Proton-hydrogen Collisions Research Articles

A statistical investigation of the rate constants for the H+ + HD reaction at temperatures of astrophysical interest.

The H+ + HD(v, j) reaction has been investigated in detail by means of a statistical quantum method. State-to-state cross sections and rate constants for transitions between reactants and rovibrational states HD(v', j') of the product arrangement with energies below 0.9eV collision energy [that is, HD(v = 0, j = 0-11) and HD(v = 1, j = 0-6)] have been calculated. For the other product channel, D+ + H2(v', j'), rovibrational states up to (v' = 0, j' = 9) have been considered for the calculation of the corresponding thermal rate. Present predictions are compared with previously reported theoretical and experimental rates. Finally, cooling functions for HD due to proton and atomic hydrogen collisions are computed in the low-density regime. We find that the much larger HD-H+ cooling function, as compared with that of HD-H, does not compensate for the low H+/H abundance ratio in astrophysical media so that HD cooling is dominated by HD-H (or HD-H2) collisions.

The effects of Heisenberg constraint on the classical cross sections in proton hydrogen collision

The interaction between a proton and a ground state hydrogen atom is studied using a standard three-body classical trajectory Monte Carlo (CTMC) and a quasi-classical trajectory Monte Carlo (QCTMC) model where the quantum feature of the collision system is mimicked using the model potential in the Hamiltonian as was proposed by Kirschbaum and Wilets (1980 Phys. Rev. A 21 834). The influence of the choice of the model potential parameters (α, ξ) on the initial radial and momentum distribution of the electron are analyzed and optimized. We found that although these distributions may not be as close to the quantum results as the distribution of standard CTMC results, we can find the combination of the (α, ξ) where the calculated cross sections are closer to the experimental data and closer to the results obtained quantum mechanically. We show that the choice of 3 < α < 5 is reasonable. To validate our observation, we present cross sections for ionization, excitation, charge exchange (CX), and state selective CX to the projectile bound state. Calculations are carried out in the projectile energy range between 10 and 1000 keV amu−1.

Singly differential cross sections for direct scattering, electron capture, and ionization in proton-hydrogen collisions

We use the two-center wave-packet convergent close-coupling approach to calculate singly differential cross sections for direct scattering, electron capture, and ionization in proton-hydrogen collisions at intermediate energies. The distinct feature of the approach is that it gives a complete differential picture of all the interconnected processes at once, subject to the unitary principle. Results obtained for the angular differential cross sections of elastic scattering, excitation, and electron capture, as well as the ionization cross sections differential in the ejected-electron angle, and in the ejected-electron energy agree well with available experimental data. It is concluded that the two-center wave-packet convergent close-coupling approach is capable of providing a realistic differential picture of all collision processes taking place in proton-hydrogen collisions.

Phenomenological NLO analysis of ηc production at the LHC in the collider and fixed-target modes

In view of the good agreement between the LHCb prompt-ηc data at s=7 and 8 TeV and the NLO colour-singlet model predictions –i.e. the leading v2 NRQCD contribution–, we provide predictions in the LHCb acceptance for the forthcoming 13 TeV analysis bearing on data taken during the LHC Run2. We also provide predictions for s=115 GeV for proton-hydrogen collisions in the fixed-target mode which could be studied during the LHC Run3. Our predictions are complemented by a full theoretical uncertainty analysis. In addition to cross section predictions, we elaborate on the uncertainties on the pp¯ branching ratio –necessary for data-theory comparison– and discuss other usable branching fractions for future studies.

Resonant charge exchange for H–H+ in Debye plasmas

The dynamics of resonant charge exchange in proton–hydrogen collisions embedded in plasma is investigated in the framework of the asymptotic approach, modified to account for the effect of Debye–Huckel screening in particle interactions. The cross sections exhibit a marked dependence on the Debye length in regimes of severe plasma confinement. Processes involving excited states H(n)–H+ are also discussed.

Electron transfer in proton-hydrogen collisions under dense quantum plasma

The effects of dense quantum plasma on 1s → nlm charge transfer, for arbitrary n,l,m, in proton-hydrogen collisions have been studied by employing a distorted wave approximation. The interactions among the charged particles in the plasma have been represented by modified Debye-Huckel potentials. A detailed study has been made to explore the effects of background plasma environment on the differential and total cross sections for electron capture into different angular momentum states for the incident energy in the range 10–1000 keV. For the unscreened case, our results agree well with some of the most accurate results available in the literature.

Erratum: “Charge transfer in proton-hydrogen collisions under Debye plasma” [Phys. Plasmas 22, 023512 (2015)

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Hybrid approach to calculating proton stopping power in hydrogen

Proton stopping power in hydrogen is calculated using a hybrid method. A two-centre convergent close-coupling method is used for calculations involving the proton fraction of the beam, while the Born approximation is used for the hydrogen fraction. For proton-hydrogen collisions rearrangement processes are explicitly included via a two-centre expansion. Hydrogen-hydrogen collisions are calculated including one- and two-electron processes. Despite using the first-order approximation in the hydrogen-hydrogen channel, overall reasonably good agreement with experiment is seen above 100 keV.

Polarization of Lyman-αemission in proton-hydrogen collisions studied using a semiclassical two-center convergent close-coupling approach

The semiclassical convergent close-coupling approach to ion-atom collisions has been extended to include electron-transfer channels. The approach has been applied to study the excitation and the electron-capture processes in proton-hydrogen collisions. The integral alignment parameter ${A}_{20}$ for polarization of Lyman-$\ensuremath{\alpha}$ emission and the cross sections for excitation and electron-capture into the lowest excited states have been calculated for a wide range of the proton impact energies from 1 keV to 1 MeV. The results are in good agreement with experimental measurements.

Proton-hydrogen collisions at low temperatures

We study the proton-hydrogen collision in the energy range from 0 to 5 K where the hyperfine structure of the hydrogen atom becomes important. A proper multichannel treatment of the hyperfine structure is found to be crucial at cold temperatures compared to the elastic approximation traditionally used at higher temperatures. Both elastic and hyperfine-changing inelastic processes are investigated, using both the multichannel quantum-defect theory (MQDT) and the coupled-channel numerical method. Results from the two methods show excellent agreement with MQDT providing an efficient and basically analytic description of the proton-hydrogen interaction throughout this energy range. We also discuss the validity of the elastic approximation and its relation to other methods.

Charge transfer in proton-hydrogen collisions under Debye plasma

The effect of plasma environment on the 1s → nlm charge transfer, for arbitrary n, l, and m, in proton-hydrogen collisions has been investigated within the framework of a distorted wave approximation. The effect of external plasma has been incorporated using Debye screening model of the interacting charge particles. Making use of a simple variationally determined hydrogenic wave function, it has been possible to obtain the scattering amplitude in closed form. A detailed study has been made to investigate the effect of external plasma environment on the differential and total cross sections for electron capture into different angular momentum states for the incident energy in the range of 20–1000 keV. For the unscreened case, our results are in close agreement with some of the most accurate results available in the literature.

‘Slow’ time discretization: a versatile time propagator for the time-dependent Schrödinger equation

We present the slow time discretization (STD) method for solving the time-dependent Schrödinger equation. The method is an extension of the slow variable discretization method for solving the stationary Schrödinger equation (Tolstikhin et al 1996 J. Phys. B: At. Mol. Opt. Phys. 29 L389), with time treated as the ‘slow’ variable. It is based on an expansion of the state vector in a discrete variable representation basis, in time, and an adiabatic basis, in Hilbert space. This approach is much more efficient in implementation than a direct solution of the Born–Fock equations. The versatility of the STD time propagator is illustrated through calculations for one-dimensional models of the ionization of hydrogen by an intense laser pulse and resonance charge transfer in proton–hydrogen collisions. The method is shown to perform well in the broad dynamical range considered, from adiabatic to nonadiabatic regimes.

Polarization of Lyman-Alpha and Balmer-Alpha in proton-hydrogen collision measured under three-body Faddeev type formalism

The alignment parameter is calculated to check the three-body Born-Faddeev formalism in excitation channel for ion impact of atomic targets.

Polarization of Lyman-α and Balmer-α emission in proton–hydrogen collisions: a study using first-order Born–Faddeev-type equations

A three-body Born–Faddeev model is devised to calculate the total cross sections of Balmer-α and Lyman-α emissions, for the excitation of hydrogen atoms by proton impact in the energy range of 100 keV–7 MeV. In addition, the polarization alignment factor A20 is calculated and compared against available experimental data to further test the theory. Specifically, here we use the Faddeev–Watson–Lovelace formalism to study the excitation of atomic hydrogen from its ground state to the excited states of n = 2 and 3 and magnetic sublevels l = 0, 1 and 2, wherever applicable. The first-order electronic, A(1)e, and the first-order nuclear, A(1)n, amplitudes are considered in order to calculate the excitation transition matrix (TPT), while a near-the-shell condition is assumed throughout. In addition, our results were used to calculate the first-order form factors. The present results are compared, where possible, with those of other theoretical and experimental works that are currently available in the literature.

Resonance charge exchange between excited states in slow proton-hydrogen collisions

The theory of resonance charge exchange in slow collisions of a proton with a hydrogen atom in the excited state is developed. It extends the Firsov-Demkov theory of resonance charge exchange to the case of degenerate initial and final states. The theory is illustrated by semiclassical and quantum calculations of charge exchange cross sections between states with $n=2$ in parabolic and spherical coordinates. The results are compared with existing close-coupling calculations.

Origin, evolution, and imaging of vortices in proton-hydrogen collisions

Using a novel computational approach, we have elucidated the origin of unexpected vortices in atomic collisions. It is shown how they could be observed in experiments and how they play a new and wide ranging role in angular momentum transfer.

Origin, evolution, and imaging of vortices in proton-hydrogen collisions

Using a novel computational approach, we have elucidated the origin of unexpected vortices in the electronic wavefunction during ion-atom collisions. It is shown how they could be observed in experiments and how they play a new and wide ranging role in angular momentum transfer and other atomic processes.

Momentum Transfer and Viscosity from Proton‐Hydrogen Collisions Relevant to Shocks and Other Astrophysical Environments

The momentum transfer and viscosity cross sections for proton-hydrogen collisions are computed in the velocity range of ~200-20,000 km s−1 relevant to a wide range of astrophysical environments such as supernova remnant shocks, solar wind, winds within young stellar objects or accretion disks, and interstellar protons interacting with the heliosphere. A variety of theoretical approaches are used to arrive at a best estimate of these cross sections in this velocity range that smoothly connect with very accurate results previously computed for lower velocities. Contributions to the momentum transfer and viscosity cross sections from both elastic scattering and charge transfer are included.

Spin exchange rates in proton-hydrogen collisions

The spin temperature of neutral hydrogen, which determines the optical depth and brightness of the 21-cm line, is determined by the competition between radiative and collisional processes. Here, we examine the role of proton–hydrogen collisions in setting the spin temperature. We use recent fully quantum-mechanical calculations of the relevant cross-sections, which allow us to present accurate results over the entire physically relevant temperature range 1–104 K. For kinetic temperatures TK≳ 100 K, the proton–hydrogen rate coefficient exceeds that for hydrogen–hydrogen collisions by about a factor of 2. However, at low temperatures (TK≲ 5 K) H–H+ collisions become several thousand times more efficient than H–H and even more important than H–e− collisions.

Analysis of an ion–atom collision at intermediate velocities by means of quantum trajectories

We present the results of a quantum calculation designed to discuss the dynamics of an ion–atom collision at intermediate velocities. The description is based on a quantum fluid picture. The time-dependent Schrödinger equation is integrated numerically for a model proton–hydrogen collision and quantum trajectories are computed. By these means, we obtain a pictural view of the scattering process. Analysis of the resulting trajectories yields insights into the dynamics of the physical phenomena involved, with special emphasis on ionization.