Cross Sections For Ionization Of Hydrogen Research Articles

Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms

We present a theoretical method for calculating multiphoton ionization amplitudes and cross sections of few-electron atoms. The present approach is based on an extraction of partial wave amplitudes from a scattering wave function, which is calculated by solving a system of driven Schroedinger equations. The extraction relies on a description of partial waves in terms of a small number of Coulomb waves with fixed wave numbers. The method can be used for photon energies below and above the ionization threshold and to treat resonance-enhanced multiphoton ionization. We use it to calculate two-, three-, and four-photon ionization cross sections of hydrogen and helium atoms for a wide range of photon energies and to determine the asymmetry parameters of photoelectron angular distributions for two-, three-, and four-photon ionization of the helium atom.

Solar wind charge exchange in cometary atmospheres

Context. Solar wind charge-changing reactions are of paramount importance to the physico-chemistry of the atmosphere of a comet, mass-loading the solar wind through an effective conversion of fast light solar wind ions into slow heavy cometary ions. Aims. To understand these processes and place them in the context of a solar wind plasma interacting with a neutral atmosphere, numerical or analytical models are necessary. Inputs of these models, such as collision cross sections and chemistry, are crucial. Methods. Book-keeping and fitting of experimentally measured charge-changing and ionization cross sections of hydrogen and helium particles in a water gas are discussed, with emphasis on the low-energy/low-velocity range that is characteristic of solar wind bulk speeds (<20 keV u−1/2000 km s−1). Results. We provide polynomial fits for cross sections of charge-changing and ionization reactions, and list the experimental needs for future studies. To take into account the energy distribution of the solar wind, we calculated Maxwellian-averaged cross sections and fitted them with bivariate polynomials for solar wind temperatures ranging from 105 to 106 K (12–130 eV). Conclusions. Single- and double-electron captures by He2+ dominate at typical solar wind speeds. Correspondingly, single-electron capture by H+ and single-electron loss by H− dominate at these speeds, resulting in the production of energetic neutral atoms (ENAs). Ionization cross sections all peak at energies above 20 keV and are expected to play a moderate role in the total ion production. However, the effect of solar wind Maxwellian temperatures is found to be maximum for cross sections peaking at higher energies, suggesting that local heating at shock structures in cometary and planetary environments may favor processes previously thought to be negligible. This study is the first part in a series of three on charge exchange and ionization processes at comets, with a specific application to comet 67P/Churyumov-Gerasimenko and the Rosetta mission.

New approach for approximating the continuum wave function by Gaussian basis set

A new approach for approximating the continuum wave functions for hydrogenic atoms with Gaussians basis sets is developed and tested. In this the plane wave is left unchanged and the distorting factor, represented by the Confluent Hypergeometric function, is expanded as a sum of Spherical Harmonics multiplied by a series of Gaussians. In this way the number of spherical waves and Gaussians will be significantly reduced and the plane wave will be responsible for the momentum conservation.As compared with previous methods that expand the full continuum, including the plane wave, our strategy does not require a great quantity of partial waves for convergence. Dense oscillations which are characteristic of the plane wave, are avoided. To test the performance of this approximation to describe a free-bound atomic form factor, the ionization cross section of hydrogen by impact of protons in first Born approximation is calculated. Compared with the exact results, a good agreement with just 4 spherical waves and ten Gaussians each is obtained. The method looks very interesting, especially to speed up atomic and molecular collision calculations involving the continuum.

Nondissociative electron and photon ionization cross sections of molecular hydrogen and deuterium

State-to-state [X 1Σ+g(vi) → X 2Σ+g(vj)] and quasi state-specific [X 1Σ+g(vi, Ji) → X 2Σ+g(vj)] photon and electron-impact ionization cross sections of hydrogen and deuterium molecules have been obtained with a combined analysis of experimental measurement and theoretical calculations. Rotation state ionization transitions are considered using the p-partial wave approximation. Previously calculated photoionization transition moments are refined and extended to ∼300 eV using accurate experimental photoionization cross sections. The transition moments are used to obtain the photoionization cross sections and oscillator strengths for the H2 and D2 X 1Σ+g(vi, Ji) → H+2 and D+2 X 2Σ+g(vj, Jj) transitions. The calculated ionization oscillator strengths, together with excitation functions derived from electron-impact ionization measurements of H2, enable accurate determination of electron-impact ionization cross sections for both H2 and D2 transitions to (vj, Jj) levels of the X 2Σ+g state at energies ranging from threshold to the non-relativistic limit. The autoionizing singlet-ungerade states contribute at least 0.6–1% of the total e+H2 →H+2 cross section. The e+D2 →D+2 and e+H2 →H+2 cross sections are very similar above the threshold energy region. The D2 cross section is ∼1.6% larger than the H2 cross section. Thermally averaged nondissociative ionization cross sections of H2 and D2 at temperatures appropriate for plasma and planetary applications have been tabulated.

Scaling and formulary of cross-sections for ion–atom impact ionization

The values of ion–atom ionization and stripping cross-sections are frequently needed for many applications that utilize the propagation of fast ions through matter. When experimental data and theoretical calculations are not available, approximate formulae are frequently used. This paper briefly summarizes the most important theoretical results and approaches to cross-section calculations in order to place the discussion in historical perspective and offer a concise introduction to the topic. Based on experimental data and theoretical predictions, a new fit for ionization cross-sections is proposed. The range of validity and accuracy of several frequently used approximations (classical trajectory, the Born approximation, and so forth) are discussed using, as examples, the ionization cross-sections of hydrogen and helium atoms by various fully stripped ions. A formulary of analytical approximations for cross-sections is presented.

Triple differential cross-sections for near threshold (e, 2e) process for hydrogen

The triple differential cross-sections for ionization of hydrogen at incident energies in the range 17.6 eV to 13.7 eV are calculated in the distorted-wave Born approximation in the equal energy sharing andϑab = 180° kinematics. It is found that a maximum in the cross-section, as was observed in the case of helium under similar conditions is also found here at excess energyEex ≤ 1.0 eV. This ‘maximum’ becomes more pronounced asEex decreases indicating dominance of short rangee-e correlations at these low energies. The angular distribution of the singlet and triplet partial waves and the asymmetry parameter have been analysed.

Single and double ionization cross sections of atoms colliding with relativistic structural heavy ions

The single and double ionization cross sections of hydrogen and helium atoms colliding with relativistic structural heavy ions are calculated within the framework of the eikonal approximation. By structural ions are implied those containing partly occupied electron shells. It is shown that an allowance for the finite size of charged ions leads to significant changes in the ionization cross sections as compared to those determined for the point ions possessing the same charges and energies.

Ionization of hydrogen by a relativistic heavy projectile

Using a relativistic analogue of the classical trajectory Monte-Carlo method we investigate the influence of the magnetic field of a relativistic heavy projectile on the ionization cross section of hydrogen. In particular we focus our attention on the angular and energy distribution of the emitted delta electrons.

Higher order corrections to the triply differential electron impact ionization cross section of hydrogen

The triply differential cross section for electron impact ionization of hydrogen has been calculated in higher order starting from a formulation of Brauner et al. (1989). The short range effects missing from a first order calculation are included by using a Sturmian representation for the full Green function. The complexity of the calculation necessitated some simplification of the wavefunction. The authors find that, at 17.6 eV and 27.2 eV incident energies, the higher order corrections cause up to an order of magnitude increase in the cross section, but do not improve the shape compared to first order.

The ionization of hydrogen and of hydrogenic positive ions by electron impact

Calculations of the ionization cross section of hydrogen and of hydrogenic positive ions are described in which the initial state is either the ground or the excited 2s state. The first procedures used are the Born (ii) and Born-exchange approximations. These results are compared with other theoretical calculations and with experimental data. It is seen that, for the case of ionization of hydrogen from its ground state, none of the theoretical results is in good agreement with the experimental data. A certain defect of the theory is then corrected by adopting a third procedure for this case in which an angle-dependent Coulomb potential is used in the description of the final state for the process. It is then found that, despite the sounder theoretical footing of this latter calculation, no improved agreement with experimental data is obtained. In the near threshold region, however, our third procedure yields a linear behaviour, whereas the first two approximations do not. This is in accord with theoretical predictions though there exists some uncertainty in the experimental situation.