On the variational methods for bound-state and scattering problems II

Abdel‐Raouf, M. A.

doi:10.1016/0370-1573(84)90057-7

Cited by 29 publications

(5 citation statements)

References 165 publications

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“…For s-wave scattering process, the variational treatment [17], [23] starts by defining a trial wavefunction |Ψ n t (x, r N ; k) . It consists of two multiplicative wavefunction…”

Section: Ii1 the Least-squares Variational Methods And Trial Wavefunmentioning

confidence: 99%

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Variational calculation of low-energy positron life time in Xe atoms

Abdel-Mageed

2010

Braz. J. Phys.

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The least-squares variational method (LSVM) is used for determining trial wavefunctions representing lowenergy positron-xenon elastic scattering, which are used to determine the positron lifetime. The trial function is taken to depend on several adjustable parameters, and is improved iteratively by increasing the number of terms. The bound state wavefunctions are obtained using Hartree-Fock-Slater method. The 2γ-rays annihilation rates of the positron in xenon atoms below Positronuim (Ps) formation threshold are calculated. Polarization potential V pl (r) is applied to enhance annihilation rates and lifetime. The present results of annihilation parameters are consistent with semiempirical, theoretical and experimental results.

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“…For s-wave scattering process, the variational treatment [17], [23] starts by defining a trial wavefunction |Ψ n t (x, r N ; k) . It consists of two multiplicative wavefunction…”

Section: Ii1 the Least-squares Variational Methods And Trial Wavefunmentioning

confidence: 99%

“…The least squares variational method was applied to low energy positron scattering from H, He [17] ,Ar [18], and Kr [19]. It was applied to obtain the wave function of the continuum Auger electron emitted from an ionized Ne atom [20] and developed to study positron-H molecules scattering [21].…”

Section: Introductionmentioning

confidence: 99%

Variational calculation of low-energy positron life time in Xe atoms

Abdel-Mageed

2010

Braz. J. Phys.

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“…19 We use the variational least squares method (for a review see Ref. 20) in order to calculate the continuum electron wavefunction, φ c , which satisfying the following Schrödinger's equation…”

Section: Theorymentioning

confidence: 99%

“…12 Liegener, Abdel-Roouf and Ladik 13 formulated a variational least-square technique for calculating general non-spherical continuum orbitals for Auger electrons emitted from macromolecules. Also, there has been increasing interest in the field of Auger emission (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Trials to Improve the Continuum Wavefunctions of Auger Electrons Emitted From Aluminium and Oxygen Ions Using a Least Squares Variational Technique

Abdel‐Raouf

El-Bakry

2000

Mod. Phys. Lett. B

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The least-squares variational method is employed in order to derive iterative improvements upon the wavefunctions of Auger electrons emitted by Aluminum and Oxygen ions. The Auger electrons are considered free electrons seen by the remaining target and not as in the conventional Hartree-Fock programmes through which the continuum wavefunction of the Auger electron was determined by assuming that it occurs in a relatively higher excited state of the related bound system and this proceeds towards the real physical picture. The core potential seen by the Auger electron is evaluated on the basis of the Hartree-Fock orbitals delivered by the conventional Hartree-Fock computer codes. The Auger transition rates are calculated for different configurations of Aluminum and Oxygen ions. Our results show the stability of our variational iteration technique for improving the continuum wavefunctions and consequently the Auger rates of Auger electrons emitted from atoms or ions.

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“…Our main objective in the present work is to develop a computer code for the investigation of the elastic collision of positrons and electrons with diatomic molecules using a leastsquares variational method (Abdel-Raouf 1984) within the framework of the adiabatic approximation. A set of prolate spheroidal coordinates is employed for describing each system.…”

Section: Introductionmentioning

confidence: 99%

Least-squares variational treatment of positron (electron)–diatomic molecule scattering

El-Aasser

Abdel‐Raouf

2007

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

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A computer code based on the least-squares variational method (LSVM) is developed for the treatment of the collisions of positrons and electrons with diatomic molecules. The code was tested and employed for the investigation of the elastic scattering of positrons and electrons by hydrogen molecules within the framework of the adiabatic approximation. The system is described by a set of prolate spheroidal coordinates which is the most suitable representation of diatomic molecules. Reliable convergence of the scattering phaseshifts has been achieved by optimizing the nonlinear parameters and increasing the number of L2 components of the trial wavefunctions. The cross section of the lowest partial wave is calculated at energies varying from 0.136 eV to 13.6 eV, under the assumption that positronium formation, exchange interactions, and all excitation channels are closed. A comparison is presented between our results and those determined by other authors.

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On the variational methods for bound-state and scattering problems II

Cited by 29 publications

References 165 publications

Variational calculation of low-energy positron life time in Xe atoms

Variational calculation of low-energy positron life time in Xe atoms

Trials to Improve the Continuum Wavefunctions of Auger Electrons Emitted From Aluminium and Oxygen Ions Using a Least Squares Variational Technique

Least-squares variational treatment of positron (electron)–diatomic molecule scattering

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