Elastic D- and higher-partial-wave phase shifts in positron-hydrogen-atom collisions using Schwinger's principle.

Abstract

The Schwinger variational K matrix is used in the momentum space to calculate D- and higher-partial-wave phase shifts for the elastic scattering of positrons from atomic hydrogen below the pickup threshold in a discrete basis-set expansion, \ensuremath{\Vert}${\mathit{u}}_{\mathit{n}}$〉 =\ensuremath{\Vert}[1-exp(-${\mathit{pr}}_{1}$)](1+${\mathit{r}}_{1}$/2)exp(i${\mathbf{k}}_{\mathit{i}}$\ensuremath{\cdot}${\mathbf{r}}_{1}$)${\mathrm{\ensuremath{\varphi}}}_{\mathit{i}}$(${\mathbf{r}}_{2}$) /(${\mathit{r}}_{12}$+a${)}^{\mathit{n}}$〉 (n=1, . . .N). The values of the Schwinger D-wave phase shifts are found to be in close agreement with the Kohn variational results as for the S- and P-wave phase shifts. To the best of our knowledge, there are no other variational calculations for the higher-partial-wave phase shifts for l\ensuremath{\ge}3. We have made use of these Schwinger variational phase shifts to compute accurate elastic differential and total cross sections at several positron energies. The differential cross section exhibits a sharp minimum at an intermediate scattering angle for incident momenta ${\mathit{k}}_{\mathit{i}}$>0.3 a.u.