Angular Differential Cross Sections Research Articles

Angular differential energy gain measurements of highly charged ion–atom collisions at 100 and 120 eV/q

Angular differential energy gain spectra of C4+ and N4+–He collisions have been measured at the collision energy of 100 and 120 eV/q, respectively. In the case of C4+–He collisions, the oscillation structure in the angular differential cross section of the double-electron capture into the C2+(1s22s21S) state has been clearly observed. On the other hand, in the case of N4+–He collisions, the N3+(1s22p21S) product channel in single-electron capture process is dominant at the forward scattering angle and the N3+(1s22p21D and/or 3P) state becomes dominant at larger scattering angle.

Angular distribution for the elastic scattering of electrons fromAr+(3s23p52P)above the first inelastic threshold

The measured angular differential cross section (DCS) for the elastic scattering of electrons from Ar{sup +}(3s{sup 2}3p{sup 5} {sup 2}P) at the collision energy of 16 eV is presented. By solving the Hartree-Fock equations, we calculate the corresponding theoretical DCS including the coupling between the orbital angular momenta and spin of the incident electron and those of the target ion and also relaxation effects. Since the collision energy is above one inelastic threshold for the transition 3s{sup 2}3p{sup 5} {sup 2}P-3s3p{sup 6} {sup 2}S, we consider the effects on the DCS of inelastic absorption processes and elastic resonances. The measurements deviate significantly from the Rutherford cross section over the full angular range observed, especially in the region of a deep minimum centered at approximately 75 deg. Our theory and an uncoupled, unrelaxed method using a local, spherically symmetric potential by Manson [Phys. Rev. 182, 97 (1969)] both reproduce the overall shape of the measured DCS, although the coupled Hartree-Fock approach describes the depth of the minimum more accurately. The minimum is shallower in the present theory owing to our lower average value for the d-wave non-Coulomb phase shift {sigma}{sub 2}, which is due to the high sensitivity of {sigma}{sub 2} more » to the different scattering potentials used in the two models. The present measurements and calculations therefore show the importance of including coupling and relaxation effects when accurately modeling electron-ion collisions. The phase shifts obtained by fitting to the measurements are compared with the values of Manson and the present method. « less

Fourier moment analysis of velocity-map ion images

An alternative to inverse Abel transform and forward convolution methods is presented for extracting dynamical information from velocity-map ion images. Unlike most competing methods, that presented here does not require the probed three-dimensional distribution to possess cylindrical symmetry. The new method involves analysis of the Fourier moments of images measured in different experimental geometries, and allows speed distributions, angular differential cross sections, and angular momentum alignment and orientation to be determined from raw images of the products of photodissociation and photon-initiated bimolecular reactions. The methodology is developed within the semiclassical framework of Dixon’s bipolar moment formalism [R. N. Dixon, J. Chem. Phys. 85, 1866 (1986)], although it is equally applicable to other common formulations of the product scattering distribution. To allow a comparison of the method with the Abel inversion, which requires that the velocity distribution of the probed product has an axis of cylindrical symmetry, the method is applied to newly acquired experimental images of atomic chlorine produced in the photolysis of NOCl. Extraction of product rotational alignment information is illustrated using newly acquired images of rotationally aligned NO formed by NO2 photolysis. Application of the Fourier moment methodology to studies of bimolecular reactions is also demonstrated, using simulated images for the reaction H+D2→HD(v=0,j=0,9)+D.

Differential charge-transfer cross sections forNa+with Rb collisions at low energies

We report on a theoretical and experimental study of state-selective differential single-electron transfer cross sections between ${\mathrm{Na}}^{+}$ ions and $\mathrm{Rb}(5s,5p)$ atoms at collision energies of 2, 5, and 7 keV. A two-center multichannel semiclassical impact parameter close-coupling method with straight-line trajectories was used to obtain single-electron capture amplitudes. By combining with the eikonal approximation, we calculated the angular differential cross sections. These results are compared to the experimental data obtained with Rb targets cooled in a magnetic optical trap. It is shown that there is generally a good agreement between the present calculations and the experiments. In spite of the higher resolution offered from the cold target, the rapid oscillations in the differential cross sections are not resolved by the experiments.

Recent Development and Validation of the Nuclear Reaction Code EMPIRE

Recent extensions of the EMPIRE-II code system are presented These include link to the Coupled Channels code ECIS, second chance preequilibrium emission, Monte Carlo preequilibrium (HMS), width fluctuations (HRTW), improvements in the γ-ray strength functions, link to the omp segment of RIPL, calculation of recoil spectra, and possibilities to plot angular distributions, energy spectra and double differential cross sections using PLOTC4 and/or ZV View package. The emphasis is on the validation of the code through comparison with experimental data and recent application to nuclear data evaluation.

Differential cross sections fornear-threshold electron impact dissociation of molecularhydrogen

At low energies, the major pathway for the electronimpact dissociationof H2 is through excitation to b 3Σu+. Ab initio calculationsusing the adiabatic nuclei, energy balance model of Stibbe andTennyson(1998 New J. Phys. 1 2.1) of total cross sections,angular differentialcross sections, energy differential cross sections and doubledifferentialcross sections for the electronic ground state initial vibrational v = 0level, dissociating into continuum states are presented. The formalexpressions needed for such calculations, which involve threefragmentsin the exit channel, are derived.

Charge-Changing Processes in Collisions between Li-like Ions and He2+

By means of a crossed-beams technique the total cross sections for charge transfer and ionization in He2+ + B2+ collisions have been measured at barycentric energies from 10 to 256 keV and from 40 to 240'keV, respectively. Moreover, the angular-differential cross sections for charge transfer at CM energies of 10.18 and 15.3 keV have been determined. The total and differential cross sections are calculated with the Basis Generator Method (BGM) and are in good agreement with the experimental data.

Hot atom reaction yields in Mu*+H2 and T*+H2 from quasiclassical trajectory cross sections on the Liu–Siegbahn–Truhlar–Horowitz surface

In order to provide an assessment of the “global” accuracy of the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential surface for H3, hot atom reaction yields, which are determined from collision processes over an energy range much wider than that of single-collision experiments, have been calculated for the Mu*+H2 and T*+H2 systems. The isotopic comparison of muonium (Mu=μ+e−), an ultralight isotope of hydrogen (mMu/mH≈1/9), with the heaviest H-atom isotope, tritium, is a novel approach in testing the global accuracy of the H3 surface. These reaction yields have been calculated using a formalism developed for (μ+) charge exchange, with input cross sections for elastic, inelastic (rovibrational excitation) and reactive collisions determined from quasi classical trajectories on the LSTH surface, in the center-of-mass energy range 0.5–11 eV. The rate of energy loss of the hot atom (Mu* or T*) due to elastic and inelastic collisions with the moderator (H2) drastically affects the hot atom reaction yield. In particular, the forwardness of the angular differential cross section for the elastic process plays a crucial role in determining the stopping power for hot atoms. Good agreement is obtained in the absolute yields for both Mu*+H2 and T*+H2, for the first time from microscopic cross sections, demonstrating that the LSTH surface remains surprisingly accurate over a wide range of energy and isotopic mass.

Improvement of Angular Differential Elastic Scattering Cross Sections in Nucleon-meson Transport Code NMTC/JAERI97 for Neutron Transmission Experiment Analysis

The nucleon-meson transport code NMTC/JAERI97 is revised in the treatment of the angular distribution of the neutron elastic scattering for the energy region from 20 to 100 MeV. The approximation of the angular distribution with the first order Bessel function is changed to the random sampling based on the database evaluated by the optical model potential parameters (OMPs). For 43- and 68-MeV quasi-monoenergetic neutrons through iron, concrete and polyethylene shields, neutron transmission experiments are analyzed with the updated NMTC/JAERI97 code. It is shown that the updated NMTC/JAERI97 calculations agree well with the measured transmission neutron energy spectra and give significantly improved C/E values for the attenuation length in comparison with the results of the original version. It is also notable that the updated calculation represents quite well the measured neutron spectra at the positions of 20 and 40 cm off beam axis of the shields. Moreover, it is found that the cross sections evaluated by an OMP gives a better result than those by the systematics for the transmission calculation of neutrons with energies below 40 MeV.

Improvement of Angular Differential Elastic Scattering Cross Sections in Nucleon-meson Transport Code NMTC/JAERI97 for Neutron Transmission Experiment Analysis.

The nucleon-meson transport code NMTC/JAERI97 is revised in the treatment of the angular distribution of the neutron elastic scattering for the energy region from 20 to 100 MeV. The approximation of the angular distribution with the first order Bessel function is changed to the random sampling based on the database evaluated by the optical model potential parameters (OMPs). For 43- and 68-MeV quasi-monoenergetic neutrons through iron, concrete and polyethylene shields, neutron transmission experiments are analyzed with the updated NMTC/JAERI97 code. It is shown that the updated NMTC/JAERI97 calculations agree well with the measured transmission neutron energy spectra and give significantly improved C/E values for the attenuation length in comparison with the results of the original version. It is also notable that the updated calculation represents quite well the measured neutron spectra at the positions of 20 and 40 cm off beam axis of the shields. Moreover, it is found that the cross sections evaluated by an OMP gives a better result than those by the systematics for the transmission calculation of neutrons with energies below 40 MeV.

Angular Differential Cross Sections and Mean Energy Gain for Single- and Multiple-Electron Capture in Slow Ar8+–C60 Collisions

We present experimental results for angular differential cross sections, dσ/dθ, and mean translational energy gain, ΔEmean, as functions of the number of electrons, s, stabilized on the projectile in 26.4 keV Ar8+ + C60 → Ar(8−s)+ + Cr60r+ + (r − s)e− collisions. The most probable scattering angle increases linearly with s for s = 1–7, while processes leading to neutralization (s = 8) scatter more strongly than expected from this trend. The ΔEmean-values are positive and increase with s between s = 1 and s = 2, are virtually constant up to s = 6, and finally decrease to negative values (energy loss) for s = 7. The experimental results are compared with Monte Carlo trajectory simulations for impact parameters ranging from small to large values.

Angular Differential Cross Sections for Slow Highly Charged Ions Interacting with C60

Angular differential cross sections are presented for collisions between 26.4 keV Ar8+ ions and C60 molecules. Using a classical overbarrier simulation the deflection function is calculated for large impact parameters. To compare with experimental data the theoretical cross section values are convoluted with an instrumental function. Both the theoretical and experimental cross sections are absolute in magnitude and position. The experimental cross section for retaining one electron on the projectile is qualitatively well described by the theoretical cross sections for initially capturing one to four electrons from the target.

State-Selective Electron Capture in Ion–Ion Collisions

For the first time, state-selective electron capture in ion-ion collisions has been investigated experimentally. An experimental method which is mainly based on the specific features arising in ion–ion collisions due to the crossed-beams kinematics has been newly developed. We are able to determine the electronic states populated in the collision process as well as angular differential cross sections for the respective reaction channels.

Measurements of Double-Differential Neutron Emission Cross Sections of 6Li, 7Li and 9Be for 11.5 MeV and 18.0 MeV Neutrons

Double-differential neutron emission cross sections (DDXs) of 6Li, 7Li and 9Be were measured for 18.0 MeV and 11.5 MeV incident neutrons produced by the T(d, n) and 15N(d, n) reactions respectively, using the Tohoku University Dynamitron time-of-flight (TOF) spectrometer. The data were obtained at 13 laboratory angles, and angular-differential cross sections (ADXs) of elastic and inelastic scattering neutrons were derived from the DDXs. For 11.5 MeV neutrons, we obtained the neutron emission spectra over the secondary neutron energies by newly employing the double TOF method as well as the conventional one. In the measurements at 18.0 MeV, we achieved better energy resolution than in our previous studies by using a neutron detector that has a larger solid angle and a thinner tritium target. The experimental results of DDXs and ADXs were compared with our previous results and the evaluated data given in JENDL-3.2, JENDL Fusion File and ENDF/B-VI. It is found that the JENDL data reproduce the experimental ones very well.

Calculation of Circular Dichroism in Helium Double Photoionization

We apply the convergent close-coupling (CCC) method to the calculation of the circular dichroism in helium double photoionization for a photon energy of 99 eV. Comparison is made with the measurements of Mergel et al. [Phys. Rev. Lett. 80, 5301 (1998)], and substantial discrepancy is found. This is the first example where the CCC theory yields such disagreement with experiment for either $(\ensuremath{\gamma},2e)$ or $(e,2e)$ angular differential cross sections. Nevertheless, we argue that there are good reasons to believe in the accuracy of the theoretical predictions.

Angular Differential Cross-Section for Electron Transfer in ION-ION Collision

Angular differential cross-sections for the formation of He 0 in collision between fast He+ ions are calculated using distorted wave Coulomb—Born approximation. The interaction potentials satisfy necessary Coulomb bound- ary conditions. In absence of any other theoretical results the present results are compared with the existing experimental data.

Thermalization of fast nitrogen atoms in elastic and inelastic collisions with molecules of atmospheric gases

Abstract The energy relaxation of fast nitrogen atoms due to elastic and inelastic collisions with molecules in the atmosphere is studied. A new formula for the energy relaxation kernel in the Boltzmann kinetic equation, which applies equally to elastic and inelastic collisions, is derived. Angular and energy dependent differential cross sections are used in calculations of the energy transfer rate. The energy relaxation kernel is evaluated for inelastic N + N2 collisions with numerically determined differential cross sections for rotational and vibrational excitation of the N2 molecules. The mean rate of energy loss, the average energy transfer per collision and mean thermalization times are calculated as functions of the kinetic energy of the nitrogen atoms. The contributions of elastic and inelastic scattering to the thermalization of N atoms in the terrestrial atmosphere are analyzed. The energy distribution functions of the fast nitrogen atoms are evaluated for thermospheric conditions. They depart significantly from a Maxwellian distribution at high energies.

Experimental determination of quantum state resolved differential cross sections for the hydrogen exchange reaction H+D2→HD+D

We have carried out a systematic crossed molecular beam study of the hydrogen exchange reaction in the H+D2→HD+D isotopic form at two collision energies: 0.53 and 1.28 eV. The Rydberg atom time-of-flight method was used to measure the D-atom product angle-velocity distribution. For the first time ro-vibrational quantum state resolved differential cross sections for the title reaction were measured, which can directly be compared to theoretical predictions at this detailed level. Experimental results are compared to theoretical predictions from both quasi classical and quantum mechanical calculations on different potential energy surfaces as well as to earlier experiments. A general good agreement is found for the converged quantum mechanical calculations with indications that the Boothroyd-Keogh-Martin-Peterson potential energy surface is better suited to describe the dynamics of the reaction. For the higher collision energy the quasi classical trajectory calculations reproduce the experimental data quite well, whereas they fail to describe the situation at the lower collision energy especially with respect to angular resolved differential cross sections.

Observation of Interference in Charge Exchange Scattering inHe2++He+Collisions

We report the first observation of interference in charge exchange collisions between two ions. Employing the crossed-beams technique in conjunction with signal recovery methods, angular differential cross sections have been measured for charge transfer in He{sup 2+}+He {sup +} collisions at barycentric energies between 0.5 and 10.2keV. The oscillatory structure observed is in agreement with quantum calculations and can be interpreted in terms of interference between scattering into {ital gerade} and {ital ungerade} molecular states, which arise due to the identity of the nuclear charges. {copyright} {ital 1997} {ital The American Physical Society}

Orientation and alignment effects for electron transfer in keV ion-atom collisions

Recent theoretical results for one-electron transfer between excited target atoms and keV ions are reviewed. Semi-classical close coupling calculations with an atomic and a molecular orbital expansion are compared for the Li +Na(3p) system in the energy range 0.17–2.25 keV/amu. The question to what extent the effects of initial and final state orbital orientation or alignment seen in angular differential cross sections can be studied with integral state-to-state cross sections is addressed. The validity of simple models such as velocity matching, a propensity rule for orientation and alignment due to orientation in the transfer region is discussed.