Non-perturbative B-spline R-matrix with pseudo-states calculations for electron-impact excitation-ionization of helium to the n = 3 states of He$^+$

We present fully-differential cross sections for electron-impact ionization plus simultaneous excitation of helium obtained from a non-perturbative close-coupling formalism with our B-spline R-matrix approach [1,2]. Using a large number of pseudo-states we obtain excellent agreement with directly measured cross-section ratios [3,4] for ionization leaving the residual He$^+$ ion in either the $1s$ ground state, the $n = 2$ ($2s + 2p$) excited states, or the $n = 3$ \hbox{($3s + 3p + 3d$)} excited states.\\[4pt] [1]~O.\ Zatsarinny and \hbox{K.\ Bartschat}, \hbox{Phys.\ Rev.\ Lett.\ {\bf 107}} (2011) 023203.\\[0pt] [2]~\hbox{O.\ Zatsarinny} and \hbox{K.\ Bartschat}, \hbox{J.\ Phys.\ B {\bf 47}} (2014) 061001.\\[0pt] [3]~S.~Bellm {\it et al.}, \hbox{Phys.\ Rev.\ A {\bf 75}} (2007) 042704.\\[0pt] [4]~S.~Bellm {\it et al.}, \hbox{Phys.\ Rev.\ A {\bf 78}} (2008) 032710.