the incident electron has an order of magnitude or more energy than the two "slow" ejected electrons is quite similar to the case of ͑␥ ,2e͒. In both cases the initial and final atomic states are three-body problems of the He 2+ nucleus interacting with the two slow electrons. The application of the CCC method to ͑e ,3e͒ process under these kinematical conditions is straightforward and expected to produce results as accurate as those for ͑␥ ,2e͒. However, the first Born CCC result of ͑e ,3e͒ on He at 5.6 keV incident energy [8] was found significantly lower in magnitude (by factors of ϳ3 and ϳ12 for 10 and 4 eV ejected electrons, respectively) as compared with absolute measurements of Lahmam-Bennani et al. [9]. Such a strong disagreement could only be attributed to deviation from the first Born regime since the treatment of the initial and final states was the same in the CCC ͑␥ ,2e͒ and ͑e ,3e͒ calculations. Some indications of that followed from the work of Berakdar [10] who reported good agreement with the absolute measurements [9] on the basis of a lowest-order implementation of a Faddeev-type approach. These calculations differed significantly for electron or positron impact (by about a factor of 2), thus apparently invalidating the first Born approximation.This conclusion, however, was challenged by the recent work of Jones and Madison [11] who managed to get good agreement, both in shape and magnitude, with the experiment of within the first Born model.

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“…It has been introduced by Pluvinage (1950Pluvinage ( , 1951 for the treatment of the helium atom, and it describes the collision of the two electrons in the absence of an external field. It can be shown (Pluvinage 1951) that the product (1/r,2)lP' (1,2)12 has no singularity for r,2=0, so that the number Qf configuratioxx necessary to obtain an accurate wavefunction.…”

Section: Introductionmentioning

confidence: 99%

Fabrication and Characterization of Diffraction Gratings Using Photosensitive Al₂O₃ Gel Films

Zhao

Tohge

Nishii

1998

Jpn. J. Appl. Phys.

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A two-electron model together with a correlated orbital method are used to compute the P, TI and S potential curves of Na, up to the states dissociating into Na(3p) + Na(3p). Crossings of the 'adiabatic' curves with the ground-state potential curve of the N a l ion occur for the 8 ' P: and 1 '8; states at internuclear distances R = 5 and 8.9 au respectively. The efficiency of the Pluvinage method for the treatment of excited states is discussed.

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Fonction d'onde approchée à un paramètre pour l'état fondamental des atomes à deux électrons

Cited by 87 publications

References 0 publications

Description of interelectronic correlation with the Pluvinage method

Description of interelectronic correlation with the Pluvinage method

Convergent calculations of double ionization of helium: From(γ,2e)to(e,3e
Kheifets
¹
,
Bray
²

2004
Phys. Rev. A
39
1
23
0
View full text Add to dashboard Cite

Fabrication and Characterization of Diffraction Gratings Using Photosensitive Al₂O₃ Gel Films

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Fonction d'onde approchée à un paramètre pour l'état fondamental des atomes à deux électrons

Cited by 87 publications

References 0 publications

Description of interelectronic correlation with the Pluvinage method

Description of interelectronic correlation with the Pluvinage method

Convergent calculations of double ionization of helium: From(γ,2e)to(e,3eKheifets1, Bray2 2004Phys. Rev. A391230View full textAdd to dashboardCite

Fabrication and Characterization of Diffraction Gratings Using Photosensitive Al2O3 Gel Films

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Convergent calculations of double ionization of helium: From(γ,2e)to(e,3e
Kheifets
¹
,
Bray
²

2004
Phys. Rev. A
39
1
23
0
View full text Add to dashboard Cite

Fabrication and Characterization of Diffraction Gratings Using Photosensitive Al₂O₃ Gel Films