  The proportionality between differential cross sections at vanishing linear
momentum transfer and Gamow-Teller transition strength, expressed in terms of
the \textit{unit cross section} ($\hat{\sigma}_{GT}$) was studied as a function
of target mass number for ($t$,$^{3}$He) and ($^{3}$He,$t$) reactions at 115
$A$MeV and 140 $A$MeV, respectively. Existing ($^{3}$He,$t$) and ($t$,$^{3}$He)
data on targets with mass number $12\leq A\leq 120$ were complemented with new
and reevaluated ($t$,$^{3}$He) data on proton, deuteron, $^{6}$Li and $^{12}$C
targets. It was found that in spite of the small difference in beam energies
between the two probes, the unit cross sections have a nearly identical and
simple dependence on target mass number $A$, for $A\geq 12$:
$\hat{\sigma}_{GT}=109/A^{0.65}$. The factorization of the unit cross sections
in terms of a kinematical factor, a distortion factor and the strength of the
effective spin-isospin transfer nucleus-nucleus interaction was investigated.
Simple phenomenological functions depending on mass number $A$ were extracted
for the latter two. By comparison with plane and distorted-wave Born
approximation calculations, it was found that the use of a short-range
approximation for knock-on exchange contributions to the transition amplitude
results in overestimated cross sections for reactions involving the composite
($^{3}$He,$t$) and ($t$,$^{3}$He) probes.
