State‐to‐state differential and integral cross sections for vibrational‐rotational excitation and elastic scattering of electrons by N2 at 5–50 eV: Calculations using extended‐basis‐set Hartree–Fock wave functions

1983 ◽  
Vol 79 (4) ◽  
pp. 1846-1858 ◽  
Author(s):  
John R. Rumble ◽  
Donald G. Truhlar ◽  
Michael A. Morrison
Keyword(s):  
Elastic Scattering ◽  
Cross Sections ◽  
Wave Functions ◽  
Basis Set ◽  
Rotational Excitation ◽  
Hartree Fock ◽  
Extended Basis

A comparison of theory and experiment for photo-ionization cross-sections I. Neon and the elements from boron to neon

1951 ◽  
Vol 208 (1094) ◽  
pp. 408-418 ◽  
Keyword(s):  
Cross Sections ◽  
General Trend ◽  
Wave Functions ◽  
Ionization Cross ◽  
Hartree Fock ◽  
Quantal Theory ◽  
Ionization Cross Sections ◽  
Photo Ionization ◽  
Near Future ◽  
Dipole Length

The quantal theory of the continuous photo-electric absorption of radiation is briefly summarized, pàrticular attention being given to the alternative formulae available and to the accuracy to be expected in practical calculations. Detailed calculations are described for the photo-ionization cross-section of neon, a system for which it is understood that experimental data should be available in the near future. The calculation is made using Hartree-Fock wave functions and the two formulae of the dipole length and the dipole velocity. The corresponding cross-sections are found to be 5.8 and 4.4 x 10- 18 cm 2 . at the spectral head and to rise slowly with increasing frequency until a broad maximum is reached for an energy of the ejected electron of about 11 eV. A comparison is made with previous calculations on the elements from boron to neon ; the general trend of the results is discussed and improved estimates for boron and fluorine are given (10 x 10 -18 cm 2 . for boron and 4.3 x 10- 18 cm 2 . for fluorine at the spectral head).

scholarly journals Differential and integral cross sections for electron elastic scattering by ammonia for incident energies ranging from 10 eV to 20 keV

2018 ◽  
Vol 64 (5) ◽  
pp. 498
Author(s):  
Hocine Aouchiche
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Optical Potential ◽  
Large Set ◽  
Quantum Calculation ◽  
Hartree Fock ◽  
Spherical Complex ◽  
Static Part ◽  
Model Point

Differential and integral cross sections for elastic scattering of electron by NH3 molecule are investigated for the energy ranging from 10 eV to 20 keV.  The calculations are carried out in the framework of partial wave formalism describing the target molecule by means of one center molecular Hartree-Fock functions.  A spherical complex optical potential used includes a static part – obtained here numerically from quantum calculation – and fine effects like correlation, polarization and exchange potentials. The results obtained in this model point out clearly the role played by the exchange and the correlation-polarization contributions in particular at lower scattering angles and lower incident energies. Both differential and integral cross sections obtained are compared with a large set of experimental data available in the literature and well agreement is found throughout the scattering angles and whole energy range investigated here.

Basis-Set Expansions of Relativistic Electronic Wave Functions

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Relativistic Quantum ◽  
Finite Basis ◽  
Wave Functions ◽  
Basis Set ◽  
Electronic Wave ◽  
Nonrelativistic Case ◽  
Hartree Fock ◽  
Electronic Wave Functions ◽  
Basis Set Expansion ◽  
Molecular Calculations

There have been several successful applications of the Dirac–Hartree–Fock (DHF) equations to the calculation of numerical electronic wave functions for diatomic molecules (Laaksonen and Grant 1984a, 1984b, Sundholm 1988, 1994, Kullie et al. 1999). However, the use of numerical techniques in relativistic molecular calculations encounters the same difficulties as in the nonrelativistic case, and to proceed to general applications beyond simple diatomic and linear molecules it is necessary to resort to an analytic approximation using a basis set expansion of the wave function. The techniques for such calculations may to a large extent be based on the methods developed for nonrelativistic calculations, but it turns out that the transfer of these methods to the relativistic case requires special considerations. These considerations, as well as the development of the finite basis versions of both the Dirac and DHF equations, form the subject of the present chapter. In particular, in the early days of relativistic quantum chemistry, attempts to solve the DHF equations in a basis set expansion sometimes led to unexpected results. One of the problems was that some calculations did not tend to the correct nonrelativistic limit. Subsequent investigations revealed that this was caused by inconsistencies in the choice of basis set for the small-component space, and some basic principles of basisset selection for relativistic calculations were established. The variational stability of the DHF equations in a finite basis has also been a subject of debate. As we show in this chapter, it is possible to establish lower variational bounds, thus ensuring that the iterative solution of the DHF equations does not collapse. There are two basically different strategies that may be followed when developing a finite basis formulation for relativistic molecular calculations. One possibility is to expand the large and small components of the 4-spinor in a basis of 2-spinors. The alternative is to expand each of the scalar components of the 4-spinor in a scalar basis. Both approaches have their advantages and disadvantages, though the latter approach is obviously the easier one for adapting nonrelativistic methods, which work in real scalar arithmetic.

First-order exchange approximation

1963 ◽  
Vol 276 (1366) ◽  
pp. 346-353 ◽  
Keyword(s):  
Elastic Scattering ◽  
Cross Sections ◽  
Born Approximation ◽  
Scattering Amplitude ◽  
Wave Functions ◽  
Hydrogen Atoms ◽  
Final State ◽  
First Order ◽  
Exchange Approximation ◽  
Exchange Scattering

It is shown that when the Born approximation is applied to rearrangement collisions in the customary way, terms of the first order in the interaction energy between the colliding particles are omitted from the exchange scattering amplitude. If these terms are retained the arbitrariness which arises from the lack of orthogonality between the initial and final state wave functions is removed. The first-order exchange approximation derived in the present paper is employed to calculate the cross-sections for the 1 s -2 s and 1 s -2 p excitations of hydrogen atoms by electron impact and the elastic scattering of electrons by hydrogen atoms.

Topological analysis of electron momentum densities and the bond directional principle: the first-row hydrides, AH, and homonuclear diatomic molecules, A2

1996 ◽  
Vol 74 (6) ◽  
pp. 1187-1191 ◽  
Author(s):  
Jiahu Wang ◽  
B. James Clark ◽  
Hartmut Schmider ◽  
Vedene H. Smith
Keyword(s):  
Diatomic Molecules ◽  
Topological Analysis ◽  
Momentum Density ◽  
Wave Functions ◽  
Basis Set ◽  
Electron Momentum ◽  
Hartree Fock ◽  
Topological Features ◽  
Homonuclear Diatomic Molecules ◽  
Slater Basis

Topological analysis of electron momentum densities of the first-row hydrides and homonuclear diatomic molecules has been carried out. The densities and their curvatures were calculated from wave functions of near Hartree–Fock quality using a Slater basis. The bond directional principle has been discussed through the topological properties of electron momentum densities. Basis set effects on the topological features have also been addressed. Key words: electron momentum density, the bond directional principle, topological analysis, first-row hydrides, homonuclear diatomic molecules.

The partial wave theory of electron-hydrogen atom collisions

1957 ◽  
Vol 53 (3) ◽  
pp. 654-662 ◽  
Author(s):  
I. C. Percival ◽  
M. J. Seaton
Keyword(s):  
Hydrogen Atom ◽  
Partial Wave ◽  
Cross Sections ◽  
Wave Theory ◽  
Wave Functions ◽  
Scattered Electron ◽  
Hartree Fock ◽  
Angular Momenta ◽  
Continuous State ◽  
Approximate Wave

ABSTRACTThe paper is concerned with the solution of the algebraic problems arising in the partial wave treatment of electron-hydrogen atom collisions. Explicitly antisymmetrized wave functions are used throughout. The boundary conditions are written in S-matrix notation and expressions for total and differential cross-sections obtained. The algebraic coefficients fλ and gλ occurring in the continuous state Hartree-Fock equations are expressed in terms of Racah coefficients, and tabulated as functions of the total angular momentum for atomic s, p and d electrons and all angular momenta of the scattered electron. Expressions are given for the calculation of first-order corrections to the results obtained using approximate wave functions.

Structure effects in low-energy electronic stopping

1969 ◽  
Vol 311 (1504) ◽  
pp. 47-51 ◽  
Keyword(s):  
Amorphous Carbon ◽  
Cross Sections ◽  
Wave Functions ◽  
Low Energy ◽  
Thomas Fermi ◽  
Hartree Fock ◽  
Theoretical Predictions

Recent experiments have shown electronic stopping cross-sections to have an oscillatory dependence on ionic atomic numbers with minima in the region of Li, Na and Cu. The amplitudes of the oscillations are enhanced when the ions are channelled. To explain these effects we have modified the Firsov theory of electronic stopping by replacing the Thomas-Fermi atom with simple Hartree-Fock wave functions, thus allowing for the different ionic sizes. Theoretical predictions are made for the stopping cross-sections of ions in amorphous carbon and of channelled ions in silicon.

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