  We conducted systematic observations of the HI Br-alpha line (4.05 micron)
and the polycyclic aromatic hydrocarbon (PAH) feature (3.3 micron) in 50 nearby
(z<0.3) ultraluminous infrared galaxies (ULIRGs) with AKARI. The Br-alpha line
is predicted to be the brightest among the HI lines under high dust-extinction
conditions (A_V>15 mag). The Br-alpha line traces ionizing photons from OB
stars and so is used as an indicator of star formation on the assumption of the
initial mass function. We detected the Br-alpha line in 33 ULIRGs. The
luminosity of the line (L_BrA) correlates well with that of the 3.3 micron PAH
emission (L_3.3). Thus we utilize L_3.3 as an indicator of star formation in
fainter objects where the Br-alpha line is undetected. The mean L_BrA/L_IR
ratio in LINERs/Seyferts is significantly lower than that in HII galaxies. This
difference is reconfirmed with the L_3.3/L_IR ratio in the larger sample (46
galaxies). Using the ratios, we estimate that the contribution of starburst in
LINERs/Seyferts is ~67%, and active galactic nuclei contribute to the remaining
~33%. However, comparing the number of ionizing photons, Q_BrA, derived from
L_BrA with that, Q_IR, expected from star formation rate required to explain
L_IR, we find that the mean Q_BrA/Q_IR ratio is only 55.5+/-7.5% even in HII
galaxies which are thought to be energized by pure starburst. This deficit of
ionizing photons traced by the Br-alpha line is significant even taking heavy
dust extinction into consideration. We propose that dust within HII regions
absorbs a significant fraction of ionizing photons.
