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.
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