  The so-called "acoustic revival mechanism" of core-collapse supernova
proposed recently by the Arizona group is an interesting new possibility.
Aiming to understand the elementary processes involved in the mechanism, we
have calculated the eigen frequencies and eigen functions for the g-mode
oscillations of a non-rotating proto neutron star. The possible excitation of
these modes by the standing accretion shock instability, or SASI, is discussed
based on these eigen functions. We have formulated the forced oscillations of
$g$-modes by the external pressure perturbations exerted on the proto neutron
star surface. The driving pressure fluctuations have been adopted from our
previous computations of the axisymmetric SASI in the non-linear regime. We
have paid particular attention to low l modes, since these are the modes that
are dominant in SASI and that the Arizona group claimed played an important
role in their acoustic revival scenario. Here l is the index of the spherical
harmonic functions, $Y_l^m$. Although the frequency spectrum of the non-linear
SASI is broadened substantially by non-linear couplings, the typical frequency
is still much smaller than those of g-modes, the fact leading to a severe
impedance mismatch. As a result, the excitations of various $g$-modes are
rather inefficient and the energy of the saturated g-modes is $\sim 10^{50}$erg
or smaller, with the g_2-mode being the largest in our model. Here the g_2-mode
has two radial nodes and is confined to the interior of the convection region.
The energy transfer rate from the g-modes to out-going sound waves is estimated
from the growth of the g-modes and found to be $\sim 10^{51}$erg/s in the model
studied in this paper.
