  In our previous DWF calculation with the Wilson gauge action at $\beta=6.0$
($a^{-1}\simeq$ 1.9 GeV) on a $16^3 \times 32 \times 16$ lattice, we found that
$\Ga$ had a fairly strong dependence on the quark mass. A simple linear
extrapolation of $\Ga$ to the chiral limit yielded a value that was almost a
factor of two smaller than the experimental one. Here we report our recent
study of this issue. In particular, we investigate possible errors arising from
finite lattice volume, especially in the lighter quark mass region. We employ a
RG-improved gauge action (DBW2), which maintains very good chiral behavior even
on a coarse lattice ($a^{-1}\simeq$ 1.3 GeV), in order to perform simulations
at large physical volume ($> (2{\rm fm})^3$). Our preliminary results suggest
that the finite volume effect is significant.
