Hyperspherical hidden crossing calculation of Ps formation cross section for low-energy $\mbox{e}^+-\mbox{Li}$ collisions

Using the hyperspherical hidden crossing method (HHCM), we have computed the $s$-, $p$-, $d$- and $f$-wave Ps formation cross sections for $\mbox{e}^+-\mbox{Li}$ collisions in the energy range $0-1.8$eV.\footnote{ S.J. Ward and J. Shertzer, Phys. Rev. A \textbf{68}, 032720 (2003).}$^,$\footnote{ S.J. Ward and J. Shertzer, Nucl. Instr. and Meth. in Phys. Res. B \textbf{221}, 206 (2004).} We have also computed the partial wave cross sections by including a correction term to the HHCM that arises from the one-Sturmian theory ($\mbox{HHCM}^{+\mbox{cor}})$. The effect of including the core polarization term in the model potential was also investigated (HHCM$_{\mbox{cp,}} $ HHCM$_{\mbox{cp}}^{+\mbox{cor}} $ ). The Stuckelberg phase varied only slightly with the incident positron momentum and decreased in a systematic way with increasing partial wave $L.$ The $f$-wave contribution to the Ps formation cross section was significant near the Li(2$p)$ threshold. In all four calculations the cross section summed over the lowest four partial waves lies between the experimental measurements of the lower and upper limits.\footnote{ E. Surdutovich, J.M. Johnson, W.E. Kauppila, C.W. Kwan and T.S. Stein, Phys. Rev. A \textbf{65}, 032713 (2002); private communication.\par }