Scattering of low-energy electrons and positrons by atomic beryllium: Ramsauer-Townsend effect

Total cross sections for the scattering of low-energy electrons and positrons by atomic beryllium in the energy range below the first inelastic thresholds are calculated. A Ramsauer-Townsend minimum is seen in the electron scattering cross sections, while no such effect is found in the case of positron scattering. A minimum total cross section of 0.016 a.u. at 0.0029 eV is observed for the electron case. In the limit of zero energy, the cross sections yield a scattering length of -0.61 a.u. for electron and +13.8 a.u. for positron scattering

Dissociative attachment to rovibrationally excited H2

Using a local-width resonant model, the cross sections for dissociative attachment of low-energy electrons to a rovibrationally excited H_2 molecule in its ground electronic state are obtained. There are 294 such rovibrational levels. Only the contribution of the ^2Σ_u^+ resonant state of H^−_2 to the attachment process is investigated. Assuming a Maxwellian distribution for electron energies, the dissociative attachment cross sections are converted into attachment rates for various rovibrational levels of H_2. A significant enhancement of attachment rates occurs for endoergic reactions only, and the maximum possible rate for attachment to the ground electronic state of H_2 is about 10^(−8) cm^3/sec. Using the same energy distribution for electrons, the average energy carried by the H^− ions is calculated for all possible rovibrational levels. More energetic ions are formed when the attachment process is exoergic, and even the most energetic H^− ions have energies less than 0.5 eV. Furthermore, the attachment rates and the average ion energy appear to depend roughly on the total internal energy and not on the exact fraction of internal energy in rotational or vibrational modes

Rovibrationally enhanced dissociative electron attachment to molecular lithium

We have investigated the role played by initial rovibrational excitation of Li_2 on the cross sections and rates for dissociative electron attachment to the molecule. For a given internal energy, the vibrational excitation enhances the attachment cross section more than the rotational excitation. The attachment cross sections and the attachment rates reach their maximum values when the process of dissociative attachment to rovibrationally excited molecules is still endoergic and, furthermore, these quantities stay close to their maximum values even when the process changes from being endoergic to exoergic. The upper bounds on the cross sections and the rates for dissociative electron attachment to Li_2 are 12.8 A^2 and 1.25×10^(−8) cm^3 s^(−1). At a fixed electron temperature, the kinetic energy of the negative ion formed by this process increases as the vibrational quantum number of the initial neutral molecule increases; the maximum kinetic energy of the Li− ion formed by attachment to the v=12 level of Li_2 is 0.153 eV

Low-energy collisions of D+ with D and He++ with He

Quantum-mechanical calculations for differential cross sections and various transport cross sections describing the thermal-energy collisions of D+ with D and He2+ with He are presented. Lowest-order Viehland-Mason theory is used to calculate mobility of D+ in D. The zero-field mobility at 77, 303, and 10000 K is, in units of cm2V−1s−1, 10.5, 7.0, and 2.1, respectively

Rates of dissociative attachment of electrons to excited H2 and D2

Calculations are reported of the contributions of the lowest 2Σ+ u and 2Σ+ g resonant states to the rates of dissociative attachment of electrons to H2 and D2. For all electron temperatures, the rate is significantly enhanced by vibrational and rotational excitation of the initial molecule. Typically, for an electron temperature of 1.5 eV, the attachment rates for various (v, J) levels are, in cm3 sec−1, 5.4×10−15 for (0,0), 7.2×10−11 for (0,20), and 7.8×10−9 for (8,0), for H2; and 4.5×10−17 for (0,0), 1.4×10−14 for (0,20), and 6.0×10−9 for (11,0), for D2

Elastic scattering of protons from hydrogen atoms at energies 15-200keV

Differential and integrated cross sections for the elastic process H^+ + H(1s) → H^+ + H(1s) were calculated with the use of results of coupled-state calculations in the energy range 15-200 keV. Results are presented and, at 60 keV, compared favorably with preliminary experimental data. The asymptotic form of the elastic amplitude for b≫a_0 (where b is the impact parameter) is derived for the two cases λ≪1 and λ≫1, where λ is the ratio of the collision duration to the orbital period. The asymptotic form for λ≫1 provides a useful test on the numerical accuracy of the amplitudes

Simple model for the resonant vibrational excitation of molecules and its application to Li2 and N2

A simple model for the resonant vibrational excitation of a molecule by electron impact is proposed in which the potential curves of the electronic states of the molecule and its resonant anion are replaced by those of linear harmonic oscillators of arbitrary frequencies and equilibrium internuclear separations. A closed-form expression for the excitation amplitude is derived. Useful recursion relations among amplitudes are obtained which allow convenient evaluation of cross sections for any inelastic or superelastic vibrational transition. The model is used to generate the cross sections for vibrational excitation of Li_2 and N_2 by the impact of low-energy electrons

Large momentum transfer limit of some matrix elements

The matrix element εfi(K), or ε, that appears in the study of elastic and inelastic electron-atom scattering from an initial state i to a final state f in the first Born approximation depends explicitly on the momentum transfer ℏK⃗ . The uncertainty in the value of the calculated cross sections arises not only from the application of the Born approximation but also from the approximate nature of the wave functions used. For the 1 S1−2 P1 transition in helium, we present an analytic expression in terms of the 1 S1 and 2 P1 wave functions for the leading coefficient C1 in the asymptotic expansion of ε as a power series in 1K; C1 is defined by ε∼C1K5 as K∼∞. An accurate numerical value of C1 is obtained by using a sequence of better and better 1 S1 and 2 P1 wave functions. An accurate value of C1 can be useful in obtaining an approximate analytic form for the matrix element. We also present analytic expressions, in terms of the 1 S1 wave function, for the coefficients of the two leading terms of ε for the diagonal case, that is, for the atomic form factor, and we obtain accurate estimates of those coefficients. The procedure is easily generalizable to other matrix elements of helium, but it would be difficult in practice to apply the procedure to matrix elements of other atoms. We also give a very simple approximate result, valid for a number of matrix elements of heavy atoms, for the ratios of the coefficients of successive terms (in the asymptotically high-K domain) in a power series in 1K. Finally, we plot ε for 1 S1 to 1 S1 and for 1 S1 to 2 P1, with the known low-K and high-K dependence extracted. One might hope that each plot would show little variation, but the 1 S1 to 1 S1 plot varies considerably as one goes to high K, and the 1 S1 to 2 P1 plot shows a very rapid variation for K∼∞, strongly suggesting that at least one element of physics —perhaps a pole outside of but close to the domain of convergence—has been omitted

Exact time-dependent evolution of electron velocity distribution functions in a gas using the Boltzmann equation

A numerical technique, starting from the Boltzmann equation, for obtaining the time-dependent behavior of the electron-velocity distribution function in a gas is presented. A unique feature of this technique is that, unlike previously used procedures, it does not make use of any expansion of the distribution function. This allows the full anisotropy of the distribution function to be included in the solution. Furthermore, the problem associated with multiterm-expansion techniques of choosing a sufficient number of terms for convergence is completely avoided. The distribution function obtained by the present method is exact and, in principle, contains all of the expansion terms of the previous procedures. Details of the algorithm, including stability conditions, treatment of the boundaries, and evaluation of the collision integrals, are presented. This technique has been applied for obtaining the time-dependent behavior of electron swarms in gaseous argon and neon for various values of E/N (the ratio of the applied uniform dc field to the gas density), and the corresponding results are presented

Exact evaluation and recursion relations of two-center harmonic oscillator matrix elements

Using vibrational wave functions of two relatively displaced harmonic oscillators of arbitrary frequencies, Franck–Condon overlap integrals and matrix elements of x^l, exp(−2cx), and exp(−cx^2) (x is the internuclear separation) are obtained. Useful three‐term, four‐term, and five‐term recursion relations among these matrix elements are derived. It is shown that all of the relevant matrix elements can be obtained from a mere knowledge of the lowest two Franck–Condon overlap integrals. Results are illustrated by computation of Franck–Condon factors for the A ^1∑^+_u –X ^1∑^+_g and the B ^1Π_u –X ^1∑^+_g systems of ^7Li_2