It is shown via a study on a Mg-26 target that the (t,He-3) reaction at 115 MeV/nucleon reaction is an accurate probe for extracting Gamow-Teller transition strengths. To do so, the data are complemented by results from the Mg-26(He-3, t) reaction at 140 MeV/nucleon that allows for a comparison of T=2 analog states excited via the mirror reactions. Extracted Gamow-Teller strengths from Mg-26(t,He-3) and Mg-26(He-3, t) are compared with those from Mg-26(d,He-2) and Mg-26(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. In anticipation of further (t,He-3) experiments on medium-heavy nuclei aimed at determining weak-interaction rates of relevance for stellar evolution, a second goal of this work is to improve the understanding of the (t,He-3) and (He-3, t) reaction mechanisms at intermediate energies because detailed studies are scarce. The distorted-wave Born approximation is employed, taking into account the composite structures of the He-3 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 because of interference between Gamow-Teller Delta L=0,Delta S=1 and Delta L=2,Delta S=1 amplitudes that both contribute to transitions from 0(+) to 1(+) states.
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