Ramsauer-Townsend Minimum Research Articles

Polarization effects on low-energy electron collisions with propane

We employed the Schwinger multichannel method to compute elastic cross sections for low-energy electron collisions with propane C3H8 . The calculations are carried out within the static-exchange and static-exchange plus polarization approximations and covered the energy range from 0 to 15 eV. The computed differential cross sections show good agreement with the experiment, and the computed integral cross sections present the same shape as the measured total cross sections. We found a broad structure in the integral cross section around 8.5 eV and also a Ramsauer-Townsend minimum around 0.1 eV. These results are in agreement with the experimental observations.

Near-threshold resonances in electron elastic scattering cross sections for Au and Pt atoms: identification of electron affinities

The recent Regge-pole methodology has been employed together with a Thomas–Fermi type potential which incorporates the vital core-polarization interaction to investigate the near-threshold electron attachment in Au and Pt as Regge resonances. The resultant stable negative ion states are found to have the discernible characteristic of very small imaginary parts of the Regge poles, which translate into long-lived resonances. The near-threshold electron elastic total cross sections are characterized by multiple resonances from which we extract the electron affinity (EA) values through the scrutiny of the imaginary part of the relevant complex angular momentum. For the Au− and Pt− negative ions the extracted binding energies of 2.262 eV and 2.163 eV, respectively are in excellent agreement with the most recently measured EA values for Au and Pt. Ramsauer–Townsend minima, shape resonances and the Wigner threshold behaviour are identified in both Au− and Pt− ions.

Dramatic resonances in low-energy electron scattering from Rb, Cs and Fr atoms: Signatures of electron affinities

Abstract We predict dramatic resonances in low-energy electron elastic total cross-sections for Rb, Cs and Fr atoms, whose energy positions are identified with the electron affinities (EA’s) for these atoms, preceded by shape resonances and Ramsauer–Townsend minima. This provides a new powerful theoretical method of determining unambiguous EA values for atoms. The extracted EA values for Rb and Cs atoms agree very well with the most recently measured values, but our value for Fr disagrees significantly with existing calculated values. The calculation used the recent Regge-pole methodology with a Thomas–Fermi potential incorporating the vital core-polarization interaction.

Absolute angle-differential elastic and vibrational excitation cross sections for electron collisions with tetrahydrofuran

Absolute angle-differential elastic and vibrational excitation cross sections for electron collisions with tetrahydrofuran were measured in the energy range 0.1–20 eV, extending existing measurements to lower energies. The elastic cross sections were measured as a function of scattering angle from 10° to 180° at energies of 2 eV, 6 eV, 10 eV and 20 eV, and as a function of electron energy at 45°, 90°, 135° and 180°. The agreement with previous measurements and with the published theoretical work was generally satisfactory. The Ramsauer–Townsend minimum was observed at low energies, down to 0.24 eV at 180°. Three additional minima were observed at 1.13, 4.74 and 15.3 eV in the 180° elastic cross section. Vibrational excitation cross sections are reported as a function of electron energy from the threshold to 16 eV. They reveal threshold peaks and broad bands at 6.2 and 10.8 eV, attributed to shape resonances, in agreement with theoretical predictions, although the calculated energies are generally somewhat higher. A broad enhancement of the CH2 scissoring vibration is observed around 2.6 eV, implying a low-lying (shape) resonance similar to that observed earlier in cyclopropane.

Fully relativisticR-matrix study of the interaction between a slow electron and atomic iodine: Scattering and photodetachment

An 11-state close-coupling calculation for the interaction between a slow electron and atomic iodine is carried out using the fully relativistic R-matrix method. The cross sections are presented for the photodetachment of a negative atomic iodine ion and for electron scattering by neutral atomic iodine from the threshold to 8 eV. The electron affinity for negative iodine is obtained as 2.958 eV. For the photodetachment process, we get fairly good agreement with experimental results for the distinct spin-orbit split between the 5p3/2 and 5p1/2 thresholds due to the relativistic effect as well as for the cross sections near the thresholds. The electron scattering cross sections display energy dependence similar to that for electron scattering by heavy rare-gas atoms, i.e., a Ramsauer-Townsend minimum well at a lower energy and a broad peak after the well. The photodetachment process of the negative iodine ion, as a good example to illustrate various electron correlation effects, has been focused on for decades. Early on, Robinson and Geltman 1 used a central-field model for both bound and free electron states to obtain the photodetachment cross section for the negative iodine ion. Radojevic et al. 2 used the relativistic random-phase approximation RRPA to calculate the photodetachment of negative halogen ions F  ,C l  ,

Regge oscillations in electron-atom elastic cross sections

We consider a system trapped in a resonance state, whose decay at zero scattering angle can be related, through the optical theorem, to the total cross section (TCS). We show that for the resonance to contribute to the TCS a peak structure the resonance conditions must be satisfied: (i) Several rotations of the complex (the Regge trajectory---viz., imaginary part versus the real part of the complex angular momentum---stays close to the real axis) and (ii) coherent addition of forward-scattering subamplitudes (the real part of the Regge pole is close to an integer). We exploit the recent complex angular momentum approach of Macek et al. [Phys. Rev. Lett. 93, 183203 (2004)], used to analyze low-energy oscillations observed in the elastic TCS for proton-H scattering, for a detailed analysis of Regge trajectories and their contributions to the TCS in electron-atom scattering for the case of $Z=75$ using the model Thomas-Fermi potential. We conclude by demonstrating through comparison with existing theory and measurements that the Thomas-Fermi potential when used with the appropriate parameters captures the essential physics (Ramsauer-Townsend minima and the Wigner threshold law) in the near-threshold $e\text{\ensuremath{-}}\mathrm{Ar}$ and $e\text{\ensuremath{-}}\mathrm{Kr}$ elastic scattering.

Mobility of electrons in supercritical krypton: Role of density fluctuations

Excess electrons were generated in supercritical krypton by means of pulsed x-ray irradiation, and the electron transport phenomena were studied. Electron signals immediately after a 30 ps pulse showed a distinctive feature characteristic of the presence of the Ramsauer-Townsend minimum in the momentum transfer cross section. The dependence of the drift velocity v(D) on field strength was found to be concave upward in the low field region and then to go through a maximum with increasing field strength, which is also typical of the presence of a minimum in the scattering cross section at an intermediate field strength. A minimum in the electron mobility was observed at about one-half the critical density. The acoustical phonon scattering model, which successfully explained the mobility change in this density region in supercritical xenon, was again found to account for the mobility in supercritical krypton.

Low-energy electron scattering byN2O

We present elastic integral, differential, and momentum-transfer cross sections for electron collisions with N{sub 2}O. We show that, with a slight modification of a method of incorporating polarization effects proposed recently by us [Winstead, McKoy, and Bettega, Phys. Rev. A 72, 042721 (2005)] along with a flexible one-particle basis set, we can reproduce features in the experimental data that were not reproduced by earlier calculations. We also find evidence of a Ramsauer-Townsend minimum, which our calculation places at about 0.2 eV.

Influence of the Ramsauer–Townsend minimum on the electron energy distribution function and electron transport in xenon

The electron distribution function in xenon in the low-energy region comprising the Ramsauer-Townsend minimum was obtained by solving the Boltzmann equation in the hydrodynamic approximation, for electric field to gas density ratios E/N in the range (0.01, 3) Td. The distortion of the electron distribution function due to the minimum is analysed and correlated to the behaviour of the electron transport coefficients: the drift velocity W d and the ratio of the transverse and longitudinal diffusion coefficient to mobility, D T /μ and D L /μ. The results are discussed in view of the different theoretical and experimental cross-section data used.

Addendum to “Elastic scattering of low-energy electrons by OCS”

In a previous publication [Phys. Rev. A. 70, 062711 (2004)] we presented results for electron collisions with OCS molecules. We found a {pi} shape resonance and discussed the existence of an s-wave virtual state through the analysis of the scattering length. The existence of the {pi} shape resonance has been reported by other theoretical and experimental studies, and the existence of an s-wave virtual state has been suggested by an experimental study. In this Addendum we show that besides the {pi} shape resonance and the s-wave virtual state, this molecule also presents a Ramsauer-Townsend minimum around 1 eV.

Electron collisions with CS2

We present elastic integral and differential cross sections for electron collisions with CS2 molecules for energies up to 10 eV. To compute the cross sections we employed the Schwinger multichannel method implemented with pseudopotentials at the static-exchange plus polarization approximation. In particular, our integral cross section shows a sharp increase near zero energy, which is an indication of the existence of an s-wave virtual state, followed by a Ramsauer–Townsend minimum around 0.7 eV. Our results agree well with available experimental and theoretical results.

Electron transport and ionization in CHF3–Ar and CHF3–N2 gas mixtures

The pulsed Townsend technique has been used to measure the electron drift velocity, the density-normalized effective ionization coefficient (α − η)/N (α and η are the ionization and attachment coefficients, respectively), the density-normalized longitudinal diffusion coefficient NDL, and the ratio between the longitudinal diffusion coefficient and the electron mobility DL/K, in CHF3 mixed with Ar and N2, over a wide range of the density-normalized electric field strength E/N, from 0.2 to 400 Td (1 Td = 10−17 V cm2). The CHF3 content in the mixtures was varied between 1% and 50%. Regions of negative differential conductivity (NDC) appear in the plots of the electron drift velocity as a function of E/N. This effect is more pronounced for the CHF3–Ar mixtures than for the CHF3–N2 ones, since it results from the presence of a Ramsauer–Townsend minimum in the momentum transfer cross section for Ar, which is absent in N2. For the CHF3–N2 case, a shallow region of NDC is observed, and it is thought to be due to various inelastic collision processes between the electrons and the buffer gas, and also to the steep fall of the scattering cross sections for CHF3 at low electron energies. Additionally, the dependence of NDL on E/N displays well-defined minima at low E/N, which are a result of the strong inelastic energy loss of the electrons. The effective ionization coefficients were found to be weakly dependent on the concentration mixture for CHF3–N2, while a strong dependence on this parameter was found for the CHF3–Ar mixture. In all cases, the attaching character of the mixtures was found to be very small. For low E/N (< 20%) in the CHF3–N2 mixture it was observed that the values of (α − η)/N are higher than those expected due to electron impact. We believe that Penning ionization may be responsible for this effect.

Electron collisions with the hydrides PH3, AsH3 and SbH3

We report integral cross sections for the elastic scattering of low-energy electrons by the hydrides PH3, AsH3 and SbH3. To calculate the cross sections, we employed the Schwinger multichannel method with pseudopotentials (Bettega et al 1993 Phys. Rev. A 47 1111) at the static-exchange plus polarization level of approximation for incident energies from 0.5 to 8 eV. For PH3, we compare our integral cross section with the recent total cross section measured by Szmytkowski et al (2004 J. Phys. B: At. Mol. Opt. Phys. 37 1833) and find good agreement in shape. In particular, our calculated elastic integral cross section for PH3 also shows the two structures reported by the experiment. We have found that the three hydrides present a Ramsauer–Townsend minimum at around 1 eV.

Chemical reactions in the limit of zero kinetic energy: virtual states and Ramsauer minima in F + H2 → HF + H

The behaviour of reactive scattering at ultracold temperatures is explored by calculating the real and imaginary parts of the scattering length for the reaction of F with a molecule composed of a pair of pseudo-hydrogen atoms of arbitrary mass. The origin of a low energy feature in the cross section for the reaction of F with H2 and its absence for the reaction with D2 is investigated. Close-coupling calculations of the scattering matrix show that the F–H2 feature arises from the presence of a virtual state associated with the van der Waals well in the entrance channel and that the virtual state is responsible for the enhanced zero temperature rate coefficient of the F–H2 reaction. For a mass of about 1.12 hydrogen masses the virtual state turns into a zero energy resonance and the corresponding zero temperature rate coefficient is 1 × 10−9 cm3 s−1 despite an energy barrier of 300 K. Evidence in support of the virtual state is also provided by the detection of a deep Ramsauer–Townsend minimum in the elastic component of the total cross section for F–H2 which the present calculations predict to occur at low energies.

Low-energy electron scattering by cubane: resonant states and Ramsauer-Townsend features from quantum calculations in the gas phase.

Calculations are carried out, using a nonempirical modeling of the interaction potential and solving the quantum scattering coupled channel equations, for low energy electron scattering from cubane (C8H8) molecules in the gas phase. Total integral cross sections are obtained and partial contributions are analyzed for the most important irreducible representations that describe the continuum electron in the Oh molecular symmetry. Several trapping resonances are found and analyzed in terms of the molecular-type features of the resonant electron states associated with them. A Ramsauer-Townsend minimum is also found and its possible behavior related to features of the scattering length as k --> 0.

Low Energy Positron Scattering by SF6 and CO2

In this work we present theoretical integral (ICS) and differential (DCS) cross section calculations for low-energy positron scattering by SF6 and CO2 molecules. Our scattering wave functions were obtained with the Schwinger Multichannel Method (SMC) at the static and static-plus-polarization levels of approximation. The elastic DCS were calculated over an energy interval ranging from 4 eV up to 50 eV for SF6 and from 1 eV up to 20 eV for CO2. The results show, in general, good agreement with recent experimental data. We found a Ramsauer–Townsend minimum in e+ - CO2 calculations, even though no signature of virtual state formation was observed, contrasting with the well-known case of electron scattering.

Nonhydrodynamic aspects of electron transport near a boundary: the Milne problem.

The nonhydrodynamic behavior of electrons near a boundary is studied with the Milne problem of transport theory. A system of electrons dilutely dispersed in a heat bath of atomic moderators is considered in the positive one-dimensional spatial half-space with an absorbing boundary at the origin which mimics an electrode. A flux of electrons is assumed to originate at an infinite distance from the boundary. The Fokker-Planck equation for the electron distribution function in space and velocity is considered. The density and temperature profiles are determined, and the departure from hydrodynamic behavior near the boundary is studied. Argon and helium are chosen as the moderators, and results with different cross sections are obtained. The Fokker-Planck equation is solved with an expansion in Legendre and Speed polynomials, and compared wherever possible with results obtained with a Monte Carlo simulation. The behavior near the boundary is shown to be strongly influenced by the Ramsauer-Townsend minimum in the electron-Ar momentum transfer cross section.

Progress with the Schwinger multichannel method in positron–molecule scattering

We report calculations for low-energy positron–C 2H 2 and –N 2 scattering obtained through the Schwinger multichannel method (SMC). Integral and differential cross-sections and the annihilation parameter, Z eff, are presented. For nitrogen, evidence of a Ramsauer–Townsend minimum and the possibility of overcorrelation in the scattering configuration space are discussed. Annihilation probability densities (APD) calculated for He and H 2 seem to bring indirect support to a model previously proposed to explain why acetylene, unlike nitrogen, presents very high low-energy annihilation rates.

Elastic electron scattering by silane in the low-energy range

Elastic differential, integral and momentum-transfer cross sections are reported for electron scattering by SiH4 at impact energies ranging from 0.1 to 40eV. A new code based on the Schwinger iterative variational method in the fixed-nuclei, static-exchange plus correlation-polarization approximation is used to calculate the scattering amplitudes. Our calculated cross sections are in general good agreement with the available experimental data as well as with some recent theoretical results. The new code is also able to reproduce the Ramsauer-Townsend minimum at 0.2eV and the resonance at 3eV. The good results of the present application reinforce the reliability of our method.

Elastic scattering of electrons byGeH4in the low- and intermediate-energy range

Elastic differential, integral, and momentum-transfer cross sections are reported for electron scattering by ${\mathrm{GeH}}_{4}$ at impact energies ranging from 0.2 to 100 eV. The Schwinger iterative variational method in the fixed-nuclei, static-exchange plus correlation-polarization approximation is used to calculate the scattering amplitudes. Large-angular-momentum contributions from the correlation-polarization potential to the scattering amplitude are taken into account via a closed formula for higher incident energies. We have observed a ${T}_{2}$ shape resonance in the ICSs and MTCSs at around 3.0 eV and we have predicted a Ramsauer-Townsend minimum at around 0.6 eV. Our calculated cross sections are compared with recent experimental data and other theoretical results.