Extension of the Schwinger variational principle beyond the static-exchange approximation

Abstract

We propose a new variational principle for scattering theory which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering. Application of this formulation to the scattering of electrons by hydrogen atoms at energies below k' = 0.64 demonstrates the rapid convergence of the phase shift with respect to the number of basis functions for both the open-and closed-channel orbitals. Furthermore, we show that the convergence of the phase shift with respect to the number of expansion functions (exact states or pseudostatesj is also fast. In our theory, the resulting phase shifts can be more accurate than those of the close-coupling method even if the same expansion basis is used. The phase shifts in our ls-2s-2p calculation are comparable to those of 1s-2s-2p-3p-3d calculation of Matese and Oberoi [Phys. Rev. A 4 569 (1971j],which are very close to the exact values. Several aspects of the convergence characteristics are also discussed.

Computation of electron-impact rotationally elastic total cross sections for methanol over an extensive range of impact energy (0.1 – 2000 eV)

“…The first electronic excitation energy of CH 3 OH is found to be 8.55 eV using the configuration interaction (CI) model, which agrees well with the calculated value of 8.53 eV reported by Vinodkumar et al [12], albeit higher compared to the theoretical value of 6.76 eV reported by Bouchiha et al [3] and the experimental value of 6.5 eV reported by Knoop et al [19]. The present dipole moment is 2.28 D, which is slightly higher compared to the theoretical value of 1.97 D [3] The most popular methodologies employed for low-energy electron collision calculations are the Kohn variational method [20,21], the Schwinger variational method [22][23][24], and the R-matrix method, of which the R matrix is the most widely used. The underlying idea behind the R-matrix method relies on the division of configuration space into two spatial regions, namely, the inner region and the outer region.…”

Electron cross section set for CHF3

“…Cross sections for elastic electron scattering by and electron-impact excitation of CHF 3 were computed using the Schwinger multichannel ͑SMC͒ method 7,8 as implemented for parallel computers. 9,10 Details of the method may be found in the references given.…”

Absolute angle-differential elastic cross sections for electron collisions with diacetylene

“…Electron-scattering calculations were carried out at the optimized geometry using a massively parallel implementation of the Schwinger multichannel (SMC) variational method [22][23][24]. The one-electron space used in the calculations was constructed along the same lines as that used in earlier work on ethylene [25,26].…”