R. Cabrera-Trujillo

Dynamics of proton-acetylene collisions at 30 eV

Collisions of protons with ground state acetylene molecules at 30 eV are studied using the electron nuclear dynamics (END) theory. This time-dependent methodology for the study of molecular processes is a nonadiabatic approach to direct dynamics, which has been successfully applied to ion–atom and ion–molecule reactive collisions. Using the minimal END theory, we calculate the direct and charge-transfer differential cross sections. Different initial conditions lead to diverse product channels, such as charge transfer, proton exchange, and collision induced dissociation. Projectile energy loss is analyzed in terms of transfer into target electronic, translational, and rovibrational excitations. The comparison of the computed results with time-of-flight measurements is discussed.

Trajectory and molecular binding effects in stopping cross section for hydrogen beams on H2

The complex interaction of an atomic projectile with a molecular target is studied by considering the time-dependent electron-nuclear dynamics of the collision. We calculate the energy loss, charge exchange, and differential cross section for a hydrogen beam colliding with molecular hydrogen targets for projectiles energies from 10 eV/amu up to 25 keV/amu. We obtain the total, electronic, nuclear, and rovibrational contribution for the orientationally averaged stopping cross section of the molecular target when scattering over all the angles is considered. We emphasize the violation of Bragg’s rule (additivity of the atomic energy loss for the compound target) and the acceptance angle dependence of the experimental stopping cross section.

Impact parameter dependence of electronic and nuclear energy loss of swift ions: H+→ He and H+→ H

Abstract In this paper we report the calculation of impact parameter dependent energy losses of protons on hydrogen and helium for projectile energies from a few eV/amu up to 900 keV/amu using electron-nuclear dynamics (END). In each case it is found that, for smaller impact parameters, there is an initial rise in energy deposition at low projectile energies due to nuclear stopping. At somewhat larger energies, the nuclear contribution decreases, and the energy loss is primarily due to electronic stopping. As the ionization channel is not explicitly open in these calculations, these results are somewhat below experimental results at energies above the ionization threshold. Agreement with other calculations and the scanty experimental evidence is good.

Bond stopping cross sections for protons incident on molecular targets within the OLPA/FSGO implementation of the kinetic theory☆

Abstract We report the predictions of the kinetic theory for proton stopping in molecular targets within the orbital local plasma approximation (OLPA) introduced by Meltzer, Sabin and Trickey [Phys. Rev. A 41 (1990) 220]. In order to present a self-contained treatment, all the quantities entering in the calculations are obtained through use of the floating spherical Gaussian orbital (FSGO) representation of localized molecular orbitals. The calculations are performed for representative molecular targets, generating S e values for cores, single, double, triple-bonds and lone pairs as a function of projectile velocity. Fair agreement is observed with available experimental data and with other theoretical estimates. The adequacy of the FSGO representation in the study of molecular stopping for protons within the spirit of the kinetic theory and the orbital implementation of the local plasma approximation is confirmed in this work.

Orientational Effects in Energy Deposition by Protons in Water

Abstract We consider here the orientational aspects of the stopping of swift protons by the water molecule. The calculations are dynamical in nature, and they are compared to the electronic structure-based calculations made by Oddershede et al. on similar quantities. The comparisons, although qualitative, show good agreement between the two approaches.

Resonant charge transfer between H+ and H from 1 to 5000 eV

We employ the electron–nuclear dynamics (END) formalism to investigate the resonant charge transfer and scattering processes in the collision of protons on atomic hydrogen as an introduction to investigations of resonant charge transfer in larger atomic and molecular systems. The END method consists of an ab initio, non-adiabatic treatment of the electronic and nuclear degrees of freedom. The results span an energy range from 1 eV to 5 keV. We present electron transfer probabilities, absolute charge transfer differential and integral cross sections, and state-to-state differential cross sections for principal energy levels n = 1 and 2. The present results compare favourably with experimental data and other theoretical results. For the total resonant charge transfer cross section, we confirm the relation σ1/2trans ~ ln E. The role of non-adiabatic couplings in transfer into the n = 2 level is confirmed, and the effect of basis set size on the dynamics of the transfer is probed.

Calculation of Cross Sections in Electron-Nuclear Dynamics

Abstract In this work, we present an overview of the study of total and differential cross section calculations within the electron-nuclear dynamics (END). END is a method to solve the time-dependent Schrodinger equation in a non-adiabatic approach to direct dynamics. The method takes advantage of a coherent state representation of the molecular wave function. A quantum-mechanical Lagrangian formulation is employed to approximate the Schrodinger equation, via the time-dependent variational principle, to a set of coupled first-order differential equations in time for the END. We obtain the final wave function for the system allowing the determination of collisional properties of interest, as for example, deflection functions, charge exchange probabilities and amplitudes, and differential cross sections. We discuss the use and selection of basis sets for both the electronic description of the colliding systems as well as for their importance in the description of electron capture. As quantum effects are important in many cases and lacking for classical nuclei, we discuss the Schiff methodology and its advantages over other traditional methods for including semiclassical corrections. Time-lapse rendering of the dynamics of the participating electrons and atomic nuclei provides for a detailed view of dynamical and reactive processes. Comparison to experimental and other theoretical results is provided where appropriate data are available.

Energy loss studies of protons colliding with ethane: preliminary results

Abstract This paper reports theoretical calculations for projectile kinetic energy loss and stopping power of protons colliding with C 2 H 6 , for projectile energies of a few eV up to 25 keV. The many body character of the system and the strong coupling of the electronic and nuclear degrees of freedom make this system suitable for study using electron–nuclear dynamics. We report the stopping cross section as well as the electron capture cross section as a function of the projectile kinetic energy. We find that chemical dissociation plays an important role in charge exchange due to the bond breaking during the collision. We also obtain the stopping cross section using Bragg’s rule in order to analyze chemical effects (bond contributions). Finally, comparison to the available experimental data is provided.

The Bethe Sum Rule and Basis Set Selection in the Calculation of Generalized Oscillator Strengths

Abstract Fulfillment of the Bethe sum rule may be construed as a measure of basis set quality for atomic and molecular properties involving the generalized oscillator strength distribution. It is first shown that, in the case of a complete basis, the Bethe sum rule is fulfilled exactly in the random phase approximation. For an incomplete (computational) basis, some guidelines are developed for constructing higher angular momentum contributions to bases that will optimize the sum of generalized oscillator strengths and thus make the basis well suited for the calculation of stopping cross sections.

Dynamical Processes in Stopping Cross Sections

Abstract When a projectile collides with a target, several processes are involved, depending on the projectile energy. However, there is no single model that can treat all processes for the whole range of projectile energies without resorting to approximations, the accuracy of which depends on the projectile energy. In this work, we present an account of the efforts toward the solution of this problem by considering the time evolution of the collision for all the projectile energies. For that, we use the Electron-Nuclear Dynamics (END) approach to solve the time-dependent Schrodinger equation. A quantum mechanical Lagrangian formulation is employed to approximate the Schrodinger equation, via the time-dependent variational principle, by a set of coupled first-order differential equations in time for the END. We obtain the final wavefunction of the system as a function of the projectile energy, allowing us to determine collisional properties of interest. We discuss the relevance of the time-dependent description of the energy loss process by presenting our results for electron capture, threshold effects, projectile energy gain and quantum effects in the scattering processes.