The shake-off mechanism, known in photon impact, has been applied to t
he analysis of two-electron transitions in slow ion-atom collisions. T
he mechanism consists of relaxation of the electronic state of an oute
r target electron upon relocalization of the inner-electron wave funct
ion from the target to projectile nucleus. Based on this mechanism, a
method is proposed to estimate cross sections of two-electron processe
s. The method is demonstrated by calculating cross sections of double
capture, transfer excitation, and transfer ionization for collisions o
f the excited He (1s2l) atom with the B5+ ion. The dependence of the c
ross sections of double capture and transfer excitation on the princip
al quantum number n of the final state is presented.