Nuclear charge-exchange reactions at intermediate energies are powerful probes of the isovector response of nuclei. They provide an opportunity to study isovector giant resonances, such as the Gamow-Teller resonance and the isovector giant monopole and dipole resonances. The properties of these giant resonances provide important insights into the bulk properties of nuclear matter and have important implications for neutrino and astrophysics. In this work, the focus is on the investigation of the properties of isovector giant resonances excited via the \isotope[60]{Ni}(\isotope[3]{He},$t$) reaction at 140 MeV/u up to excitation energies of 60 MeV to study the Gamow-Teller resonance, isobaric analog state, isovector (spin) monopole, dipole, and quadrupole giant resonances.The (\isotope[3]{He},$t$) reaction was used as an isovector probe to investigate the properties of isovector giant resonances in \isotope[60]{Cu}. To investigate these isovector giant resonances, the analysis was done through a multiple decomposition analysis (MDA). The differential cross sections were fitted with a linear combination of the distorted wave Born approximation (DWBA) angular distributions associated with different angular momentum transfer $\Delta L$. The angular distributions were calculated in DWBA by using the code package FOLD code. Different giant resonances were seen at different excitation energies. The results were compared with shell-model, and normal-mode calculations.It was found that the Gamow-Teller strengths extracted from the experiment could be reproduced reasonably well by the shell-model calculations. The extraction of the isovector dipole and monopole resonances was complicated by the presence of the quasi-free continuum. A detailed extraction of the isovector monopole resonances was not possible. For isovector dipole resonance, a reasonable consistency was found with the normal-mode calculations, after applying a simple estimate for the contributions from the quasifree continuum. Overall, this work provides valuable insights into the properties of isovector giant resonances, highlights the importance of continuum subtraction, and provides a detailed analysis of the (\isotope[3]{He},$t$) reaction for probing these resonances at high excitation energies.
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