Session QR1: Heavy Particle Collisions

State-to-state measurements of low-energy ion-molecule and ion-ion collisions by three dimensional momentum imaging

While the measurement of total absolute cross sections remains challenging, the insight provided by differential cross sections and branching ratios is invaluable to assess the quality of theoretical predictions. Satisfactory agreement at the latter level gives better confidence in the proper identification of the reaction mechanism and key parameters. The three dimensional imaging of molecular dissociation, and more generally, the determination of all momentum vectors of the reaction products, gives direct access to the differential quantities of interest. For the prototype reaction of a proton colliding with H$_2$, the secondary H$_2^+$ current may be recorded to provide the total charge transfer yield. The dissociative charge transfer of the product ions with alkali targets leaves a characteristic signature in the total kinetic energy imparted to the H fragments. Its measurement is readily achieved by coincident detection on position sensitive detectors [1]. This allows us to extract vibrational populations as a function of collision energy. A resonant enhancement of the charge transfer around 45 eV/amu is observed, that leaves the molecular ion in its vibrational ground state [2]. Those observations are supported by state-of-the-art calculations. We have similarly explored the ionization of molecular oxygen by proton and alpha particle impact, at velocities characteristic of the solar wind. A somewhat more involved vibrational analysis of the O$_2^+$ cations [3] indicates a Franck-Condon like vibrational population of the ground electronic state from 50 eV to 10 keV, unlikely to modify the branching ratios of dissociative recombination, itself responsible for airglow emissions. More interestingly, a significant population of the $^4\Pi_u$ excited state is measured at velocities typical of the fast solar wind. Finally, we shall address the implementation of three dimensional imaging in merged ion-ion beam studies. Mutual neutralization involving anions and cations is a very efficient process, characterized by a uniquely defined initial state and a limited range of final states readily identified by the total kinetic energy released to the products. Detailed branching ratios may be obtained at near zero collision energy where the reaction rate is maximum and the system behaves as a quasi-molecule undergoing in flight dissociation. As an example, we shall discuss the mutual neutralization of C$^+$ and various anions of the second and third row of the periodic table [4]. [1] X. Urbain et al., Rev. Sci. Instrum. 86, 023305 (2015). [2] X. Urbain et al., Phys. Rev. Lett., 111, 203201 (2013). [3] A. Dochain and X. Urbain, EPJ Web of Conferences 84, 05001 (2015). [4] R. F. Nascimento et al., J. Phys. Conf. Ser. 635, 022043 (2015).   

Two-Centre Convergent Close-Coupling Approach to Ion-Atom Collisions: Current Progress

There are two versions of the convergent close-coupling (CCC) approach to ion-atom collisions: quantum-mechanical (QM-CCC) and semi-classical (SC-CCC). Recently, both implementations have been extended to include electron-transfer channels. The SC-CCC 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-$\alpha$ 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. It has been established that for convergence of the results a very wide range of impact parameters (typically, 0-50 a.u.) is required due to extremely long tails of transition probabilities for transitions into the 2$p$ states at high energies. The QM-CCC approach allowed to obtain an accurate solution of proton-hydrogen scattering problem including all underlying processes, namely, direct scattering and ionisation, and electron capture into bound and continuum states of the projectile. In this presentation we give a general overview of current progress in applications of the two-centre CCC approach to ion-atom and atom-atom collisions.   

Experimental and theoretical fully differential study of coherence effects in ionization of He by proton impact

We have measured and calculated fully differential cross sections (FDCS) for ionization of He by 75 keV proton impact. Results were obtained for transverse projectile coherence lengths of 3.3 and 1.0 a.u. The coherence length is related to the maximum dimension of a diffracting object that can be coherently illuminated by the projectiles. In the calculation impact parameter dependent amplitudes a(b) are computed and multiplied by a wave packet of varying width, reflecting the coherence length, which describes the projectile. The scattering angle dependent transition amplitude is then obtained from a Fourier transform. Pronounced coherence effects observed in the data are qualitatively well reproduced by the calculation. Along with extensive data published already the present work therefore confirms the presence of such effects beyond reasonable doubt.   

Numerical calculation of charge exchange cross sections for plasma diagnostics

The diagnostics of impurity density and temperature in the plasma core in tokamak plasmas is carried out by applying the charge exchange recombination spectroscopy (CXRS) technique [R. C. Isler, Plasma Phys. Control. Fusion 36, 171 (1994)], where a fast beam of H atoms collides with the plasma particles leading to electron capture reactions with the impurity ions. The diagnostics is based on the emission of the excited ions formed in the electron capture. The application of the CXRS requires the knowledge of accurate state-selective cross sections, which in general are not accessible experimentally, and the calculation of cross sections for the high n capture levels, required for the diagnostics in the intermediate energy domain of the probe beam, is particularly difficult. In this work, we present a lattice numerical method to solve the time dependent Schr\"{o}dinger equation. The method is based on the GridTDSE package [J. Suarez et al., Comput. Phys. Commun. 180, 2025 (2009)], it is applicable in the wide energy range 1 - 500 keV/u and can be used to assess the accuracy of previous calculations. The application of the method will be illustrated with calculations for collisions of multiply charged ions with H.   

Search for an explanation for neutralization rates of atomic ion-ion reactions.

We have measured well over a hundred rate coefficients $k$ for cation-anion mutual neutralization reactions at thermal energies. For molecular ions, the $k$ at 300 K tend not to vary more than a factor of two or three, presumably because a great many neutral states cross the incoming Coulombic potential energy curve. Atomic-atomic systems, for which there are few favorable curve crossings between the neutral and Coulombic curves, show variation of at least a factor of 60 in the measured $k$ values at 300 K. For reactions involving the noble-gas cations, we assume that the final state is the lowest excited state of the neutral, plus the ground state of the neutralized anion, because otherwise the crossing distance $R$ is so small that the curve-crossing probability is nil. We plotted measured $k$ values (in cm$^{\mathrm{3}}$/s) vs the distance $R$ (in bohr) at which the neutral and Coulombic curves cross, the found that the data are fairly well fit by a power law for $k$, 10$^{\mathrm{-4}}R^{\mathrm{-2.8}}$. The question is, is there a physical explanation for the observed dependence on $R$? We will discuss the data and the expectations of Landau-Zener theory.   

Effects of Angular Scattering on Ion Velocity Distribution Functions.

An approximation model for total elastic and charge exchange ion-atom angular differential scattering cross sections is developed for simulations of the ion velocity distribution functions (IVDF) [1-2], which is validated by the experiment data of mobility and diffusion. IVDFs are simulated using the developed model and compared with recently published experimental data [3-4]. The IVDFs obtained with this model are compared to that from two other conventional models of less accurate differential cross sections [5-6]. The simulation results show the necessity to take into account the accurate differential cross sections, especially for strong $E$/$N$. The study reveals that IVDF cannot be separated into product of two independent IVDFs in the transverse and parallel to the electric field directions due to the significant effect of scattering. [1-2] H. Wang, et al., Two Papers Submitted to "\textit{Plasma Sources Sci. Technol.}" (2016) [3] Mustafaev A S, et al. \textit{Technical Physics }\textbf{60} 1778 (2015) [4] Sukhomlinov V, et al. \textit{42nd EPS Conference on Plasma Physics }P5.168 (2015) [5] Phelps A V \textit{Journal of Applied Physics }\textbf{76 }747 (1994) [6] Lampe M, et al. \textit{Physics of Plasmas }\textbf{19} 113703 (2012).