We considered the Harris-Nesbet variational method for an accurate calculation of phase shifts in positron-He+ collisions. Calculations have been carried out for L = 0, 1, 2, 3, 4, 5, 6 partial waves. Very accurate results of phase shift have been obtained for the first time. The accuracy has been double-checked by carrying out the calculations with the use of different large-coupling schemes. We compare our results with those available in the literature.

The Harris–Nesbet variational method has been considered for the calculation of electron collisions with He+ at low energy. Calculations have been done for both singlet and triplet scattering. Very accurate results of phase shift have been obtained, for the first time, for partial waves with L equal to up to six. The results of the present calculation are compared with those available in the literature that have been calculated by other research groups employing various numerical methods.

The Harris-Nesbet variational method has been considered for an accurate calculation of positron collisions with hydrogen-like ions. We applied our newly developed computer code for positron collisions with hydrogen-like ions to a benchmark calculation at energies below the first excitation threshold of the ions. Very accurate results of phase shift have been obtained for the first time for partial-wave scattering from various hydrogen-like ion targets, with L equal up to 6. The accuracy of the results has been double-checked by carrying out calculations using different large coupling schemes. Our results were compared with those calculated by other research groups who had employed different numerical methods for their calculations.

Sequences of S, P and D resonances in positron - hydrogen scattering were shown to still exist below the n = 2 H excitation threshold in a coupled-state calculation employing a large coupling scheme. The positions of the resonances were found to shift slightly away from the threshold and their widths to broaden slightly, compared with those previously determined with smaller schemes. The energy ratios and width ratios of the successive resonances of a sequence still reasonably satisfy the predicted `scaling law'.

An algebraic coupled-state calculation of positron-hydrogen scattering carried out with an enlarged eightstate ͑E8S͒ coupling scheme, that is composed of a sufficiently high number of short-ranged correlation terms and eight hydrogen and positronium states ͓(1s,2s,2p,3p)HϪ(1s,2s,2p,3p)Ps͔, provides results of the phase shift and cross section, agreeing excellently with our accurate enlarged six pseudostate ͑E6PS͒ values in both e ϩ -H and Ps(1s)-p entrance channels. Our results serve to assert that very accurate values of the phase shift and cross section in both entrance channels have been attained with our E6PS, E8PS, and E8S Harris-Nesbet calculations. The present E8S calculation supersedes our deficient modified enlarged six-state one done previously.