  We developed the deformed proton-neutron quasiparticle random phase
approximation (QRPA) and applied to the evaluation of the Gamow-Teller (GT)
transition strength distributions including high-lying excited states, which
data becomes recently available beyond one or two nucleon threshold by charge
exchange reactions using hundreds of MeV projectiles. Our calculations started
with single-particle states calculated by a deformed axially symmetric
Woods-Saxon potential. Neutron-neutron and proton-proton pairing correlations
are explicitly taken into account at the deformed Bardeen Cooper Schriffer
theory. Ground state correlations, and two-particle and two-hole mixing states
are included in the deformed QRPA. In this work, we use a realistic two-body
interaction given by the Brueckner $G$-matrix based on the CD Bonn potential to
reduce the ambiguity on the nucleon-nucleon interactions inside nuclei. We
applied our formalism to the GT transition strengths for $^{76}$Ge,
$^{76,82}$Se, and $^{90,92}\textrm{Zr}$, and compared to available experimental
data. The GT strength distributions were sensitive on the deformation parameter
as well as its sign, {\it i.e.}, oblate or prolate. The Ikeda sum rule, which
is usually thought to be satisfied under the one-body current approximation
irrespective of nucleon models, is used to test our numerical calculations and
shown to be satisfied without introducing the quenching factor, if high-lying
GT excited states are properly taken into account. Most of the GT strength
distributions of the nuclei considered in this work turn out to have the
high-lying GT excited states beyond one nucleon threshold, which are shown to
be consistent with available experimental data.
