The average hamiltonian view of low-energy scattering by a vibrating molecule

The average hamiltonian theory is used to examine the effect of molecular vibration on low-energy scattering. When the relative motion of the colliding molecules is slow on the timescale of molecular vibration, it is appropriate to transform the problem into an oscillating reference frame and to describe the collision in that frame by the average hamiltonian over one period of oscillation. The first-order result is identical to the distorted-wave Born approximation. High-order corrections introduce phase shifts for elastic scattering due to molecular vibration and provide transition amplitudes for inelastic scattering. The extent to which the higher-order corrections modify the distorted waves establishes criteria for the validity of the DWA. These criteria are used to examine recent distorted-wave calculations of V-V energy transfer rate constants.     

Relativistic calculation of Stokes' parameters for intermediate energy electron impact excitation of cesium atoms

The integrated and differential Stokes' parameters of the light emitted in the decay 6p ² P _1/2,3/2→6s ² S _1/2 fore-Cs scattering in the intermediate energy range are presented. These have been calculated using scattering amplitudes obtained by a relativistic distorted-wave method.     

Spin asymmetry in near threshold (e, 2e) process for lithium and hydrogen

The singlet and triplet cross sections and the asymmetry parameter for e-H and e-Li ionization have been calculated in a distorted-wave Born approximation for incident energies in the range 0.5 to 20 eV above the ionization threshold. The two final-state continuum electrons are assumed to share equal energy and to come out 180° apart. The variation with respect to the angle of scattering is found to be qualitatively very different in the two cases. It is found that, in the case of lithium, the ¹D and ³F components in the scattering amplitude are quite significant even at very low energies.     

Reorientation in H-NH2 collisions,a spin correlated interaction

We present polarised fluorescence data and a theoretical study of inelastic energy transfer in the NH₂-H system. Rotational transfer lines are weakly polarised, and branching ratios and polarisations depend on the spin component of the radical initially excited. Polarisation ratios are calculated using the distorted-wave Born approximation with a spin correlated potential operator. Spin-dependent terms are predicted to be more reorienting than the spin-independent part.     

State multipoles and Stokes parameters for the 51,3 D 2 excitation of cadmium

Relativistic distorted-wave calculations have been performed for the excitation of the 5^1,3 D ₂ state from the ground state of cadmium by polarised and un-polarised electrons. A full set of state multipoles of experi-mental interest have been obtained for 20 and 40 eV collision energies. From these results we have calculated the Stokes parameters of the light emitted in the decay to the relevant P states.     

An elementary method for calculating orientation-averaged fully differential electron-impact ionization cross sections for molecules

Currently there are no reliable theoretical approaches for calculating fully differential cross sections (FDCS) for low-energy electron-impact ionization of large molecules. We have recently introduced the distorted-wave impulse approximation as a first step in developing improved theoretical approaches. One significant obstacle to evaluating improved theoretical approaches which require significant computer resources lies in the fact that the existing experimental data require taking averages over all molecular orientations. To circumvent this problem, it has been proposed to approximate the orientation-average by using an orientation-averaged molecular orbital in the calculation of the FDCS. The theoretical justification and expected range of validity for the approximation is given in this paper. Examples are presented for electron-impact ionization of H(2) and N(2).     

Second-order relativistic electron capture

Starting with the impulse approximation, we analyse second-order effects in relativistic electron capture. The relation of this model with relativistic distorted-wave approximations is clarified. In particular it is shown that the second-order spin-coupling terms in the RCDW theory are consistent with the correct form given by perturbation theory. In the semirelativistic limit, the RCDW results are shown to accord with the formulae of Moiseiwitsch for flip and nonflip transitions in the ultra-relativistic limit. This confirms that the continuum-distorted-wave model generalises to relativistic spinors, and highlights the defects of scalar models. We also present a new symmetric eikonal theory which gives reliable results for capture without change of spin, but leads to a divergent total cross section for spin-flip transitions in the second-order term. This effect, which is quite distinct from the spurious spin-flip amplitudes of the scalar symmetric eikonal theory, is taken as further evidence that the eikonal approximation is not valid for magnetic transitions.     

Electron impact polarization and correlation properties of the inert gases

For the heavier rare-gas targets, Ne, Ar, Kr, there is now a reasonable amount of experimental electron impact coherence parameter data available for excitation of the lowestJ=1 states. Theoretical results for those rare-gas targets, have been restricted to distorted-wave approximation (DWA) type theories. We present a systemization of the experimental data and compare them with available theoretical results. In the case of the heavy rare gases, we compare the experimental and theoretical data available for the three species, Ne, Ar, Kr, in order to identify trends. We compare the experimental data with results from available theories (mainly DWA type) and discuss the importance of spin-orbit coupling effects and “shell” effects. We present our point-of-view as to the physical picture that is emerging from all collisional data, and conclude by recommending future experimental and theoretical activities that will, from our perspective, provide new insight into the physics of these processes.     

Grazing-incidence transmission small angle X-ray scattering from thin films of block copolymers

Thin films of lamellar and cylindrical block copolymers are popular systems for low-cost nanolithography. To be useful as nanoscale templates, the lamellae or cylinders must be oriented perpendicular to the substrate. Domain orientations are usually characterized by microscopy measurements of the film surface, but these techniques cannot detect tilted, bent, or tortuous domains in the film interior. We report a simple method to quantify out-of-plane disorder in thin films of block copolymers based on a variant of grazing-incidence small angle X-ray scattering (GI-SAXS). A typical GI-SAXS experiment illuminates the center of a substrate-supported film at a grazing angle of incidence (near the film/substrate critical angle), and the strong reflected signal is interpreted with the distorted-wave Born approximation. In a new approach, the beam footprint is moved to the far edge of the sample, allowing the acquisition of a transmission pattern. The grazing-incidence transmission data are interpreted with the simple Born approximation, and out-of-plane defects are quantified through analysis of crystal truncation rods and partial Debye-Scherrer rings. Significantly, this study demonstrates that grazing-incidence transmission small angle X-ray scattering can detect and quantify the buried defect structure in thin films of block copolymers. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Comparison of close-coupling and approximate methods for F(2P12) + H2 non-reactive collisions: Translational wavefunction analysis

Electronic-rotational energy transfer in F(²P_{$\text{1}\text{2}$}) + H₂ (j = 0) non-reactive collisions is studied by analyzing the translational wavefunctions (TW) and transition probabilities of four model problems: full close-coupling (CC), diabatic (DDW) and adiabatic (ADW) distorted-wave Born theories, and an asymptotic sine-wave model. Comparisons among the approximate models are discussed and their accuracy is examined. DIM theory provides the diabatic electronic matrix elements, and the close-coupled equations are solved by the R-matrix method. The resulting S-matrix elements times their appropriate asymptotic wavefunctions when propagated in along the reaction coordinate generate the TW. For the CC results, relations between the TW and the adiabatic electrotational energy correlation diagrams are emphasized, while for the other models the effects of classical turning points, diabatic energy level structure, unitarization techniques, and other dynamical factors on the state-to-state transition probabilities are examined.     

Low energy (e,2e) measurements of CH4 and neon in the perpendicular plane

Low energy experimental and theoretical triple differential cross sections for the highest occupied molecular orbital of methane (1t(2)) and for the 2p atomic orbital of neon are presented and compared. These targets are iso-electronic, each containing 10 electrons and the chosen orbital within each target has p-electron character. Observation of the differences and similarities of the cross sections for these two species hence gives insight into the different scattering mechanisms occurring for atomic and molecular targets. The experiments used perpendicular, symmetric kinematics with outgoing electron energies between 1.5 eV and 30 eV for CH(4) and 2.5 eV and 25 eV for neon. The experimental data from these targets are compared with theoretical predictions using a distorted-wave Born approximation. Reasonably good agreement is seen between the experiment and theory for neon while mixed results are observed for CH(4). This is most likely due to approximations of the target orientation made within the model.     

Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.     

Examination of (e,2e) scattering models by comparison of momentum profiles of noble gases between experiment and theory

Momentum profiles have been measured for the two outermost atomic orbitals of noble gases, Ar, Kr and Xe, at incident electron energy of about 2 keV using a newly developed multichannel (e,2e) spectrometer. The experimental results exhibit significantly improved statistics compared with those achieved in previous studies while covering a wide range of momenta up to 3.6 a.u. The results are compared with theoretical calculations using four (e,2e) scattering models, the plane-wave impulse and Born approximations (PWIA and PWBA), and the distorted-wave impulse and Born approximations (DWIA and DWBA). The DWIA and DWBA scattering models have been found to satisfactorily reproduce the experimental momentum profiles in terms of both shape and intensity over the entire momentum range covered, indicating the importance of distorted wave effects for quantitatively describing (e,2e) reaction.     

Silver nanoparticle monolayer-to-bilayer transition at the air/water interface as studied by the GISAXS technique: application of a new paracrystal model

An original diffraction model for the analysis of grazing-incidence small-angle X-ray scattering (GISAXS) from the nanoparticle Langmuir films was developed. This model relies on the concept of the 2D hexagonal paracrystal and employs the distorted-wave Born approximation that is relevant for GISAXS measurements at the air/water interface when the angle of incidence is close to the critical value. The model comprises the cases of the close-packed nanoparticle monolayer and bilayer with the AB-type layer stacking. In this way, both the lateral (along the interface) and vertical (normal to the interface) correlations of the nanoparticle positions can be analyzed. The model was applied to an in situ GISAXS study of the formation of a silver nanoparticle Langmuir film during compression at the air/water interface in the Langmuir-Blodgett trough. Spherical nanoparticles of 5.8 ± 0.6 nm diameter were employed. Different compression stages starting from the submonolayer up to the monolayer collapse via bilayer formation were analyzed in terms of the mean lateral interparticle distance, degree of paracrystal disorder, interlayer distance, vertical disorder, and layer-stacking type in the bilayer as well as the ratio between the monolayer and bilayer coverage in the final film. The model developed is applicable to any nanoparticle Langmuir film formed at the air/liquid interface to extract structural parameters on the nanoscale. The particular results obtained have direct implications on the preparation of silver plasmonic templates with "hot spots" for surface-enhanced Raman scattering.     

Distorted-wave Born approximation calculations of (e, 2e) reactions

The distorted-wave Born approximation (DW-BA) is discussed and samples of calculations are presented for ionization of the 2p inner shell of Ar, the 5p, 5s and 4d shells of Xe, and for ionization of He in asymmetric perpendicular plane geometry. Agreement with measurements of inner shell ionization of Ar is excellent. It is pointed out that triple differential cross sections for ionization of heavy atoms can exhibit much structure, which presents a challenge to both theory and experiment. Particular cases of 5s and 4d ionization of Xe are given as examples of situations worthy of experimental investigation. Comparison is made with very recent measurements of ionization of He in asymmetric perpendicular plane geometry. In agreement with experiment, DWBA shows at all incident energies a single main peak at φ=180°, where φ is the angle between the outgoing electrons. It is demonstrated that at high energies this peak arises from a double collison mechanism. This contrasts with energy-sharing ionization into the perpendicular plane where the double collision mechanism, dominant at high energies, gives a peak at φ=90°, and where with reducing energy this peak is replaced by one at φ=180° coming from the single collision mechanism. Suggestions are made for further experiments.     

The kernel of DWBA transition amplitude in atom–diatom reactive scattering

The kernel of the distorted-wave Born approximation (DWBA ) transition amplitude will be explored with attention to the atom–diatomic molecule reactive scattering process of A + BC → AB + C. Our study of the kernel reveals valuable intrinsic properties regarding the state-to-state reactive scattering process. In particular, such a study will help us to better understand (i) the favored geometric configuration during collision, (ii) the spatial domain of contribution to the differential and total cross sections, and (iii) the structural dependence of the kernel distribution on the mass ratio of the reactant molecule BC and the departing atom C, particularly in the case of colinear rearrangement collisions. In this study we choose the FH₂ system as an illustration.     

Coherence and correlation parameters for thed 3 Π u − (v=0,1,2,3;N=1) states of H2

We have applied the density matrix formalism and the distorted-wave approximation to calculate the Stokes parameters for thed ³ Π _u ^? (v=0,1,2,3;N=1) states of H₂ excited from the X¹ ∑ _g ⁺ (v=0,N=1) state by electron impact at the incident energies ranging from 15 to 40 eV. Our results show that these parameters are nearly independent of the vibrational quantum number of the excited states. However, the polarization of the radiation emitted by the target in the subsequent decay process increases with increasing incident energies.     

Inelastic and superelastic scattering of electrons from sodium

Recent experimental results of the NIST, Flinders and Münster groups on superelastic scattering of intermediate-energy polarized electrons from laser-excited polarized and unpolarized sodium atoms have been analyzed theoretically together with those on inelastic scattering data. Based on the Persival-Seaton hypothesis specific model-independent relations between correlation and polarization parameters measured in superelastic scattering experiments of different types have been suggested. The differential cross section as well as the parametersL _⊥,L ^S(T) _⊥, γ,r, and \(\bar S\) _A (J) for the 3²S?3² P transition in a broad range of scattering angels have been calculated within the distorted-wave approximation. Problem of constructing the e + Na optical potential is discussed.     

Thickness Determination of Ultra-Thin Films on Si Substrates by EPMA

Results from thickness determination of single-element ultra-thin (<10nm) films by electron probe microanalysis (EPMA) are presented. The studied samples were Ge, Sn, Ag and Au thin films deposited by resistive evaporation on Si substrates. The thickness of the films was controlled during evaporation by means of a quartz crystal, previously calibrated using samples with overlayers of different thicknesses (>20nm) measured by Rutherford backscatter spectrometry and optical interferometry. EPMA measurements were performed on an electron microprobe CAMECA SX-50, with incident electron energies ranging from 4keV to 20keV. Film thicknesses were derived from the measured k-ratios using the analytical programs X-Film and Layerf and the Monte Carlo simulation code Penelope. The ionization cross sections used in the simulations were calculated with the distorted-wave Born approximation. Film thicknesses obtained from the EPMA measurements using the various computational methods are compared with those measured with the quartz crystal. The maximum relative difference between results from the different techniques does not exceed 5%.