Elastic positron and electron scattering from helium using a one-electron model potential

We have computed Kohn and inverse Kohn S- and P-wave phase shifts for positron-helium scattering using a one-electron model potential [1,2] for the helium atom. Using the S- and P-wave variational phase shifts and D- and F-wave phase shifts determined from the O’Malley et al. effective range theory (ERT) [3] we have calculated the elastic-integrated, elastic-differential, and momentum-transfer cross sections. We found that the S- and P-wave phase shifts generally agree well with Kohn and inverse Kohn variational phase shifts in which helium is treated fully as a two-electron atom [4].

Currently, we are using the one-electron model potential for elastic electron-helium scattering. Using the Kohn and inverse Kohn variational methods we are calculating the S-wave phase shifts and we plan to compute the P-wave. Using these phase shifts and the D- and F-wave partial waves evaluated from the O’Malley et al. ERT we plan to compute cross sections for electron-helium scattering and to compare them with the corresponding ones for positron scattering.

[1] J. T. Dunn, P. Van Reeth, J. W. Humberston, and G. Peach, J. Phys. B 33, 2589 (2000).

[2] G. Peach, Private Communications (2014, 2022).

[3] T. O’Malley, L. Spruch, and L. Rosenburg, J. Math Phys. 2, 4 (1961).

[4] P. Van Reeth and J. W. Humberston, J. Phys. B 32, 3651 (1999).