  Charge-exchange reactions are an important tool for determining
weak-interaction rates. They provide stringent tests for nuclear structure
models necessary for modeling astrophysical environments such as neutron stars
and core-collapse supernovae. In anticipation of (t,3He) experiments at 115
MeV/nucleon on nuclei of relevance (A~40-120) in the late evolution of stars,
it is shown via a study of the 26Mg(t,3He) reaction that this probe is an
accurate tool for extracting Gamow-Teller transition strengths. To do so, the
data are complemented by results from the 26Mg(3He,t) reaction at 140
MeV/nucleon which allows for a comparison of T=2 analog states excited via the
mirror reactions. Extracted Gamow-Teller strengths from 26Mg(t,3He) and
26Mg(3He,t) are compared with those from 26Mg(d,2He) and 26Mg(p,n) studies,
respectively. A good correspondence is found, indicating probe-independence of
the strength extraction. Furthermore, we test shell-model calculations using
the new USD-05B interaction in the sd-model space and show that it reproduces
the experimental Gamow-Teller strength distributions well. A second goal of
this work is to improve the understanding of the (t,3He) and (3He,t) reaction
mechanisms at intermediate energies since detailed studies are scarce. The
Distorted-Wave Born Approximation is employed, taking into account the
composite structures of the 3He and triton particles. The reaction model
provides the means to explain systematic uncertainties at the 10-20% level in
the extraction of Gamow-Teller strengths as being due to interference between
Gamow-Teller dL=0, dS=1 and dL=2, dS=1 amplitudes that both contribute to
transitions from 0+ to 1+ states.
