Local Complex Potential Research Articles

Local against non-local complex potential in resonant electron-molecule scattering

Resonant scattering of electrons from molecules is discussed in the context of both a non-local complex potential and a local complex potential (boomerang model). Vibrational excitation cross sections are computed for an exactly solvable model and compared with those calculated within the boomerang approach. The range of applicability of the local complex potential approach is analysed in detail. A semi-local approximation to the cross sections is introduced which is only slightly different from the boomerang approximation, but leads to improved results.

A source of errors in cross sections of curve-crossing processes

Total inelastic cross sections for atomic collisions are usually obtained by computing the complex phaseshifts of the incident wavefunction often using perturbation techniques. Such calculations are generally based on a theoretical formalism in which a local complex potential, V(R)-i1/2 Gamma (R), is employed to describe the entrance channel. However, the assumption that the imaginary component is local breaks down when there are only a few final states energetically open. The characteristics of the effects associated with this breakdown are discussed through a numerical study of the associative detachment process H+H-(1 Sigma g+) to H2(2 Sigma u+)+e- at incident energies of 0.0129, 0.129 and 0.646 eV. The cross sections to individual vibrational-rotational levels of H2 are also reported. It is shown that the breakdown in the expression often used for a local complex potential can produce substantial errors in computed cross sections. Methods of detecting and analysing the divergence of calculated cross sections from true ones are presented, along with means of estimating actual values within uncertainty brackets.

Complex potential and electron spectrum in atomic collisions involving fast electronic transitions: Penning and associative ionization

Beginning with a Feshbach projection-operator analysis, formulas for the local complex potential in the entrance-channel radial wave equation are reviewed and developed in detail for inelastic atom-atom collisional processes that involve an electronic transition between Born-Oppenheimer states. Penning and associative ionization are used as illustrative examples in the presentation. A complete derivation of $T$-matrix elements involving radial wave functions is then presented in the context of transition rates and inelastic differential cross sections (both for energy and angle). Two approximate formulas for the energy spectrum of the particle ejected in the electronic transition are developed in which quantities obtained from exact, complex radial wave functions are replaced by those obtained from approximate, totally real radial wave functions. Numerical computations for the electron energy spectrum of the Penning process $\mathrm{He}(1s2s, 2^{3}S)+\mathrm{H}(1s, 1^{2}S)\ensuremath{\rightarrow}\mathrm{He}(1{s}^{2}, 1^{1}S)+{\mathrm{H}}^{+}+{e}^{\ensuremath{-}}$ are then presented to probe the effects of the imaginary width of the complex potential. It is found that the real component of the entrance-channel radial wave function is not much affected by the imaginary width when the width is small compared to other energy terms. In such cases, the imaginary component of the wave functions is then $\frac{\ensuremath{\pi}}{2}$ out of phase with respect to the real component, even at fairly close separations, owing to their asymptotic boundary conditions. This result also leads to a method of estimating the contribution of the imaginary radial wave functions to matrix elements using information obtained only from approximate, totally real wave functions. Finally, the eigenenergies of all 149 rotational-vibrational states of $\mathrm{He}{\mathrm{H}}^{+}(^{1}\ensuremath{\Sigma}^{+})$ are reported, along with the computed cross sections of associative ionization to each state.

Electron detachment from negative ions: The effects of isotopic substitution

Absolute total electron-detachment cross sections and relative elastic-scattering cross sections are presented for collisions of ${\mathrm{H}}^{\ensuremath{-}}$ (${\mathrm{D}}^{\ensuremath{-}}$) + He, Ne, Ar, ${\mathrm{N}}_{2}$ for collision energies ranging from about 2 eV up to 100 eV. Special emphasis has been given to the effect of isotopic substitution. It was found that, with the exception of the helium target, the results cannot be in accord with a model using a localized complex potential. On the other hand, the results for ${\mathrm{H}}^{\ensuremath{-}}$ (${\mathrm{D}}^{\ensuremath{-}}$) + He are in excellent agreement with predictions based upon a previous (local complex potential) analysis of differential elastic-scattering measurements.

Theoretical Investigation of Complex Potentials for Atomic Collisions. I. Numerical Solution of Model (H−,H) Collisions

A set of coupled equations for rearrangement collisions involving processes such as scattering, electron transfer (${A}^{\ensuremath{-}}+B\ensuremath{\rightarrow}A+{B}^{\ensuremath{-}}$), collisional detachment (${A}^{\ensuremath{-}}+B\ensuremath{\rightarrow}A+B+e$), and associative detachment (${A}^{\ensuremath{-}}+B\ensuremath{\rightarrow}AB+e$) is solved numerically for the (${\mathrm{H}}^{\ensuremath{-}}$,H) collision system at low energies. In this calculation, the interaction potential between the ground states of H and ${\mathrm{H}}^{\ensuremath{-}}$ is approximated by a set of local complex potentials. The energy dependence and scattering-angle dependence of the electron-detachment and electron-transfer probabilities, and of differential cross sections for scattering, electron transfer, and detachment processes, are calculated. A detailed analysis of the interference structures in the various differential cross sections is made for the diffraction and multipath scatterings, and for the gerade-ungerade and nuclear symmetry interferences. The effect of damping due to the imaginary parts of the complex potentials and the effect of isotope substitutions are investigated. To examine the sensitivity of the calculated results to the potentials adopted, the calculations are carried out for several sets of such complex potentials. Important differences, which may provide useful information for further investigations, are found for different sets of potentials.

Theoretical Considerations on Penning Ionization Processes

Penning ionization process is discussed from two standpoints of view, namely on the basis of quasiadiabatic and adiabatic representations of electronic states. New cross-section formulas are derived. Green operator technique is applied in the first formalism and a non-local complex potential is derived for the relative motion in the initial channel. In the second formalism Fano's method is applied and a local complex potential is defined. In a certain limiting case these two formulas reduce to the corresponding B I I approximation and the formula obtained by Katsuura, respectively. Though the first formalism is exact as it stands, it is not convenient to use this for more refined practical calculations. It is concluded that the second formalism is more suitable for practical calculations of low energy metastable Penning ionization.

Quasi-optical method and asymptotic behaviour of many-channel amplitudes

The asymptotic behaviour of many channel amplitudes is investigated by means of Lippman-Schwinger equations with local complex potentials. It is shown that in the case of potentials without subtraction the amplitudes have a Regge behaviour with the same trajectory. The role of subtraction terms which may lead to non-Regge type behaviour is discussed.