Ramsauer-Townsend Minimum Research Articles

Theoretical support for a Ramsauer-Townsend minimum in electron-CF4scattering

We describe complex Kohn calculations for elastic ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{CF}}_{4}$ scattering at incident electron energies of 0.04--20 eV. An accurate representation of the electronic correlation effects involving target polarization is critical in the explicit demonstration of a Ramsauer-Townsend minimum. We use a set of polarized virtual orbitals to form a compact representation of closed channels in the trial scattering function to include these effects. These are the first ab initio calculations to verify the Ramsauer-Townsend minimum in ${\mathrm{CF}}_{4}.$ We find excellent comparison between the complex Kohn results and measured differential and integral cross sections.

Low-energy elastic scattering of electrons by ethylene

Elastic differential, integral, and momentum-transfer cross sections are reported for electron scattering by ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ at impact energies ranging from 1 to 50 eV. The Schwinger iterative variational method in the fixed-nuclei, static-exchange plus correlation-polarization approximation is used to calculate the scattering amplitudes. Integrated cross sections are also calculated below 1 eV, showing the existence of a Ramsauer-Townsend minimum in this region. Our calculated cross sections are compared with recent experimental data and other theoretical results.

The influence of the Ramsauer-Townsend effect on free-free absorption coefficients of the negative argon ion at far infrared wavelengths

free-free absorption coefficients in the far-IR are calculated using relativistic continuum wavefunctions from solutions of the Dirac equation. Absorption coefficients are shown to exhibit a Ramsauer-Townsend minimum near 1200 K. We compare these results with coefficients derived from non-relativistic and experimental atomic data.

Quasifree electron scattering on atoms in the inverse kinematic system

The measurement of elastic electron scattering is a sensitive tool to test ionic and atomic potentials. Because a dense ionic target is difficult to produce, we use inverse kinematics, i.e. we exchange the roles of projectile and target and transform the cross sections. The absolute singly and doubly differential cross sections for the projectile ionization of He 0 (0.1 MeV/u) scattered by Ne 0, measured for the direct and the inverse system in the whole angular range from 0° to 180°, show the validity of the transformation. We find a pronounced generalized Ramsauer-Townsend minimum in the angular-dependent singly differential cross section. Changing to the Ne 3+ target the loss peak is absent in our measurements for larger emission angles. This may be explained by a large capture cross section into bound states of the neon ion, which depends on the impact parameter.

Vacuum polarization effects in low-energy muonic atom collisions.

We estimate the vacuum polarization (VP) correction to the Coulomb interaction in collisions of muonic atoms. It is shown that the VP effect, amplified by the low-lying virtual state ${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{\ensuremath{\vartheta}}}$\ensuremath{\sim}10 eV, is of the order of \ensuremath{\sim}1--2 % in the S-wave cross sections for p\ensuremath{\mu}+p collisions as \ensuremath{\varepsilon}\ensuremath{\le}${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{\ensuremath{\vartheta}}}$. The VP amplitude becomes comparable to the anomalously small pure Coulomb amplitude for the singlet t\ensuremath{\mu}+t scattering as \ensuremath{\varepsilon}\ensuremath{\rightarrow}0 and near the Ramsauer-Townsend minima in the d\ensuremath{\mu}+p and t\ensuremath{\mu}+p scattering.

Time-dependent and temperature-dependent aspects of electron distribution functions: H, Ar, and Cs atomic gases

Time-dependent and temperature-dependent aspects of the thermalization of electrons in atomic gases are studied by using the Boltzmann equation. H, Ar, and Cs gases were chosen for the present study because of the characteristic and significantly different dependences of their momentum-transfer cross sections on electron energy; H has a smoothly varying cross section, Ar has a conspicuous Ramsauer–Townsend minimum, and Cs has a resonance-like peak. The effects of these cross section shapes on electron distribution functions and degradation spectra are examined.

The Ramsauer minimum of methane

Vibrationally elastic, rotationally-summed cross sections for electron collisions with CH4 are calculated with ab initio static+exchange (SE) interactions and using a symmetry-adapted, single-centre expansion (SCE) representation for the close-coupled (CC) equations. The dynamical correlation forces are included through a local density-functional theory (DFT) approach. Both integral and differential cross sections are calculated at the Ramsauer-Townsend (RT) minimum and at energies close to it. Comparisons with experiments and with previous calculations show that the present approach exhibits one of the best overall accords with measurements while still keeping the computational effort within modest limits.

Electron scattering from acetylene: elastic integral and differential cross sections at low energies

Calculations have been carried out for the scattering of slow electrons from acetylene molecules in the gas phase, using the fixed-nuclei (FN) dynamical approximation and computing elastic cross sections only, integral and differential. Ab initio results at the exact static-exchange (ESE) level have been supplemented by a model local potential describing short-range and long-range polarization forces. The target wavefunction was obtained at the SCE level from a multicentre expansion over Gaussian orbitals (GTOs). Both the static and exchange interactions, Vst and Vex, were obtained from a discrete basis by using multicentre orbitals and the separable exchange approximation. The final results are compared with available experiments and a detailed search for the 2.6 eV shape resonance is discussed. The very-low-energy computed cross sections also reveal the presence of a Ramsauer-Townsend (RT) minimum.

Analytical independent-particle model for electron scattering by argon at low energy

The analytical independent-particle model of Berg, Purcell, and Green (BPG) is extended to describe low-energy scattering of electrons by the argon atom. The Ramsauer-Townsend minimum and the scattering length are only well reproduced when the BPG model is supplemented with a polarization potential as proposed by Sandhas.

Low energy (0.01-20 eV) electron scattering from acetylene

We report elastic differential, integral and momentum transfer cross sections for the electron-C2H2 system in the energy range of 0.01-20 eV. A parameter-free model potential approach is employed under the fixed-nuclei, single-centre, and close-coupling formalism. The electron exchange interaction is treated via a modified version of the semi-classical exchange model, while the short range correlation and long range polarization effects are included under the correlation-polarization approximation. This local and non-empirical potential, for both the exchange and charge distortion effects, is very successful in describing the 2 Pi g shape-resonance phenomenon around 2 eV. Our final results for both the differential and integral cross section compare very well with recent measurements. A Ramsauer-Townsend minimum is found around 0.2 eV in the total and momentum transfer cross sections.

Theoretical study of low-energy positron scattering on alkaline-earth atoms in the relativistic polarized orbital approximation

The elastic low-energy positron scattering on Be, Mg, Ca, Sr, Ba and Ra atoms has been investigated at energies below 100 eV. The ab initio calculated polarization potentials applied in these calculations were obtained by solving the coupled Dirac-Hartree-Fock equations. Comparison between present results and those of previous model calculations shows serious discrepancies. Particularly, we do not predict existence of the Ramsauer-Townsend minima in total elastic cross sections.

Momentum Transfer Cross Section for e??Kr Scattering

The momentum transfer cross section for electrons in krypton has been derived over the energy range Q-4 eV from an analysis of drift velocity and DT/I-' data for hydrogen-krypton mixtures. At energies in the vicinity of the Ramsauer-Townsend minimum, the present work differs significantly from derivations based on analyses of drift velocity data alone. The overall uncertainty in the derived cross section reflects the experimental errors in the transport coefficients, the uncertainty in the cross sections used to represent the hydrogen component in the mixtures, and the uncertainty associated with the X2 minimisation. The present cross section is compared with recent theoretical calculations and other experimental derivations.

Ab initio study of low-energy electron-ethane scattering

We report the results of the first ab initio study of low-energy electron-ethane scattering which includes the effect of target polarization. The complex-Kohn method is used in scattering calculations that employ both static-exchange and polarized-self-consistent-field (polarized-SCF) trial functions. Integral, momentum transfer, and differential elastic cross sections are reported for both staggered and eclipsed conformations. Overall agreement between our studies and the most recent experimental data is very good. For staggered ethane, our integral cross section shows a Ramsauer–Townsend minimum at 0.18 eV. This is only the second theoretical study to find such a minimum in a molecule that possesses a nonzero quadrupole moment. We find that a polarized-SCF wave function is needed to obtain reliable cross sections in the vicinity of the Ramsauer–Townsend minimum and that this polarized-SCF wave function also provides a good description of the 7.5 eV f-wave shape resonance. The low-energy cross sections we obtain for staggered and eclipsed C2H6 differ very little from each other near the Ramsauer–Townsend minimum, but significant differences are found at higher energies.

Theoretical studies of low-energy electron-silane scattering with an ab initio description of target response.

Theoretical studies of low-energy electron-silane scattering are reported in which target polarization is included by using an ab initio optical potential. These calculations employ the complex Kohn scattering method and were undertaken both at the static-exchange level and with target polarization. A polarized virtual-orbital method, which was introduced in our earlier study of electron-methane scattering, was also employed in this study to generate a compact description of the closed channels included in the optical potential. Differential, integral, and momentum-transfer cross sections are reported at incident energies ranging from 0.2 to 20 eV. The computed total cross section shows a Ramsauer-Townsend minimum at 0.3 eV and a broad d-wave shape resonance at 3.0 eV. Excellent agreement is found between our polarized Kohn results and the recent experimental results of Wan, Moore, and Tossell [J. Chem. Phys. 91, 7340 (1989)].

Momentum transfer cross section of xenon deducted from electron drift velocity data

Momentum transfer cross section of xenon is deduced from experimental electron drift velocity data over the energy range from 0.02 to 10 eV by using an algorithm based on a Boltzmann equation method. The result shows that the Ramsauer-Townsend minimum is located at an electron energy of 0.7 eV with a magnitude of 9*10-17 cm2. It is found that the present momentum transfer cross section is in excellent agreement with the experimental data points of Register et al. (1986) and that the calculated diffusion coefficient (parallel direction to the electric field) from the deduced cross section agrees very well with the measurements of Hashimoto and Nakamura (1990) for E/N above 0.07 Td. The fractional difference between the calculated electron drift velocity and the experimental one is suppressed within 1.2% at E/N below 0.1 Td and within 3% at E/N above 0.1 Td. Above an electron energy of 8.32 eV, inelastic collision cross sections are necessary for the deduction of the momentum transfer cross section. Therefore, the total excitation cross section of Hayashi (1983) and the ionization cross section of Krishnakumar and Srivastava (1988) are used to deduce the momentum transfer cross section over a range of high electron energies. As a result, the peak of the deduced momentum transfer cross section is located at an electron energy of 5 eV with a magnitude of 3*10-15 cm2.

Ab initio study of low-energy electron-methane scattering.

The complex Kohn method is used to study electron-methane scattering with polarized trial functions at incident energies ranging from 0.2 to 10 eV. A perturbative method, which only requires the construction of Fock operators, is used to generate a set of polarized virtual orbitals. These polarized orbitals are then used to construct a compact ab initio scattering function that produces cross sections that are in excellent agreement with experiments in the region of the Ramsauer-Townsend minimum and at higher energies, where a broad maximum is present in the integral cross section. This is the first ab initio study to accurately characterize low-energy electron-methane scattering.

Momentum transfer cross section of argon deduced from electron drift velocity data

The momentum transfer cross section of argon is deduced from experimental electron drift velocity data over the energy range from 0.02 to 100 eV. A method proposed earlier by Suzuki et al. (1989) which is improved by adding a minimising procedure of the fractional difference between calculated and experimental electron drift velocities, is used. In an E/N range below 0.1 Td, the electron drift velocity data of Robertson (1977) at a gas temperature of 89.6 K are analysed and the cross section for the low-energy region is deduced. The result shows that the Ramsauer-Townsend minimum is located at an electron energy of 0.23 eV with a magnitude of 9.35*10-18 cm2. It is found that the present result is in excellent agreement with the theoretically determined values of Dasgupta and Bhatia (1985) and that the characteristic energy calculated from the present cross section agrees very well with the measurements of Milloy and Crompton (1982). In an E/N range above 0.1 Td, the experimental electron drift velocity data of Nakamura and Kurachi (1988) and Kucukarpaci and Lucas (1981) are analysed to deduce the cross section for the high-energy region. In order to obtain consistency among the present momentum transfer cross sections, ionisation cross sections by Krishnakumar and Srivastava (1988) and excitation cross sections by de Heer et al. (1979), reference is made to the ionisation coefficient data by Kruithof (1940), Abdulla et al. (1981) and Ishizuka et al. (1987). It is found that the peak of the momentum transfer cross section is located at an electron energy of 10 eV with a magnitude of 1.5*10-15 cm2.

Momentum transfer cross section of krypton deduced from electron drift velocity data

The momentum transfer cross section of krypton is deduced from experimental electron drift velocity data over the energy range from 0.01 to 100 eV by using an algorithm based on a Boltzmann equation method. This energy range covers the Ramsauer-Townsend minimum and the peak of the momentum transfer cross section. The results show that the Ramsauer-Townsend minimum is located at an electron energy of 0.6 eV and the magnitude of the cross section there is 2.3*10-17 cm2, while the peak is located at an electron energy of 8.0 eV with a magnitude of 2.0*10-15 cm2. For electron energies above 9.91 eV, the threshold of inelastic collisions, a set of cross sections for these collisions is necessary. Since the total excitation cross section used seemed less accurate than the ionisation cross section, the momentum transfer cross section was determined by consulting the experimental ionisation coefficient data as well as electron drift velocity data and by modifying the excitation cross section. It is found that the momentum transfer cross section is not affected by choice of excitation cross section for electron energies below 30 eV. The diffusion coefficient and the characteristic energy are also calculated by using the momentum transfer cross section determined here to find good agreement with experiment. The energy distributions are calculated and compared with the energy distributions proposed by Morse et al. (1935). The agreement of these two energy distributions is very good at E/N=0.1 Td.

Polarization effects in low-energy electron-CH4 elastic collisions in an exact exchange treatment.

We have investigated the polarization effects in very-low-energy (below 1 eV) electron- ${\mathrm{CH}}_{4}$ collisions in an exact-exchange treatment. The two models of the parameter-free polarization potential are employed; one, the ${V}_{\mathrm{pol}{}^{\mathrm{JT}}}$ potential, introduced by Jain and Thompson [J. Phys. B 15, L631 (1982)], is based on an approximate polarized-orbital method, and two, the correlation-polarization potential ${V}_{\mathrm{pol}{}^{\mathrm{CP}}}$, first proposed by O'Connel and Lane [Phys. Rev. A 27, 1893 (1983)], is given as a simple analytic form in terms of the charge density of the target. In this rather very low-energy region, the polarization effects play a decisive role, particularly in creating structure in the differential cross section (DCS) and producing the Ramsauer-Townsend minimum in the total cross section. Our DCS at 0.2, 0.4, and 0.6 eV are compared with recent measurements. We found that a local parameter-free approximation for the polarization potential is quite successful if it is determined under the polarized-orbital-type technique rather than based on the correlation-polarization approach.

Collisions of electrons with polyatomic molecules: Electron-methane scattering by the complex Kohn variational method.

The complex Kohn variational method, which is an anomaly-free algebraic variational procedure, is implemented for the case of collisions of electrons with polyatomic molecules. The complex Kohn method requires only Hamiltonian matrix elements and, in this formulation, does not require any exchange matrix elements involving continuum functions. Direct matrix elements of the scattering potential(s) which involve continuum functions are evaluated by an adaptive three-dimensional quadrature scheme. The entire procedure is applied to elastic electron-methane scattering at the static-exchange level and proves to be both efficient and accurate. No Ramsauer-Townsend minimum is found at low energies, and it is concluded that this feature of the experimental cross section cannot be described theoretically without the inclusion of target polarization.