Quantum Mechanical Differential Cross Sections Research Articles

Low-energy scattering of ultracold atoms by a dielectric nanosphere

We theoretically study the low-energy scattering of ultracold atoms by a dielectric nanosphere of silica glass levitated in a vacuum. The atom and dielectric surface interact via dispersion force of which strength sensitively depends on the polarizability, dielectric function, and geometry. For cesium and rubidium atoms, respectively, we compute the atom-surface interaction strength and characterize the stationary scattering states by taking adsorption of the atoms onto the surface into account. As the energy of the incoming atoms is lowered, we find that differences between quantum and classical scatterings emerge in two steps. First, the quantum-mechanical differential cross section of the elastic scattering starts to deviate from the classical one at an energy scale comparable to a few microkelvin in units of temperature due to the de Broglie matter-wave diffraction. Second, the differences are found in the cross sections in a regime lower than a few nanokelvin, where the classically forbidden reflection occurs associated with the $s$-wave scattering and the discrete nature of angular momentum. We also study the dependencies of quantum and classical scattering properties on the radius of the nanosphere. This paper paves the way to identify the quantum regime and to understand the physical origin of quantum effects in the collisions between a nanoparticle and environmental gas over various temperatures.

Multiple scattering mechanisms causing interference effects in the differential cross sections of H + D2 → HD(v' = 4, j') + D at 3.26 eV collision energy.

Differential cross sections (DCSs) for the H + D2 → HD(v' = 4, j') + D reaction at 3.26 eV collision energy have been measured using the photoloc technique, and the results have been compared with those from quantum and quasiclassical scattering calculations. The quantum mechanical DCSs are in good overall agreement with the experimental measurements. In common with previous results at 1.97 eV, clear interference patterns which appear as fingerlike structures have been found at 3.26 eV but in this case for vibrational states as high as v' = 4. The oscillatory structure is prominent for low rotational states and progressively disappears as j' increases. A detailed analysis, similar to that carried out at 1.97 eV, shows that the origin of these structures could be traced to interferences between well defined classical mechanisms. In addition, at this energy, we do not observe the anomalous positive j'-θ trend found for the v' = 4 manifold at lower collision energies, thus reinforcing our explanation that the anomalous distribution for HD(v' = 4, j') at 1.97 eV only takes place for those states associated with low product recoil energies.

Energy and shape relaxation in binary atomic systems with realistic quantum cross sections

We use the spatially homogeneous linear Boltzmann equation to study the time evolution of an initial non-equilibrium distribution function of an ensemble of test particles dilutely dispersed in a background gas at thermal equilibrium. The systems considered are energetic N in He and Xe in He. We employ the quantum mechanical differential cross section to define the collision operator in the Boltzmann equation. The Boltzmann equation is solved with a moment method based on the expansion of the distribution function in the Sonine (Laguerre) polynomials as well as with a direct simulation Monte Carlo method. The moment method provides the approximate eigenvalues and eigenfunctions of the linear Boltzmann collision operator. The reciprocal of the eigenvalues is a measure of the relaxation times to equilibrium. For hard sphere cross sections, the relaxation of the average energy and the shape of the distribution function can be characterized by a single time scale determined by the momentum transfer cross section. We show that this is also the case for realistic quantum cross sections with dominant small angle scattering contributions.

Inelastic Scattering of He Atoms and NO(X2Π) Molecules: The Role of Parity on the Differential Cross Section

Quasiclassical trajectory (QCT) and quantum mechanical (QM) close-coupling calculations have been used to study the state-resolved rotationally inelastic scattering of NO(X(2)Pi(1/2),v = 0,j = 1/2,e/f) by He on the most recent ab initio potential energy surface of J. Kłos et al. [J. Chem. Phys. 2000, 112, 2195.]. Opacity functions, and integral and differential cross sections are reported at collision energies of 63 and 147 meV and compared with previous theoretical calculations and experimental measurements on this and other systems. The existence of double peaks in the QCT and QM differential cross sections is examined in detail. While at a collision energy of 147 meV two rotational peaks appear in both the QCT and open-shell QM results, only a single peak is found in the QM calculations at the lower collision energy. The double peaks in the quantum-state-resolved differential cross sections (DCS) are found to be closely related to structure found in the corresponding state-resolved opacity functions. The structure in the QCT and QM DCSs is attributed to a flattening of the potential energy surface for sideways approach of He to the near-symmetric NO(X) molecule, and in both sets of calculations, it is shown to arise from a specific odd term in the expansion of the intermolecular potential. Although significant differences are found between the QCT and QM data in the forward scattered direction, and for higher final rotational levels, reflecting differences in the nature of the rotational rainbows observed in these two methods, in general, the QCT calculations are shown to give similar results to quantum theory. Furthermore, they provide valuable clues as to the mechanism of rotational energy transfer in this system.

On the theory of complex-forming chemical reactions: effect of parity conservation on the polarization of differential cross sections

For complex-forming triatomic reactions such as the prototypical insertion reactions intensively studied in the last few years, quantum mechanical differential cross sections (DCS) present sharp forward/backward polarization peaks when the reagent rotational angular momentum quantum number j is zero. Moreover, the size of the peaks decreases rapidly with increasing j values so that for j = 3, they are no longer visible. In contrast, the polarization peaks are always missing in the classical mechanical DCSs. Apart from the peaks, however, the quantum and classical DCSs are usually in good agreement. In a recent rapid communication, we showed that the fundamental reason for the previous differences in the quantum and classical scenarios is that parity conservation leads in quantum mechanics to an angular momentum constraint without equivalent in classical mechanics. We also proposed a parity-restoring approximation leading to an accurate semi-classical description of the peaks. While only the main lines of the demonstration were given in the communication, we report here the whole developments. We also analyse why the peaks disappear when the reagent diatom is rotationally excited. As a by-product of the previous developments, we finally discuss the possibility of a general statistico-dynamical semiclassical approach.

A rigorous test of the statistical model for atom–diatom insertion reactions

The statistical model of atom–diatom insertion reactions is combined with coupled-channel capture theory and used to calculate differential cross sections for the reactions of C(1D), N(2D), O(1D) and S(1D) with H2. In the case of C(1D) and S(1D), the resulting statistical differential cross sections are found to be in excellent agreement with the recent quantum reactive scattering calculations of Honvault and Launay. They are therefore also in good agreement with molecular beam experiments for the S(1D)+H2 reaction, in contrast to the results of earlier calculations based on a less rigorous statistical theory. However, because the exact quantum mechanical differential cross sections for N(2D) and O(1D) exhibit a slight forward–backward asymmetry, the agreement with the statistical model for these reactions is not quite so good. The difference between the two cases can be rationalized in terms of the greater exoergicities of the N(2D) and O(1D) reactions, which lead to broader resonances and hence to shorter lifetimes of the H2O and NH2 collision complexes than those of CH2 and H2S.

Approximate quantum differential cross section for the atomic fluorine + hydrogen deuteride .fwdarw. hydrogen fluoride + atomic deuterium and deuterium fluoride + atomic hydrogen reactions

In a previous paper we proposed a novel way to obtain approximate quantum mechanical differential cross sections. Here, we use this approximate method to study the reactions F + HD(nu = 0) ..-->.. FH(nu' = 2) + D and F + DH(nu = 0) ..-->.. DF(nu' = 3) + H. Backward and forward scattering are found for the first reaction and only backward scattering for the second one. These results agree qualitatively with experiment. 1 figure.

Complex-valued trajectories in semiclassical potential scattering

The semiclassical theory of potential scattering leads naturally to an inclusion of complex-value classical paths which describe classically forbidden processes. However, only a few of the existing complex trajectories contribute. The authors discuss which of these forbidden paths should be retained and a detailed investigation of the complex contributions is given for the special class of repulsive inverse-power potentials. The oscillatory structure of the quantum-mechanical differential cross section is resolved as an interference pattern of classically allowed and forbidden trajectories. The region of validity of the complex-trajectory approximation is investigated. For potentials with a minimum the forbidden trajectories contribute to scattering angles larger than the rainbow angle. This is demonstrated for a superposition of inverse-power potentials.