Inelastic Collision Cross Sections Research Articles

The rapid calculation of rotationally and vibrationally inelastic molecular collision cross sections

Several new approximate methods for the calculation of rotationally and vibrationally inelastic molecular collision cross sections are presented. Sample calculations have been performed in all cases and comparison made with exactly calculated cross sections. For rotationally inelastic scattering we present the Centrifugally Decoupled Exponential Distorted Wave (CDEDW) approximation. This approximation uses the same centrifugal decoupling technique as is used in the coupled states or p-helicity decoupling approximations, to reduce the number of channels which are coupled together in the differential equations of scattering theory. The simplified set of equations which results is then solved using the exponential distorted wave approximation. The method is applied to rotationally inelastic scattering in the Ar + N2 system and is shown to give highly reliable results. For processes involving simultaneous vibrational and rotational inelasticity we have developed a fast, nearly entirely analytic, method which treats the rotational inelasticity using the infinite order sudden approximation and the vibrational inelasticity using an adiabatic distorted wave approximation. Results are presented for vibrationally inelastic cross sections in the He + H2 system. For this very light system, the sudden approximation for the rotational inelasticity breaks down. We argue, however, that for heavier systems, for which exact computations are presently impossible, the approximation will be valid.

Foreign-gas-induced relaxation of RydbergSandDstates in atomic sodium

We have measured the He-, Ne-, and Ar-induced relaxation properties of the $3S\ensuremath{-}nS$ ($3S\ensuremath{-}nD$) superposition states of atomic sodium, where $n$ ranges from 5 to 20 (4 to 34). The measurements were made using the trilevel echo effect. We find that the effective collisional cross section first increases (as a function of $n$) at low $n$, and then decreases to a lower asymptotic limit at high $n$. This behavior is similar to that previously observed for the $3S\ensuremath{-}nP$ series. We also find that the difference between the collisional cross sections for $S$ and $D$ series superpositions closely approximates the inelastic collision cross sections measured elsewhere for the $d$ states. A theoretical description of the trilevel echo effect used to make the measurements is presented.

Sea Level Muon Spectrum and Muon Charge Ratio derived from CERN Results for Nucleon?Nucleus Inelastic Interactions

The sea level cosmic ray spectrum and muon charge ratio have been estimated by using the energy moments of the cross section for proton-air inelastic collisions. These energy moments have been determined by interpolation from CERN results for proton-nucleus inelastic interactions in pion production. The derived results are compared with previous work.

Electron-exciton inelastic collision cross sections for different semiconductors

The electron-exciton inelastic collision cross sections for the different semiconductors CdS, ZnO, CdSe, Si, Cu 2O, CuCl, CuBr and CuI have been calculated in the Glauber approximation. The transitions 1 s–2 s, 1 s–3 s, 1 s–2 p and 1 s–3 p have been considered. The calculations are carried out as function of the different available values of σ = m ∗ e m ∗ h where m ∗ e and m ∗ h are, respectively, the electron a corresponding semiconductors.

Electron-exciton inelastic collision cross-sections for different semiconductors

Electron-exciton inelastic collision cross-sections for different semiconductors

Angular Scattering Distribution By Doppler Spectroscopy:Na(3P12)+Ar→Na(3P32)+Ar

We have developed a new method for determining state-resolved differential cross sections in inelastic collisions. A single-frequency laser provides level-specific detection of scattered atoms, while the Doppler shift of the same laser provides a completely non-mechanical angular selectivity in the detection. We have used this technique to make the first measurement of an alkali fine-structure transfer cross section in which both the scattering angle and final state are determined.

The centrifugally decoupled exponential distorted wave (CDEDW) approximation for the calculation of rotationally inelastic molecular collision cross se

A new approximate method is presented for the rapid calculation of rotationally inelastic molecular collision cross sections. The method is called the centrifugally decoupled exponential distorted wave (CDEDW) approximation and involves the combination of two well known approximations. The first approximation is the neglect of the off-diagonal coupling terms which arise from the orbital angular momentum operator in the coupled differential equations in the body-fixed axis system. The second approximation is to treat the remaining coupling terms, which arise from the interaction potential, using a unitary perturbation approximation. The CDEDW method is applied to the calculation of total and partial rotationally inelastic cross sections in the ArN 2 system, and detailed comparisons are made with exact and several other types of approximate calculations. Agreement with exact calculations is good and often comparable with the coupled states and p-helicity decoupled approximations. The CDEDW method requires a similar amount of computational effort to the infinite order sudden (IOS) approximation, and we show that for the present system the CDEDW method gives more reliable results.

Rotational relaxation of homonuclear diatomic molecules by classical trajectory computation

The rotational relaxation times of molecular nitrogen and molecular chlorine have been obtained using an exact classical mechanical calculation and Wang Chang—Uhlenbeck's theory of polyatomic gases. The intermolecular potential used was an extended Lennard-Jones potential of the form V( R, X1, X2) = C 12 R −12 1+ b [ P 2(cos X1)+ P 2(cos X2)]- C 6 R −6 1+ a[ P 2(cos X1) + P 2(cos X2)]. Numerical results were obtained for a number ef values of the anisotropy parameters ( a, b) for nitrogen and for a single set of values for chlorine. Comparison with experimental ultrasonic results for nitrogen gave very good agreement for ( a, b) around (0.1, 0.7). Using a box-quantization procedure we have furthermore obtained detailed cross sections for inelastic collisions from which a surprisal analysis was carried out. The analysis showed that our results follow the exponential gap law of Polanyi, Ding and Woodall reasonably well although this law was suggested for atom—diatom collisions.

Analytic approximations to distorted wave integrals, for inelastic molecular collision cross sections

Several methods-for approximating distorted wave integrals using analytic formulae are presented and compared. The various methods are applied to the calculation of rotationally and vibrationally inelastic HeH 2 collisions and the resulting integrals compared with their exact counterparts. Some of the methods involve the use of the modified wave number approximation. This approximation is shown to break down seriously at large values of the orbital angular momentum. A further important point which is demonstrated is the importance of the region around the outer classical turning point of the two channels involved in the calculation. Among all the methods examined, a recently proposed one based on a generalisation of the well-known Mies formula is found to be the most reliable. A slightly improved version of this method is also developed and tested. Comparison of this improved method with exact calculations establishes its reliability over a large range of energies and total angular momentum quantum numbers.

Laser fluorescence studies of molecular iodine

We have studied quantitatively the circular polarization of rotationally resolved features in the laser-induced fluorescence from I2 excited by the 5145 A argon laser line, and its variation with various experimental parameters such as light intensity, iodine and foreign gas pressure. Optical pumping of the ν″ = 0, J″ = 13 level of 1Σ g + has been unambiguously demonstrated and the variation of C with gas pressure has been analysed to yield cross sections for elastic and inelastic collisions which relax the oriented ground state. Experiments on the dipolar array of oriented 3Π0u + molecules at very high pressures show that the circular polarization ratio does not change under conditions of many gas kinetic collisions per lifetime. This indicates that a selection rule ΔM = 0 operates on elastic collisions of I2* with other atoms and molecules, which appears to be rigorously adhered to.

On the general form of the cross section of deep inelastic collisions

The general form of the energy-averaged “macroscopic” cross section for deep inelastic (DI) collisions is derived on the basis of semiclassical approximations. The amplitude for DI reactions is related to the incompletely relaxed part of the fluctuating S-matrix. The possibility of diffraction effects modifying the DI cross section is investigated. In the limit of a classical treatment of the external variables, the average DI cross section is shown to be uniquely determined by a classical distribution function.

Determination of state resolved rotationally inelastic cross sections: LiH(j=1) –Ar

Laser induced fluorescence is used to determine rotationally inelastic relative integral cross sections for collisions of state-selected Litt with Ar.(AIP)

Novel computer simulation of electron swarm motion

A novel computer simulation technique for the study of properties of electron swarms in gases is presented. As an example, the method is applied to nitrogen at E/N values of 10−16–10−15 V cm2. A strong directional anisotropy in the electron velocity distribution function is observed. The anisotropy is especially strong at electron energies for which the inelastic collision cross section is large relative to the total collision cross section. The first asymmetric term in the expansion of the distribution function in spherical harmonics can be as high as 70% of the value of the symmetric part of the distribution. A comparison with the computer simulation shows, however, that in spite of such strong anisotropy in nitrogen at these values of E/N, the solution of the Boltzmann equation based on the first two terms of the spherical harmonic expansion, gives correct values of electron drift velocity, average electron energy, and average vibrational excitation frequency.

On the general form of the cross section of deep inelastic collisions: Klaus Dietrich. Physik-department of the Technische Universität München, 8046 Garching, James Franck Strasse, München, Germany; and Christiane Leclercq-Willain. Université Libre de Bruxelles, Physique théorique et mathématique, B-1050 Bruxelles, Boulevard du Triomphe

On the general form of the cross section of deep inelastic collisions: Klaus Dietrich. Physik-department of the Technische Universität München, 8046 Garching, James Franck Strasse, München, Germany; and Christiane Leclercq-Willain. Université Libre de Bruxelles, Physique théorique et mathématique, B-1050 Bruxelles, Boulevard du Triomphe

The distorted wave infinite order sudden (DWIOS) approximation for the calculation of vibrationally inelastic molecular collision cross sections

An approximate method is presented for the rapid calculation of rotationally—vibrationally inelastic molecular collision cross sections. The method, called the distorted wave infinite order sudden (DWIOS) approximation, treats the coupling between rotational states associated with a given vibrational level using the infinite order sudden approximation. Transitions between the different vibrational manifolds are treated using a generalised form of the distorted wave approximation. The method is a further development of one recently proposed by Gerber. Its most important new feature is that it yields a symmetric T matrix. In applying the method further approximations are made so as to reduce the formulae for the T matrix elements to an almost entirely analytic form, and an analytic expression for a new type of distorted wave integral is developed and presented in the paper. This expression is a generalisation of the well known Mies formula. The DWIOS method is applied to the calculation of rotationally—vibrationally inelastic HcH 2 cross sections, and comparisons are made with exact and other approximate calculations. Despite the fact that this system is one to which the sudden approximation is poorly suited, good agreement — often within 20% — is obtained over a wide energy range. Over a more limited energy range the method yields better agreement with the “exact” close-coupling results than does the coupled states approximation.

Effect of partial wave parameter identification on IOS opacities and integral cross sections for rotationally inelastic collisions

The effect of identification of the partial wave parameter of the Jz CCS and IOS approximations as an orbital angular momentum rather than the total angular momentum is studied. Comparison with accurate close coupling calculations for Ar–N2 and He–CO2 collisions is made, and it is found that this identification results in a marked improvement, both quantitative and qualitative, in calculated IOS opacity functions and integral cross sections for both elastic and inelastic collisions. Use of the correct energy in the cross section formula also makes a marked improvement even though T matrices are computed with an average energy.

Monte Carlo Simulation of Electron Swarms in H2

A Monte Carlo simulation of the motio'n of an electron swarm in molecular hydrogen has been studied in the range E/N = 1,4-170 Td. The simulation was performed for 400-600 electrons at several values of E/N for two different sets of inelastic collision cross sections at high E/N. ,Results were obtained for the longitudinal diffusion coefficient DL , lateral diffusion coefficient D, swarm drift velocity W, average swarm energy <Ii) and ionization and excitation production coefficients, and these were compared with experimental data where available. It is found that the results differ significantly from the experimental values and this is attributed to the isotropic scattering model used in this work. However, the results lend support to the experimental technique used recently by Blevin et al. to determine these transport parameters, and in particular confirm their results that DL > D at high values of E/N.

Rotational relaxation in HD–inert gas mixtures

An expression for the inelastic collision cross section σ (lm→l′m′) has been derived for the rotational transition in the HD molecule caused by a collision with an inert gas atom. The interaction potentials for the HD systems have been derived from the theoretical potentials for the H2 systems by shifting the center of mass of the molecule. The rotational relaxation number values have been calculated for HD–He, HD–Ne, and HD–Ar systems in the temperature range from 10 to 100 °K. A good agreement has been obtained between theory and experiment. Temperature dependence and the effect of replacement of an isotope in a homonuclear molecule have been discussed in detail.

Cross sections for rotational energy transfer: An information-theoretic synthesis

State-to-state cross sections are readily computed by combining the capabilities of the classical trajectories method with an information-theoretic (’’surprisal’’) synthesis. The method is illustrated by an application to rotational energy transfer in several systems, (Ar+N2, Li++H2, Li++D2, H+CO). It is shown that by using classical trajectories to compute a single moment of the distribution of final rotational energy (for a given initial rotational energy) and then maximizing the entropy of the distribution subject to the given value of the moment one can obtain a good prediction of the distribution. Invoking microscopic reversibility, the entire matrix of state-to-state, σ (j→j′), rotational energy transfer cross sections (at the given total energy) is then determined. More averaged quantities, such as the cross sections for inelastic collisions σ (j), are thereby easily obtained. When a realistic potential energy surface is not available or when one requires a simple but reliable prediction, the synthesis can be based on invoking a sum rule. Here the moment of the distribution is not computed via classical trajectories but is expressed as a simple function of the initial conditions. It is shown that available cross sections often satisfy the simplest possible sum rule and hence a synthesis can be readily carried out where the only inputs are the total energy and the rotational constant of the diatomic molecule. The distribution of final rotational states predicted in this way is independent of the nature of the collision partner. The method is illustrated by applications to H+CO, Ar+N2, Li++H2, He+HD, H+H2, and H+D2. Results for the distribution of final rotational state and the dependence of the cross section on the initial rotational state and on the collision energy are in very good accord with classical trajectory and with quantal close-coupling computations.

Shapes of Optical Emission Lines from Atoms Excited by Fast Ion Impact: I. Calculated Profiles

After an inelastic collision between a neutral gas atom and a fast ion incident in a beam the excited gas atom emits radiation. The emitting gas atom has a variety of line-of-sight velocities relative to some fixed observer. This is a consequence of the kinematics of the collision and the angular dependence of the collision cross section. An expression for the intensity as a function of the frequency of the radiation is derived and then synthetic profiles for several viewing angles are obtained through numerical integration of this expression. Then the utility of the line profile as a means of determining the angular dependence of the inelastic collision cross section is examined.