Cross Sections For Rotational Transitions Research Articles

Cross sections for rotationally inelastic scattering of formaldehyde. III. Differential measurements on D2CO–H2 scattering

Differential cross sections for rotational transitions in D2CO induced by collisions with H2 are measured at a collision energy of 17 meV. The 110 state of D2CO is prepared with high state purity by a combination of rotational cooling in a seeded beam expansion and electrostatic state selection. The final state after scattering is probed as a function of the scattering angle by laser-induced fluorescence detection with excitation at 325 nm. The first results with the final states 110, 111, 211, and 212 are presented. The differential cross section for the ΔJ=1 transition 110→211 displays a relatively large contribution at large angles compared to the cross sections for the other transitions.

Rotational rainbows in electron-molecule scattering: theory

The authors report numerical computations of differential cross sections for rotational transitions in electron-Na2 scattering at collisional energies between 25 and 300 eV. In addition a simple spectator model is proposed, which leads to a closed-form expression for the rotational transition probabilities. The model is found to be in excellent agreement with numerical computations. All results reproduce recent experimental measurements of rotational-rainbow structures for backward scattering.

Rotational rainbow scattering with large Δ j: Energy dependence of the anisotropy of the Na2–Ne, Ar interaction potential

Differential cross sections for rotational transitions in Na2–Ne, Ar collisions are measured up to very large Δj. It is shown that the energy dependent anisotropy ΔR(E) of the interaction potential can be determined from these data using simple classical relations of ΔR and the rainbow angle θR. Excellent agreement with ab initio data is demonstrated and underlines the usefulness of this concept.

Cross sections for rotational/vibrational transitions in HF-HF collisions: effect of initial state

Recent semiclassical calculations of cross sections for vibrational and rotational transitions in HF + HF collisions have been extended by considering the effect of changing the initial state, resonance rotational excitation and by increasing the basis set expansion to a 157- and 249-state “dynamical” basis.

Photoionisation of the H2molecule

The total and differential cross sections for individual rotational and vibrational transitions in the photoionisation of the H2 molecule by 584 AA radiation are calculated in the static-exchange approximation with the addition of the adiabatic dipole polarisation potential. Further, it is demonstrated that the measurement of the relative intensities of the Q and S rotational branches for the transition to the nu 'th vibrational state of H2+ at two angles determine the vibrationally resolved asymmetry parameter beta nu '. The value of beta nu ', obtained from the data of Ruf et al (1983), is 1.87 for nu '=0, and agrees with the calculated value 1.89.

Scattering of slow electrons by molecules

This review presents the current advances in the theory of collision of slow electrons with molecules. First the fundamental experimental results are reviewed. Then main attention is paid to the semiphenomenological and modeling approaches to the problem. The adiabatic approximation and its application to calculating elastic scattering cross-sections and cross-sections for rotational transitions are treated. The long-wavelength approximation (effective-range theory) is presented in greater detail. The problem is discussed of taking account of rotation in the collision process. In particular, a mechanism is revealed of formation of dipole resonances in the scattering of an electron by a rotating polar molecule. Different semiphenomenological methods are treated for calculating the resonance vibrational excitation of simple molecules. The quasiclassical representation for the cross-sections for vibrational transitions in the theory of Herzenberg is discussed. This representation is applied to analyze the process of dissociative recombination. The model is treated of emergence of a term into the continuous spectrum and it is applied to explain the threshold resonances in the vibrational excitation cross-sections of certain molecules. The role is discussed of dipole interaction in forming these resonances. The results of the theoretical calculations are compared with the experimental data.

A frequency-corrected sudden approximation for rotationally inelastic collisions between polar molecules

An approximate theory is presented which allows cross sections for rotational transitions in collisions between polar molecules to be estimated. The theory converges to the time-dependent sudden approximation and to the first-order perturbation theory in the appropriate limits; it can be regarded as an approximate form of strong-coupling correspondence principle approximation. Unlike previous theories which have attempted to correct the sudden approximation for adiabatic effects, it treats rotational transitions of 'resonant' and 'non-resonant' type consistently. Its predictions are compared with close-coupling results for the system HF-HF.

The modified connection formulae for the rotational transition cross sections in diatomic molecules for slow collisions

The formulae connecting the cross sections (or the rate constants) for various rotational transitions in diatomic molecules colliding with atomic particles were discussed in the authors' earlier paper (1981) and are valid in the framework of the sudden approximation. In order to extend the applicability domain of these formulae to the slow-collision region a semi-empirical correction factor is introduced with an exponential dependence on the translation-rotation energy transfer and on the inverse collision velocity (or the inverse square root of the temperature). The modified connection formulae are applied to the rotational transitions in an HD molecule colliding with an H2 molecule. The parameters entering the connection formulae are fitted to the effective potential calculations of Chu (1975). Another application based on the experimental data of Sudbo and Loy (1982) is made for NO-NO collisions where both the rotational and electronic spin-orbit states of the molecule are changed.

Beam maser investigation of inelastic scattering of NH3. III. Cross sections for rotational transitions induced by CO2, N2, and H2

Cross sections for rotational transitions between various low-lying inversion doublets of NH3 in collisions with CO2, N2, and H2 are measured in a double-resonance beam maser setup. A modification of Anderson’s theory [D. B. M. Klaassen, J. J. ter Meulen, and A. Dymanus, J. Chem. Phys. 77, 4972 (1982)] yields values for the cross sections that are in good agreement with the experimental results for CO2 and N2. For the system NH3–H2, transition probabilities are evaluated in Anderson’s theory using ‘‘bent’’ trajectories. Induction and dispersion terms up to R−7 are considered in the long-range intermolecular potential. For the short-range repulsive part, two empirical potentials are proposed with parameters that are fitted to the experimental results. Integral cross sections for rotational transitions calculated with these potentials are also presented.

Vibrationally elastic scattering of electrons by HCl

Results of close-coupling calculations are reported, in which several models of the interaction potential are investigated. Cross sections for rotational transitions involving the lowest ten levels are obtained in the first detailed application of the MEAN approximation. The results are subject to a strong cooperative effect involving exchange and polarization. Rotationally elastic transitions are shown to be quite important at thermal energies and to dominate the total cross section above 4.0 eV. Transitions for which the angular momentum changes by two are found to be responsible for a broad resonance at \ensuremath{\sim} 2.5 eV. No structure indicative of a resonance or virtual state at very low energies is, however, obtained. Total differential, momentum-transfer, and integrated cross sections are in satisfactory agreement with measured values.

Low-energy electron scattering from CO. III. Analytic method for outer region in frame-transformation theory

For pt.III see Phys. Rev. A, vol.16, p.80-108 (1977). A non-perturbative approximation, suitable for electron scattering from both weakly and strongly polar molecular, has been proposed. The coupling in the scattering equations due to the presence of the non-central electron-dipole interaction is removed by merely shifting the relative positions of the rotational levels but without either making them degenerate or neglecting their energies. This method has been used to simplify application of the frame-transformation theory (FT) to electron scattering from polar systems. The problem in the outer region of the FT can now be solved without numerical integration and the solution written in a form suited for an R-matrix treatment of the molecular core. The proposed procedure achieves very high level of efficiency and economy of calculation without much sacrifice of accuracy. This method has been applied to electron scattering from weakly polar carbon monoxide. The integrated cross sections for various rotational transitions have been calculated from 0.005 to 10.0 eV and compared with previously obtained accurate results. The usefulness of this method for electron scattering from strongly polar neutral and ionic systems has been discussed.

Beam maser investigation of inelastic scattering of NH3. II. Cross sections for rotational transitions induced by polar gases

A molecular beam maser is used in a double-resonance scheme to measure cross sections for rotational transitions between levels of different inversion doublets of NH3 induced by collisions with NH3, CH3F, and CF3H. Theoretical values, calculated with a modification of Anderson’s theory, are in good agreement with present experimental results and steady-state double-resonance experiments of Oka [J. Chem. Phys. 48, 4919 (1968)].

The K-shell ionisation of90Th by protons and alpha particles

The cross sections have been measured for K-shell ionisation of 90Th by 1.2-6.0 MeV protons and 2.5-16 MeV alpha particles. The results are derived from comparisons with well known Coulomb excitation cross sections for nuclear rotational transitions. The measured cross sections for protons are in good agreement with the predictions of both the SCA and PWBA models provided both models are supplemented by the same Coulomb deflection, binding and relativistic corrections. The cross sections measured for alpha particles are on the average 30% higher than predicted by the two models mentioned above.

The connections between the rotational transition cross sections in diatomic molecules

The collisions of diatomic (or linear) molecules with atomic particles are considered in the adiabatic (or infinite order sudden) approximation. All rotational transition cross sections are expressed via a small number of independent parameters in the general case when the collision is also accompanied by the electronic-vibrational transition in the molecule. In the simplest cases, the parameters are the cross sections of various transitions from the initial ground rotational state. Various angular momenta coupling schemes are considered in the initial and final electronic states of the molecule. The rotational transitions in bimolecular collisions are also discussed. The rotational transition cross sections in the homonuclear diatom with one nucleus substituted by its isotope are expressed in terms of the cross sections in the homonuclear molecule. The connections between the cross sections are similar to the expressions for radiational transition intensities since they do not depend on the interaction potential of the colliding partners. Due to their generality and simplicity the cross section connections will be useful in various problems of molecular collision physics and its applications.

Rotational distribution of N2 in Ar free jet

The rotational distribution, temperature, and collision number of N2 in the Ar free jet are studied using the rotational transition cross sections of the exponential gap and power laws. The relaxation of the rotational distribution along the axis of the free jet is described by the master equation, where the velocity distribution is taken as the local Maxwell distribution. The effects of the stagnation density level n0d and temperature T0 are investigated. The rotational distribution indicates a non-Boltzmann distribution with overpopulation at the higher rotational levels. The degree of deviation from the Boltzmann distribution at the same axial distance increases with decreasing n0d and decreases with increasing T0. The rotational temperature ratio Tr/T0 depends weakly on T0, which is consistent with the experimental result of Poulsen and Miller in the N2-Ar system. The rotational collision number Zr is neither constant nor a monotonically increasing function of the translational temperature; still, the downstream Zr depends weakly on n0d and T0 consistent with the experimental result of Poulsen and Miller and is in quantitative agreement with their N2-Ar value of 2±1.

On a close correspondence between inversion methods for atom–molecule and symmetric exchange scattering

The similarity between Gerber, Buck and Bucks1 method for obtaining atom-diatom anisotropy potential from differential cross sections for rotational transitions and the authors12 symmetric exchange systems is commented upon. (AIP).

Rotational distribution of N2 in Ar shock wave

The rotational distribution of N2 in the Ar shock wave is quantitatively studied using the rotational transition cross sections of the exponential gap and power laws. The relaxation of the rotational distribution in the shock wave is described by the master equation, where the velocity distributions are taken as the local Maxwell distribution at a low Mach number and the Mott–Smith bimodal distribution at a high Mach number. The rotational distribution indicates a near Boltzmann distribution at a low Mach number. At a high Mach number a merging pattern of the Boltzmann distributions at the lower and higher rotational levels corresponding to temperatures before and after the shock wave, respectively, is obtained at the fore part of the shock wave, where the rapid increase in the populations of the higher levels is caused by the accumulation of the fluxes from the lower levels. The merging pattern is well established by the existence of hot molecules in the Mott–Smith bimodal velocity distribution. The rotational temperature profile precedes the density profile both at low and high Mach numbers. The fact that the pattern of the rotational distribution in the N2–Ar system is in qualitative agreement with the measured pattern in the pure N2 system may indicate that the rotation–rotation transition does not play an important role in the pattern of the rotational distribution of N2 in the shock wave.

State-to-state rotational transition cross sections from unresolved energy-loss spectra

In energy-loss spectra of electrons or ions scattered by molecules, rotational lines are usually unresolved except for a few lightest molecules. It is shown how to analyze unresolved profiles, under the adiabatic-rotation approximation, to obtain state-to-state cross sections for rotational transitions from any initial rotational state including the ground state.

State-to-state differential cross sections for rotationally inelastic scattering of Na2 by He

State-to-state differential cross sections for rotational transitions of Na2 in collisions with He are measured in the electronic and vibrational ground state at thermal collision energies using a new laser technique. Single rotational levels ji are labelled by modulation of their population via laser optical pumping using a dye laser. The modulation of the fluorescence induced by an Ar+ laser tuned to the level jf=28 is proportional to the cross section for collisional transfer ji→jf and is detected at the scattering angle ϑ. A single optical fiber and a fiber bundle provide a flexible connection between the detector and the laser and photomultiplier, respectively. Transitions as large as Δj=20 are observed. At small angles elastic scattering is dominant, but rotationally inelastic processes become increasingly important at larger scattering angles. Rotational rainbow structure causing a steep onset of the cross section with the scattering angle ϑ (at fixed Δj) or a sharp cutoff with Δj (at fixed ϑ) is found. Preliminary results on rotational energy transfer in v=1 indicates that vibrational motion of the molecule favors larger rotational quantum jumps. semiclassical picture for the scattering of a hard ellipsoid gives a

State-to-state differential cross sections for rotational transitions in Na2+He collisions

Laser induced fluorescence was used to study the rotational energy transfer for elastic and inelastic Na2-He collisions. (AIP)