  Neutrino reactions on $^{40}$Ar via charged and neutral currents for
detecting solar and core collapsing supernovae (SNe) neutrinos and the Gamow
Teller strength are calculated by considering the high-lying excited states up
to a few tens of MeV region. The nucleus was originally exploited to identify
the solar neutrino emitted from $^{8}$B produced in the pp-chains on the Sun.
With the higher energy neutrinos emitted from the core collapsing SNe,
contributions from higher multi-pole transitions including the spin dipole
resonances (SDR) as well as the Gamow Teller (GT) and Fermi transitions are
shown to be important ingredients for understanding reactions induced by the
SNe as well as solar neutrinos. In this work, we focused on the role of
high-lying excited states which are located beyond a few low-lying states known
in the experiment. Expected large difference between the cross sections of
$\nu_e$ and ${\bar \nu_e}$ reactions on $^{40}$Ar, which difference has been
anticipated in previous calculations because of the large Q value in the ${\bar
\nu}_e$ reaction, is significantly diminished. The reduction leads only to
about 2 times difference between them. Our calculations are carried out by the
Quasi-particle Random Phase Approximation (QRPA), which takes account of the
neutron-proton pairing as well as proton-proton and neutron-neutron pairing
correlations. They were successfully applied in the description of the nuclear
beta decay and relevant neutrino reaction data on $^{12}$C and $^{56}$Fe, and
the GT data on the $^{138}$La and $^{180}$Ta.
