Correlation-polarization Potential Research Articles

On the elastic cross sections for low-energy e-CH4 and e-SiH4 scattering in a spherical model potential

The spherical approximate wavefunctions and electronic densities of CH4 and SiH4 are obtained using a spherical approximate molecular Hamiltonian, employing the numerical Xalpha method with the self-interaction correction. The spherical parameter-free model potentials for the interaction between the incident electron and the target molecules are generated from the electronic densities, and include the static potential, the Hara (1967) free-electron-gas exchange (HFEGE) potential and O'Connell and Lane's (1983) correlation-polarisation potential. Total, momentum transfer and differential cross sections are calculated via partial-wave analysis.

Electron-N2 scattering calculations with a parameter-free model polarization potential.

We have extended our variationally determined nonadiabatic polarization potential [Gibson and Morrison, Phys. Rev. A 29, 2497 (1984)] to the e-${\mathrm{N}}_{2}$ system and calculated elastic, total momentum transfer, and rotational excitation cross sections. This model potential, which requires no scaling and contains no adjustable parameters, is presented in tabular and analytic (fitted) form for possible use in future studies. We evaluated the static potential at the near-Hartree-Fock level of accuracy and included exchange effects exactly via the linear algebraic method of Collins and Schneider [Phys. Rev. A 24, 2387 (1981)]. Diverse cross sections based on this model are in excellent agreement with existing experiment. We also compare various scattering quantities calculated with our model to prior theoretical results and to newly determined numbers using two other model potentials: a cutoff phenomenological form and the correlation-polarization potential of O'Connell and Lane [Phys. Rev. A 27, 1893 (1983)].

Total (elastic plus inelastic) cross sections for positron-methane (helium) collisions at low, intermediate, and high energies.

Theoretical calculations on the total (elastic plus inelastic) cross sections ${\ensuremath{\sigma}}_{t}$ for positron (${e}^{+}$)-methane collisions are reported at 2--600 eV. We evaluate a complex optical potential (COP) for the ${e}^{+}$-${\mathrm{CH}}_{4}$ system and treat it exactly in a partial-wave analysis to obtain the S matrix. The real part is composed of an accurate repulsive static potential plus a parameter-free attractive correlation polarization potential. The imaginary part of the COP, ${V}_{\mathrm{abs}(\mathrm{r})}$, is derived semiempirically in order to reproduce the sharp rise in ${\ensuremath{\sigma}}_{t}$ just above the positronium-formation threshold (${E}_{\mathrm{Ps})}$. This form of ${V}_{\mathrm{abs}}$ is a function of target charge density, static plus polarization potential, local kinetic energy of the projectile, Fermi momentum, and the mean excitation energy of the system. Our final ${e}^{+}$-${\mathrm{CH}}_{4}$ ${\ensuremath{\sigma}}_{t}$ compare very well with measurements in the ${E}_{\mathrm{Ps}\mathrm{\ensuremath{-}}600}$-eV region. Below ${E}_{\mathrm{Ps}}$, the present results are in good accord with close-coupling calculations of Jain and Thompson and the measurements of Charlton and co-workers. We also test this absorption potential for the ${e}^{+}$-He system and find qualitative agreement with measurements. It is also possible from this model to extract approximate values of the Ps-formation cross sections in the ore gap.

Investigation of parameter-free model polarization potentials for electron-molecule scattering calculations including the nuclear motion.

A correlation-polarization potential originally introduced by O'Connell and Lane [Phys. Rev. A 27, 1893 (1983)] is used in e-${\mathrm{H}}_{2}$ scattering calculations in which the vibrational motion of the target is taken into account. Eigenphase sums (as a function of internuclear separation) and cross sections for elastic scattering and for rovibrational excitations are compared to their counterparts calculated using the ab initio nonadiabatic model polarization potential of Gibson and Morrison [Phys. Rev. A 29, 2497 (1984)]. At low energies, these scattering quantities are found to be quite sensitive to the treatment of polarization. To assess these model potentials, theoretical total, momentum transfer, and rotational- and vibrational-excitation cross sections are compared to experimental data.

Erratum: Ab initio calculations of low-energy electron scattering by HCN molecules

We report results for vibrationally elastic scattering over the energy range 0.0006--11.6 eV. The interaction potential is composed of a near-Hartree-Fock static term plus a parameter-free model of the correlation-polarization potential. The exchange interaction is included exactly through a separable expansion. Results with a model-exchange potential (free-electron-gas plus orthogonalization) are also reported. A resonance appears in Pi symmetry near 2.7 eV (width 1.9 eV) that may be the same feature observed in several experiments. In the model-exchange calculation the Pi resonance is shifted toward higher energy (3.8 eV, width 2.4 eV). The ..sigma.. symmetry was also found to be very sensitive to the treatment of exchange and to the effect of polarization. Differential and rotational excitation cross sections are evaluated in the multipole-extracted adiabatic-nuclei approximation. Results are compared with the available experimental and theoretical data.

Positron-CO scattering below the positronium threshold

The author presents the first calculations on the total cross sections of e+-CO vibrationally elastic scattering in the energy range from 0.25 eV up to the positronium threshold. In the adiabatic-nuclei approximation, a single-centre expansion approach is employed to determine the fully converged scattering parameters. The e+-CO interaction energy is composed of an accurate repulsive static term and a parameter-free attractive correlation-polarisation potential. The results for the total cross sections are compared with recent measurements; the agreement is fair except below 2 eV, where theory underestimates the experimental data by about 50%. Results on the differential, momentum transfer and rotational excitation are also reported in the same energy region.

Glauber-eikonal study of electron-molecule scattering at intermediate energies with the use of the free-electron-gas model: H2.

An improved version of the Glauber-eikonal amplitude for electron-molecule scattering, originally developed by Bhattacharyya and Ghosh, that includes the effects of nonspherical potential terms up to \ensuremath{\nu}=6 is presented. Application is made to e-${\mathrm{H}}_{2}$ scattering at intermediate energies to test a recently proposed, parameter-free, correlation-polarization potential. This potential is based, as suggested by O'Connell and Lane, on the hybridization of local-electron-gas theory and the long-range polarization. Results obtained are found to be very encouraging.

Ab initio calculations of low-energy electron scattering by HCN molecules.

We report results for vibrationally elastic scattering over the energy range 0.0006--11.6 eV. The interaction potential is composed of a near-Hartree-Fock static term plus a parameter-free model of the correlation-polarization potential. The exchange interaction is included exactly through a separable expansion. Results with a model-exchange potential (free-electron-gas plus orthogonalization) are also reported. A resonance appears in Pi symmetry near 2.7 eV (width 1.9 eV) that may be the same feature observed in several experiments. In the model-exchange calculation the Pi resonance is shifted toward higher energy (3.8 eV, width 2.4 eV). The ..sigma.. symmetry was also found to be very sensitive to the treatment of exchange and to the effect of polarization. Differential and rotational excitation cross sections are evaluated in the multipole-extracted adiabatic-nuclei approximation. Results are compared with the available experimental and theoretical data.

Parameter-free model of the correlation-polarization potential for electron-molecule collisions

A model potential that includes both correlation and polarization effects is proposed for electron-molecule collisions. It is based, as suggested by O'Connell and Lane, on a hybridization of local electron-gas theory for short distances and the asymptotic form of the polarization potential. It is energy independent and very simple to apply, depending only on the molecular charge density and polarizabilities. The potential has been calculated for several molecules (${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, C${\mathrm{O}}_{2}$, HF, HCl, and CO); the crossing point between the correlation and polarization potentials is remarkably constant, averaging 0.96 eV. Application in scattering calculations for ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ yields very encouraging results.