38 research outputs found
Calculation of the free-free transitions in the electron-hydrogen scattering S-wave model
The S-wave model of electron-hydrogen scattering is evaluated using the
convergent close-coupling method with an emphasis on scattering from excited
states including an initial state from the target continuum. Convergence is
found for discrete excitations and the elastic free-free transition. The latter
is particularly interesting given the corresponding potential matrix elements
are divergent
Hyperspherical partial wave theory applied to electron hydrogen-atom ionization calculation for equal energy sharing kinematics
Hyperspherical partial wave theory has been applied here in a new way in the
calculation of the triple differential cross sections for the ionization of
hydrogen atoms by electron impact at low energies for various
equal-energy-sharing kinematic conditions. The agreement of the cross section
results with the recent absolute measurements of R\"oder \textit {et al} [51]
and with the latest theoretical results of the ECS and CCC calculations [29]
for different kinematic conditions at 17.6 eV is very encouraging. The other
calculated results, for relatively higher energies, are also generally
satisfactory, particularly for large geometries. In view of the
present results, together with the fact that it is capable of describing
unequal-energy-sharing kinematics [35], it may be said that the hyperspherical
partial wave theory is quite appropriate for the description of ionization
events of electron-hydrogen type systems. It is also clear that the present
approach in the implementation of the hyperspherical partial wave theory is
very appropriate.Comment: 16 pages, 9 figures, LaTeX file and EPS figures. To appear in Phys.
Rev.
Measurements of the ionization of atomic hydrogen by 17.6-eV electrons
We report triply differential measurements of atomic hydrogen ionization by 17.6-eV electrons, with the outgoing electrons both having 2 eV energy. These measurements supersede some of the existing data. The complete set is critically analyzed and is found to be much more internally consistent than before, thereby providing one of the most stringent tests for theory to date. Comparison with the calculations from the exterior complex scaling and convergent close-coupling theories shows excellent overall agreement in both shapes and magnitude
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Solving the three-body Coulomb breakup problem using exterior complex scaling
Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a "reduction to computation" of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations, and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wave function can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium
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Solving the three-body Coulomb breakup problem using exterior complex scaling
Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a ''reduction to computation'' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations, and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wave function can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium