Electron capture and excitation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>He</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>He</mml:mi> </mml:mrow> </mml:math

We present theoretical results on state-selective total and angular-differential cross sections for single-electron-capture and excitation occurring in the ${\mathrm{He}}^{+}+\mathrm{He}$ collisions using the four-body boundary-corrected continuum intermediate state approximation in both prior and post forms. The theoretical cross sections are reported in the energy range of 50--2500 keV/amu. The purpose of the present study is to investigate the relative importance of the intermediate ionization continuum of the two electrons in the projectile and target. In the prior form, the effect of the dynamic electron-electron correlation is taken into account through the complete perturbation potentials. In this form, the final channel is described by the Coulomb continuum states of the electrons and projectile in the field of the target. Similarly, in the post form, the interaction of the electrons with the target and projectile is represented by the Coulomb continuum functions. The initial state of the two electrons in helium is considered to be a one-active-electron target. Therefore, the initial state of the active electron is described by the Roothaan-Hartree-Fock wave function, which is a more sophisticated single-electron wave function for the target. State-selective total and angular-differential cross sections are presented and compared with experimental and previous theoretical data where available. The differential cross sections exhibit minima and maxima in the projectile scattering angles, which are more pronounced in the region of high impact energy. The position of such minima moves towards smaller scattering angles. This structure demonstrates quantum matter wave scattering in atomic collision physics. We also investigated the projectile excitation for the same collision and compared it with other theoretical models.