  The proportionality between single charge-exchange reaction cross sections in
the forward direction as found, for example from $(p,n)$ and $(^3$He,$t)$ and
from $(n,p)$ and $(d,^2$He) reactions, and the Gamow-Teller (GT) strength into
the same final nuclear states has been studied and/or assumed often in the
past. Using the most physically justified theory we have at our disposal and
for the specific example of the ${}^{76}$Ge-${}^{76}$Se system that may undergo
double beta-decay, we demonstrate that the proportionality is a relative good
assumption for reactions changing a neutron into a proton, i.e.
${}^{76}$Ge$(p,n){}^{76}$As. In this channel, the main contribution to the GT
strengths comes from the removal of a neutron from an occupied single-particle
(SP) state and putting a proton into an unoccupied SP state having either the
same state quantum numbers or those of the spin-orbit partner. In contrast to
this, in the second leg of the double beta decay a single proton must be taken
from an occupied SP state and a neutron placed in an unoccupied one. This
second process often is Pauli forbidden in medium-heavy nuclei and only can be
effected if the Fermi surface is smeared out. Such is the case for
${}^{76}$Se$(n,p){}^{76}$As. Our results suggest that one may not always assume
a proportionality between the forward-angle cross sections of the
charge-exchange reactions and the GT strength in any such medium-heavy nuclei.
The discrepancy originates from a pronounced effect of the radial dependence of
the nucleon-nucleon ($NN$) interaction in connection with the Pauli principle
on the cross sections in the $(n,p)$ reaction channel. Such a radial dependence
is completely absent in the GT transition operator.
