State selective total and angular differential cross sections for positronium formation in e+−He collisions

State-selective total and angular differential cross sections for positronium formation are presented in the collision of positron with helium atoms in their ground state by using the four-body formalism of the boundary-corrected continuum-intermediate-states approximation. The main purpose of the present study is to investigate the relative importance of intermediate ionization continuum states that has been incorporated with a suitable choice of distorting potential. In addition, the nine-dimensional integrals of the transition amplitude are analytically reduced to a one-dimensional real integral, which can be easily calculated numerically. The influence of the target static electron correlations on the capture probability is investigated using the different bound-state wave functions of He. The theoretical model for the calculation is fairly accurate and predicts a number of interesting features of the state-selective total and differential cross sections in the range of positron impact energy varies from 20 to $250\mathrm{eV}$. The total cross sections are highly peaked at an impact energy of 50 eV. The results are compared with those of other theories and the available experimental data. The present theoretical results and other measurements show satisfactory agreement in the wide energy range. Moreover, surface plots for the state-selective differential cross sections are also presented to illustrate the interesting feature of the positronium formation in this collision process.