The S-wave elastic scattering of positrons by helium in the coupled static approximation

S-wave phase shifts for the positron-helium elastic scattering problem are presented in the coupled static approximation ( i.e. the trial function contains the ground states of both the target atom and positronium but no other terms). Various models of the target atom wavefunction are employed, two of which confirm qualitatively the marked effect on the results as reported by Wardle (1973) for these models. While none of the target models used in this approximation appears to lead to an adequate description of the system, as is also the case in positron-hydrogen scattering in the same approximation, a qualitative comparison of the best results presented here and the corresponding approximation in the hydrogen case suggests a manageable calculation with two open channels (i.e. with real positronium formation) could produce meaningful results.