We investigate the problem of two-electron capture from heliumlike ato
mic systems by bare nuclei Z(p)+(Z(T);e1,e2)i-->(Z(p);e1,e2)f+Z(T) at
high incident energies, using the four-body formalism of the first- an
d second-order theories. Our goal is to establish the relative importa
nce of the intermediate ionization continua of the two electrons in co
mparison with the usual direct path of the double electron transfer. F
or this purpose we presently introduce the boundary-corrected continuu
m-intermediate-state (BCIS) approximation, which preserves all the fea
tures of two-electron capture as a genuine four-body problem. The prop
osed second-order theory provides a fully adequate description of the
fact that, in an intermediate stage of collision, both electrons move
in the field of the two Coulomb centers. The previously devised bounda
ry-corrected first Born (CB1) approximation can be obtained as a furth
er simplification of the BCIS model if the invoked two-electron Coulom
b waves are replaced by their long-range logarithmic phase factors def
ined in terms of the corresponding interaggregate separation R. The BC
IS method is implemented on the symmetric resonant double charge excha
nge in collisions between alpha particles and He(1s2) at impact energi
es E greater-than-or-equal-to 900 keV. The obtained results for the di
fferential and total cross sections are compared with the available ex
perimental data and satisfactory agreement is recorded. As the inciden
t energy increases, a dramatic improvement is obtained in going from t
he CB1 to the BCIS approximation, since the latter closely follows the
measurement, whereas the former overestimates the observed total cros
s sections by two orders of magnitude.