Proton-hydrogen Collisions Research Articles

Second Born approximation differential cross sections for p+H and p+He charge-exchange collisions.

Charge-exchange differential cross sections are calculated by the second Born approximations without a recourse to any further approximation. The exact second Born approximation cross sections show satisfactory agreement with the experimental data for proton-helium collisions at all the energies of 2.82, 5.42, and 7.4 MeV while they are considerably smaller than the existing experimental cross sections in the Thomas peak region for proton-hydrogen collisions at 2.8 MeV. Discussions are given on how to choose the interactions for two-electron systems in order to satisfy the boundary condition of neutral-atom collisions.

Absence of the Thomas peak in the classical-trajectory Monte Carlo calculations for proton-hydrogen collisions in the MeV region.

Large-scale classical-trajectory Monte Carlo calculations are executed in three-dimensional space for proton-hydrogen collisions at 2.8 and 5 MeV. The Thomas peak that has been confirmed in the experimental data and in the quantal calculations is invisible in the classical calculations. This unexpected result is due to the peculiar character of classical bound states that have no minimum binding energy. The Oppenheimer-Brinkmann-Kramers-type capture by means of the velocity-matching mechanism dominates even in the MeV region owing to this classical peculiarity, and the Thomas double-scattering contribution is embedded in this background.

Orientation and alignment in H+-H collisions.

We have calculated probabilities, orientation parameters, and alignment angles for 2p excitation and capture in proton-hydrogen collisions at 50- and 100-keV projectile energy. The results, obtained from solving the Schr\"odinger equation in a multistate atomic-orbital expansion, are compared to those of a similar, recently published investigation. In both studies, similar results for excitation are found, and also for capture at large impact parameters. The origin of different predictions for capture at intermediate impact parameters is discussed.

Vibrational excitation in proton-hydrogen collisions at medium energies

The vibrational populations of H2(X1 Sigma g+, nu ) produced by H+ projectiles at energies 90<or=E<or=1000 eV have been measured as a function of the scattering angle theta . A strong vibrational excitation is observed at large angles for all energies studied. Measurements of charge exchange and electronic excitation have also been performed in order to examine whether this vibrational excitation may be related to these processes. A relative increase of the charge transfer differential cross section is thus observed when the collision energy increases. A simple model is tried to rationalize the variations with E and theta of the vibrational excitation. A fairly good agreement between the experimental and theoretical results is obtained especially at low energy. The discrepancies found at higher energy may be explained in terms of interactions neglected in the model such as charge transfer and electronic excitation.

Impulse approximation in proton-hydrogen collisions.

Analytic expressions for 1{ital s}-{ital nlm} differential-capture cross sections in proton-hydrogen collisions are derived. We employ the partially peaked impulse approximation and retain terms up to first order in an expansion of the Fourier transform of the potential. The exact impulse approximation is also computed using numerical integration of a three-dimensional integral. The exact and analytic calculations are compared with each other and with experiment.

Phase-integral halfway-house variational continuum distorted waves

Symmetric resonant charge transfer in proton-hydrogen collisions is examined theoretically using phase-integral halfway-house variational continuum distorted wave theory. The formulation involves the factorization of the scattering matrix into two Moller matrices, one describing the motion for - infinity <or=t<or=O- and the other the motion for + infinity >or=t>or=O+. The authors use outgoing continuum distorted waves for t(O and incoming continuum distorted waves for t)O with a matching at t=O, the associated heavy particle motion remaining incoming for t(O and outgoing for t)O. Results for total cross sections are presented and compared to previous theoretical models and experimental results. Differential cross sections in the centre-of-mass range 0-3.2 mrad are presented at 25, 60 and 125 keV and are compared with the same theoretical models and previous experimental results.

A time-dependent molecular orbital approach to electron transfer in ion-atom collisions

A time-dependent molecular orbital approach has been developed for describing the dynamics of atomic and molecular interactions. Equations derived for the time-dependent electronic density matrices in the TDHF approximation are locally linearized in time with the use of a time-dependent reference density. It contains a time-dependent driving term due to the nuclear motions. Nuclear motions are obtained from the gradients of effective potentials which change with electronic states and account for couplings of nuclear and electronic motions. Results are presented for electron transfer in proton-hydrogen collisions, to compare to other calculations.

Faddeev approach to electron capture

The Faddeev-Watson-Lovelace scattering formalism is applied to the rearrangement problem in three-body collisions. In a second-order approximation, the transition operator is seen to generalize the second Born approximation by replacing each appearance of a two-body potential with a corresponding two-body transition operator, except for the first Born electron-nuclear potential term which remains the same. Application to electron capture in ion-atom collisions for both forward- and large-angle projectile scattering is discussed and the particular role of the internuclear potential in each case considered. Extension is made of results obtained within the second Born approximation, particularly the zero contribution of the internuclear potential at forward angles and the structure of critical-angle scattering. The treatment of initial- and final-state binding effects is also addressed. Differential capture cross sections for proton-hydrogen and proton-helium collisions in the MeV energy range are presented.

State-Selective Capture Cross Sections in Proton-Hydrogen and Proton-Helium Collisions at Intermediate and High Energies

Total cross sections are computed for electron capture from the ground states of H and He by fast protons using the Corrected first-Born (CB1) approximation. Particular emphasis is given to the formation of atomic hydrogen in excited states 2s, 2p, 3s, 3p, 3d and 4s for which experimental data are available. Detailed comparisons with the measurements are carried out, with the purpose of assessing the validity and utility of the CB1 method for prediction of state-selective cross sections.

Ionization in antiproton-hydrogen collisions

Employing the semiclassical approximation we calculate within the coupled-state formalism the ionization probability in antiproton-hydrogen (p+H) collisions. In particular we investigate the adiabatic ionization at the distance of closest approach in almost central collisions. Striking differences in the electron excitation probability compared with proton-hydrogen (p+H) collisions are predicted.

Complex formation in proton-hydrogen collisions. II. Isotope effects

Classical trajectory calculations have been performed on the DIM potential energy surface of H +H 2 for collision energies between 20 meV and 2 eV. Complex formation cross sections have been determined for many combinations of projectile and target masses, showing that capture behind the centrifugal barrier is a necessary but by no means sufficient condition for the formation of a long-lived complex. Its probability depends on energy and masses in a way which suggests that the initial energy loss of the projectile on its approach to, and first encounter with the target plays a crucial role in the “trapping” process. H/D isotope effects exceed 20% at energies above 1 20 of the potential well depth, and reach more than 200% at higher energies. At collision energies below 1 100 of the well depth the isotope effect disappears, and the complex formation cross section becomes equal to the capture cross section if the target has no (classical) internal excitation. If, on the contrary, the target is internally excited this equality is invalidated, and an isotope effect of a few percent due to different zero point energies remains. Microreversibility arguments show that these effects should have a perceptible influence on the results of a “dynamically biased” phase space theory.

Differential cross sections for electron capture in fast proton-hydrogen collisions.

Differential cross sections for the electron-capture process in proton-hydrogen collisions at incident proton energies of 25, 60, and 125 keV are calculated with use of the eikonal approximation in which the distortion by the internuclear interaction is included. The results agree very well with experiments. Capture into excited final states is appreciable, particularly at low energies.

The maximum momentum transfer in proton-hydrogen collisions

The upper limit of momentum transfer by a proton to K-shell electrons is calculated in a restricted three-body classical model. The model shows that the infinite upper limit used in practice, is generally good except for low energy protons passing through an extremely rarefied gas.

Radiative electron capture in proton-hydrogen collision.

The 1s-1s proton-hydrogen radiative electron capture is studied within the nonrelativistic semiclassical approximation. Several three-particle theoretical methods currently used in collision theory are applied. Double, single, and total cross sections are computed. The continuum distorted-wave method is found to present a projectile angular distribution with two critical angles, i.e., two enhancements, which can be physically visualized in terms of combined processes of a mechanical collision followed (or preceded) by an interaction with the radiation field. It is shown that for high projectile velocities, the contribution of these critical angles to the total cross section is negligible. Prior and post impulse approximations are also calculated.

Calculations of the energy distribution of electrons ejected in ion-atom collisions using pseudostates

Calculations of the energy distribution of electrons ejected in ion-atom collisions have been performed by representing continuum wave functions in terms of pseudostates. It is illustrated that for proton-hydrogen collisions the electron spectrum in the low-energy region is in good agreement with that calculated by the use of exact continuum wave functions. In the case of ionization of helium by proton impact, the present results are compared with experimental data as well as with Born Hartree-Fock calculations.

Exact two-channel variational continuum distorted-wave theory: results for symmetric resonant exchange

Symmetric resonant charge exchange in proton-hydrogen collisions is examined theoretically using continuum distorted-wave (CDW) travelling atomic orbitals. The formulation involves a fully variational, unitary, non-perturbative calculation. The CDW wavefunctions are normalised and refined orthogonal corrections are included. Specimen-weighted impact parameter probabilities for charge exchange are presented at 25 keV and contrasted with undistorted travelling atomic-orbitals results (UTAO, also known as BMcC-TSAE). Fully variational CDW total cross sections are compared with the experimental results of McClure (1966), the non-variational CDW theoretical results of Cheshire (1964) and the fully variational UTAO theoretical results of McCarroll (1961). Differential cross sections in the centre-of-mass angle range 0 to 3.1 mrad are compared at 25 and 60 keV with the experimental results of Martin et al. (1981), the non-variational CDW theoretical results of Belkic et al. (1979) and the fully variational UTAO theoretical results of Lin.

Electron capture into highly excited states in proton-hydrogen collisions

A new straightforward technique for the evaluation of the rearrangement-scattering amplitude for the process H/sup +/+H(1s)..-->..H(nlm)+H/sup +/ has been presented in the continuum--intermediate-state approximation. We reduce the scattering amplitude to a closed analytical form. The asymptotic behavior of the capture cross sections with respect to n has also been derived. It has been shown conclusively that the charge-exchange cross sections asymptotically obey the n/sup -3/ power law throughout the entire energy range of the projectile. It is found that the cross sections for capture into different angular momentum states can be calculated from the respective asymptotic cross-section values with the help of a simple scaling law. The present calculated results have been compared with the available experimental findings.

Direct and capture processes in proton-hydrogen scattering. III. Differential cross sections and charge exchange probabilities

For pt.II see ibid., vol.15, no.16, p.2703, 1982. In a series of publications the authors presented a solution of the time-dependent Schrodinger equation for collisions between one-electron ions and atoms by an expansion in terms of two-centre wavefunctions of the Hylleraas type. They present differential cross-sections for direct and electron exchange processes in proton-hydrogen collisions 1 and 2 keV. The scattering angle dependence as well as the energy dependence of the related charge exchange probability is studied and compared with competing theoretical approaches and experiment.

Charge transfer in positron-hydrogen collisions

The nonperturbative approach developed recently by Tripathy and Rao for the study of charge transfer in proton-hydrogen collisions has been applied to the problem of positronium formation in positron-hydrogen collisions. The cross section for capture into the ground state has been calculated by partially taking into account the Coulomb distortions but neglecting the polarization effect of the target atom. The calculated cross section has a maximum at an incident energy of 10.2 eV, and as the incident positron energy increases it approaches the results of the first Born approximation (FBA) of Massey and Mohr. The calculated results for capture cross sections and differential scattering cross sections for various incident energies have been compared with those from the FBA and other theoretical calculations.

Charge transfer in proton-hydrogen collisions. II

Charge transfer in proton-hydrogen collisions. II