Variational Calculations on Electron-Helium Scattering

Abstract

Calculations have been made on the elastic scattering of low-energy electrons by helium using a variational procedure which takes polarization and correlation effects into account by means of continuum Bethe-Goldstone equations. The convergence of the results is examined using two methods to obtain a complete set of basis functions. Results for the s, p, d, and f waves are presented. The width of the 28 closed-channel resonance below the n =2 threshold is found to be 0.015 eV, in comparison with the 0.015-0.020-eV estimates of Andrick and Ehrhardt from experiment and the 0.01-eV estimate of simpson and Pano.

Density Variation in Heat- and Pressure-Treated Egg White during Gel-to-Glass-like Transition

“…Below 20 eV they are in fair agreement with the close-coupling calculations, and at low energies ( < 5 eV) with the variational results of Sinfailam and Nesbet (1973). The situation Walters (1976) who suggests a downward renormalization of the experimental values in this energy range by about 25%.…”

“…These results, together with both the similar results of McConkey and Preston (1975), Sethuraman et al (1974). Crooks (1972) and other workers and values obtained from the theoretical phaseshifts of LaBahn and Callaway (1970) and Sinfailam and Nesbet (1972) have been carefully analysed by de Heer and Jansen (1975a). Their adopted values agree above 7 eV with those obtained from our phaseshift analysis.…”

“…Variational (Sinfailam and Nesbet 1973) and close-coupling calculations (two-state, Burke and Taylor 1969;three-state, Norcross 1971) give consistent values of the singlet and triplet scattering lengths, and we may take A" = -4.58. The direct part of the zero-energy Born amplitude may be obtained from the form factor using analytic Hartree-Fock wavefunctions (Inokuti and McDowell 1974) as f: (O, k 2 ) = 6.211 and is unlikely to be in error by more than 5%.…”

New possibilities of a cylindrical probe in gas-discharge plasma

“…Such conditions were 1 2 (1 cos )cos t t + ω ω chosen in connection with the fact that elastic electron scattering by atoms is the predominant mechanism of electron beam relaxation in this case [12]. The ener getic behavior of the cross section of this process has been studied sufficiently well [13][14][15]. The choice of helium as a filling gas was caused by its high excitation and ionization potentials (Е ion ≈ 24.6 eV) and small (as compared to alkali metals) transport cross section of elastic collisions of plasma electrons with atoms, which leads to the largest deviation of the electron dis tribution from the Maxwellian distribution as com pared to plasma of other gases and metal vapors.…”

On the Mordell-Weil and Shafarevich-Tate Groups for Weil Elliptic Curves

“…Theoretical results have been provided by polarised orbital calculations (e.g. Callaway et a1 1968, Duxler et a1 1971, application of the close-coupling procedure (Burke et a1 1969, Burke andRobb 1972) and also from a variational method (Sinfailam andNesbet 1972, Oberoi andNesbet 1973). As noted by Andrick and Bitsch (1975), there is good agreement between sand p-wave phaseshifts computed from these theories and with those derived from the phaseshift analysis of their measured angular distributions of elastically scattered electrons.…”