  Neutrino-induced reactions on $^{40}$Ar are investigated by shell model for
Gamow-Teller transitions and random-phase-approximation (RPA) for forbidden
transitions. For the 1$^{+}$ multipole, an effective interaction in $sd$-$pf$
shell obtained by the extended Kuo-Krenciglowa (EKK) method from chiral
interactions is used to study $B(GT)$, charged-current reaction $^{40}$Ar
($\nu_e$, $e^{-}$) $^{40}$K, $B(M1)$ in $^{40}$Ar and neutral-current reaction
$^{40}$Ar ($\nu$, $\nu$') $^{40}$Ar. A considerable quenching for spin modes is
found in the analysis of $B(M1)$, and this quenching is taken into account for
the evaluation of the cross sections of the neutral-current reaction. The
sensitive dependence of the reaction cross sections on the quenching of the
axial-vector coupling constant, $g_A$, is pointed out.
