  We describe a practical procedure to calculate the Coulomb matrix elements of
2D spatially separated and confined charge carriers, which are needed for
detailed theoretical descriptions of important condensed matter finite systems.
We derive an analytical expression, for arbitrary separations, in terms of a
single infinite series and apply a u-type Levin transform in order to
accelerate the resulting infinite series. This procedure has proven to be
efficient and accurate. Direct consequences concerning the functional
dependence of the matrix elements on the separation distance, transition
amplitudes and the diagonalization of a single electron-hole pair in vertically
stacked parabolic quantum dots are presented.
