High-resolution Differential Cross Sections Research Articles

Measurement of the ^{13}C(α, n_{0})^{16}O Differential Cross Section from 0.8 to 6.5MeV.

The cross section of the ^{13}C(α,n)^{16}O reaction is needed for nuclear astrophysics and applications to a precision of 10% or better, yet inconsistencies among 50years of experimental studies currently lead to an uncertainty of ≈15%. Using a state-of-the-art neutron detection array, we have performed a high resolution differential cross section study covering a broad energy range. These measurements result in a dramatic improvement in the extrapolation of the cross section to stellar energies potentially reducing the uncertainty to ≈5% and resolving long standing discrepancies in higher energy data.

High resolution crossed molecular beams study of the H+HD→H2+D reaction

The H+H2 reaction is the simplest chemical reaction system and has long been the prototype model in the study of reaction dynamics. Here we report a high resolution experimental investigation of the state-to-state reaction dynamics in the H+HD→H2+D reaction by using the crossed molecular beams method and velocity map ion imaging technique at the collision energy of 1.17 eV. D atom products in this reaction were probed by the near threshold 1+1′ (vacuum ultraviolet+ultraviolet) laser ionization scheme. The ion image with both high angular and energy resolution were acquired. State-to-state differential cross sections was accurately derived. Fast forward scattering oscillations, relating with interference effects in the scattering process, were clearly observed for H2 products at H2(v′=0, j′=1) and H2(v′=0, j′=3) rovibrational levels. This study further demonstrates the importance of measuring high-resolution differential cross sections in the study of state-to-state reaction dynamics in the gas phase.

On obtaining interatomic potentials from multiproperty fits to experimental data

High-resolution differential cross section (DCS) and accurate new limiting diffusion measurements for all the unlike-pair He+rare-gas systems are combined in constructing new multiproperty interatomic potentials. The new potentials predict most properties available for these systems, including independent high-resolution DCS measurements. Remaining discrepancies with earlier multiproperty potentials for HeKr and HeXe are attributed to incompatibilities among data sets used in the multiproperty fitting procedure. It is also shown that the 5% difference in well depths between two recently proposed potentials for HeXe is due to some of the data used in constructing these potentials, and that the DCS measurements of those studies are mutually consistent. Finally, the present potentials are refined slightly for agreement with high-energy cross section measurements. At the present level of reliability for DCS and dilute-gas data, it seems likely that high-resolution DCS and accurate (limiting) diffusion measurements will assist in determining He+molecule potentials. These two properties are particularly useful because they are independent of uncertainties in the corresponding molecule+molecule potentials.

Determination of the Na-Xe interaction potential from differential scattering cross-section measurements

High-resolution differential cross sections for the scattering of Na from Xe atoms have been measured. They were used to check the parameters of potential models previously proposed for the interaction of these particles. Special attention was given to the question of whether the use of different potential models leads to significant differences in the main potential parameters ε and r m. It is concluded that the use of well-chosen models for the Na-Xe interaction gives a uncertainty of no more than about 1% in the values of ε and r m.

Polarized, rotationally state-selected cross sections and anisotropic intermolecular potentials for LiF on Ar

High resolution differential cross sections of LiF in the J=1 rotational state in both a polarized condition and an unpolarized condition were experimentally studied with an Ar target for a range of LiF energies from 0.3 to 1.9 eV. The technique for performing such experiments is described in detail, including a description of the high resolution state selector and the seeded supersonic source. High frequency and rainbow features are observed in the differential cross sections. Manifestations of these oscillations are also observed in the significant difference in cross section due to polarization. The infinite order sudden approximation was used in a preliminary way to interpret the data. A model potential was used that had an inverse radial power series and appropriate angular dependent Legendere polynomials. The differential cross section is sensitive to the anisotropy parameters chosen. The cross section is generally larger for the (J, M) = (1, 1) polarization along the relative velocity for the energies and the small angles observed here.

Optical interaction potentials from high-resolution differential cross section measurements at thermal energies II. He(21S) + Ar

For pt.I see ibid., p.2693 (1976). Differential cross sections for He(21S)+Ar have been measured for six relative kinetic energies between 21 and 180 MeV. At low kinetic energies the small-angle oscillations are clearly resolved. Except for the lowest energy (21 MeV) a well resolved rainbow peak is observed in the differential cross sections. The real and imaginary parts of the interaction potential are obtained from the data. The real part has an intermediate maximum in the potential ( Delta E=25 MeV, rmax=7 au) which causes the rainbow peaks. The imaginary part can be expressed by an exponential plus a Gaussian. The velocity dependence of the total and ionization cross sections is calculated and the possibility of an energy-dependent width of the potential is indicated.

Intermolecular potential of anisotropic systems: LiF–Ar and LiF–Kr

High resolution differential cross sections for LiF scattering from Ar and Kr were measured in the thermal velocity range with varying LiF rotational temperature. An extremely narrow velocity distribution in the LiF beam, which reduced the equivalent temperature of the experiment to typically below 1 K, made it possible to resolve the high frequency oscillations of the differential cross section. Rainbow oscillations were identified and measured. Effects of experimental convolution were discussed and treated. Average potential well depths and radii were determined. It was inferred from the breadth of the primary rainbows that the potential well is not pathological in possessing extremely deep or shallow depths (ε) for certain orientations: standard deviation of ε is about 50%. The persistency of the high frequency oscillations with angle is evidence of a quite spherical locus of rm, although the locus is not necessarily concentric with the center of mass. The high frequency oscillations and in part the rainbow oscillations are damped by rotational transitions. The differential cross section is largely independent of the rotational state distribution. Calculations using an optical model for the scattering and assumed angular dependent potentials permitted a quantitative test of a theoretical long range potential model and also permitted a fit of an empirical angular dependent model at the radius of the onset of these transitions. The quantitative test indicated that neglected repulsive terms are important in the theory. The fitted empirical model was consistent with the measured dispersion in ε. The radius at which rotational transitions become significant has been determined and lies outside rm, approximately at the rainbow radius, but inside the radius probed by total scattering cross section measurements. The potential well parameter rm=3.8 Å, ε=4.1×10−14 erg and rm=3.7 Å, ε=5.3×10−14 erg were obtained for LiF–Ar and LiF–Kr, respectively.

Optical interaction potentials from high-resolution differential cross section measurements at thermal energies. II. He(21S)+Ar

For pt.I see ibid., p.2693 (1976). Differential cross sections for He(21S)+Ar have been measured for six relative kinetic energies between 21 and 180 MeV. At low kinetic energies the small-angle oscillations are clearly resolved. Except for the lowest energy (21 MeV) a well resolved rainbow peak is observed in the differential cross sections. The real and imaginary parts of the interaction potential are obtained from the data. The real part has an intermediate maximum in the potential ( Delta E=25 MeV, rmax=7 au) which causes the rainbow peaks. The imaginary part can be expressed by an exponential plus a Gaussian. The velocity dependence of the total and ionization cross sections is calculated and the possibility of an energy-dependent width of the potential is indicated.

Observation of High-Resolution Differential Cross Section of Polarized, Rotationally State-Selected LiF on Ar

We report high-resolution differential cross sections at thermal energy for polarized, rotationally state-selected LiF on Ar. They were 2-8% larger with LiF in the $J=|M|=1$ orientation along the relative velocity than in the $J=1$ unpolarized state. The differential cross section in the present case is much more sensitive to change in polarization than is the total cross section. The high-frequency oscillations of the differential cross sections were found substantially independent of $J$ when the present $J=1$ data were compared with non-state-selected data for $\overline{J}=15$ or $\overline{J}=25$.

Electrostatic optical device for high-resolution differential cross section measurements in scattering experiments

A new electrostatic optical system designed for high angular and energy resolution in ion–molecule-scattering experiments is described. This device is based upon a theoretical lens model (’’zero gap electrostatic double-aperture lens’’) proposed by Read. A first pair of these lenses accelerates a low-energy ion beam, with a relatively wide angular spread, up to a chosen collision energy and makes the beam parallel in the scattering region, without any system of slits. A second pair of lenses, symmetrical to the first, decelerates the ions scattered at a given angle and focuses them on the entrance slit of a 127° electrostatic analyzer. This analyzer and the final lens are scanned in order to obtain energy loss spectra. A simple theoretical study of the system which allows the angular spread of the ion beam in the collision region to be predicted as a function of the initial energy and the chosen scattering energy (between about 100 and 3000 eV) is given, the respective positions of the lenses being adjustable parameters. These positions are chosen according to the theoretical results in order to achieve the best angular resolution. The first experimental data obtained are in very good agreement with the theoretical predictions. An example of application to elastic He+–He collisions is presented.

High resolution differential cross sections and intermolecular potentials I: Li–Kr and Li–Xe

High resolution differential cross sections for the systems Li–Kr and Li–Xe have been measured with resolution sufficient to obtain the amplitudes as well as the positions of all features including the highest frequency oscillations in d σ/d Ω. Two different relative velocities per system were selected for measurement in the range from 1–3 × 105 cm/sec. The data were analyzed by fitting model potentials. Values obtained for the range and depth parameters of the potential are rm =4.78 Å, ε = 1.35 × 10−4 erg for Li–Kr, rm =4.80 Å, ε = 2.03 × 10−14 erg for Li–Xe. The data are of sufficient quality to yield additional information about the shape of the intermolecular potential.

Absolute total cross sections for Li-molecule scattering

Absolute total scattering cross sections were measured for 7Li scattered by D2, N2, CO, CO2, CH4, and SF6 over a range of Li beam velocities of 0.75–4.75 × 105 cm/sec corresponding to a range of relative kinetic energies of 0.04–0.33 eV for Li–D2 to 0.02–0.79 eV for Li–SF6. In the observed cross sections random experimental errors were less than 1.5% and systematic errors were between −0.3% and +1.4%. Two spherically symmetric potentials, the Lennard-Jones (12,6) and the Buckingham-Corner were fit to deconvoluted and statistically smoothed data using a non-linear least squares fitting routine. For each Li-molecule system a satisfactory fit could be obtained with standard deviations of approximately 1%–2%. The best fit potentials gave accurate values for the average long range attractive part of the potentials over the range of limiting impact parameters. Evidence from high resolution differential cross section experiments is introduced that indicates that there should be relatively little damping of the glory features of the total scattering cross sections for the Li-molecule systems studied here, and hence the ability of spherical potentials to reproduce the data is not surprising.

Intermolecular Potentials from Crossed Beam Differential Elastic Scattering Measurements. III. He+He and Ne+Ne

High-resolution differential cross sections for elastic scattering extending to wide scattering angles for He–He and Ne–Ne have been measured at two collision energies in the thermal range. The experiments were carried out by crossing two supersonic nozzle atom beams at right angles and detecting the atoms scattered in the plane of the beams with a rotatable electron-bombardment mass-filter universal detector. The results are analyzed to yield information on the interatomic potentials for these systems using a realistic and flexible potential function, and comparison is made with previously proposed potentials. For He2, a somewhat ``harder'' low-energy repulsion than that of most such potentials is inferred, while for Ne2 the potential well depth found is ∼ 30 % larger than earlier estimates and in good agreement with a preliminary spectroscopic finding.