  We describe the importance of charge-exchange reactions, and in particular
Gamow-Teller transitions, in astrophysical processes and double beta decay, and
in understanding of nuclear structure. We first provide an overview of the
central role played by the isovector pairing and the quadrupole-quadrupole
channels in the description of energy spectra and in the manifestation of
collective modes, some associated with deformation of the nuclear shape. We
then turned our focus to Gamow-Teller (GT) transitions in relatively light
nuclei, especially in the 2p1f shell, where isoscalar pairing may be playing a
role in competition with the isovector pairing that dominates in heavier
regions. Following a summary of the progress made in recent years on this
subject, we report a systematic shell model study aimed at providing further
clarification as to how these pairing modes compete. In this study, we use a
schematic Hamiltonian that contains a quadrupole-quadrupole interaction as well
as both isoscalar and isovector pairing interactions. We first find an optimal
set of Hamiltonian parameters for the model, to provide a starting point from
which to vary the relevant pairing strengths and thus assess how this impacts
the behavior of GT transitions and the corresponding energy spectra and
rotational properties of the various nuclei involved in the decays. The
analysis includes as an important theme a comparison with experimental data.
The need to suppress the isoscalar pairing mode when treating nuclei with a
neutron excess to avoid producing spurious results for the ground state spin
and parity with the simplified Hamiltonian is highlighted. Varying the strength
parameters for the two pairing modes is found to exhibit different but
systematic effects on GT transition properties and on the corresponding energy
spectra, which are detailed. (abridged)
