Effects of Approximate Cluster Functions on Scattering Parameters and an Improved Pseudostate Expansion for Many-Particle Scattering

Abstract

The effects on scattering parameters of approximate cluster functions which appear in the asymptotic boundary conditions are examined by a model calculation of the elastic electronhydrogen scattering. It is shown that (i) the resonance energies calculated with functions which are orthogonal to the approximate open-channel functions could be spurious, (ii) the phase shifts could deviate from the correct values as much as the relative error in the cluster functions, and (iii) the threshold mismatch may cause an enhancement of phase shifts. An improved pseudostate expansion is studied in which the prediagonalization of the cluster energy matrix is emphasized. This is seen not only to improve the threshold energies and incorporate the effect of the continuum states, but also to optimize the input functions in a given calculation. An additional diagonalization of the closed-channel energy matrix provides a set of quasistates far the resonance and distortion potentials.

Self-consistent field theory of collisions I. Scattering channels

“…As Table 3 shows, the calculated phase shifts using different approximate forms of the He function vary considerably. This is not surprising, since it has been shown [10] that the scattering phase shifts depend critically on the approximate form used for the target helium function. The present theory, however, gives better results than that of effective Z and HF.…”

“…Hence, the question of how good these cluster functions should be in general cases and how they affect the scattering amplitudes arises. In fact, the sensitivity of the scattering amplitudes to the accuracy of the cluster functions has been discussed [21]. Accuracy of the cluster function ψ i in (4) must be at least an order of magnitude greater than the scattering function u.…”

“…We now turn to explore electron-hydrogen scattering and the effects of exchange on such a system as more configurations are added. This system has been studied extensively using varying approaches [19][20][21][22][23]. In the case of CCA, the singlet state recovers somewhere between 80% and 90% of the polarization effect using only the static approximation.…”

“…Hahn [10] critically examined this problem by parametrizing the ground state of the hydrogen atom in a nonlinear way. This model wave function of hydrogen was then used in the case of single channel elastic scattering of electrons by a hydrogen atom.…”

“…In the past, numerous attempts to extend the approach to scattering problems involving continuum (positiveenergy) orbitals have been made [7][8][9][10], but, no correspondingly satisfactory methods have been found until very recently [11,12]. The principal difficulties in extending the theory are well-known: (i) the non-normalizability of the continuum scattering function makes the SCF determination of the potentials inoperative, and (ii) the strong asymptotic boundary condition which requires exact target internal wave functions for all the open (allowed) channels.…”