  We produce a catalogue of polycyclic aromatic hydrocarbon (PAH) 3.3 $\mu$m,
Br$\alpha$ and infrared luminosity ($L$(IR)) of 412 local galaxies, and
investigate a relation between these physical parameters. We measure the PAH
3.3 $\mu$m and Br$\alpha$ flux using AKARI 2-5 $\mu$m spectra and the $L$(IR)
using the AKARI-all-sky-survey data. The $L$(IR) and redshift ranges of our
sample are $L$(IR)=$10^{9.7-12.8}$L$_\odot$ and $z_{\rm spec}=0.002-0.3$,
respectively. We found that the ratio of $L$(PAH 3.3 $\mu$m) to $L$(IR) is
constant at $L$(IR) $<$ $10^{11} \rm L_\odot$ whereas it decreases with the
$L$(IR) at higher $L$(IR). Also, the ratio of $L$(Br$\alpha$) to $L$(IR)
decreases with the $L$(IR). The both $L$(PAH)/$L$(IR) and
$L$(Br$\alpha$)/$L$(IR) ratios are not strongly dependent on galaxy type and
dust temperature. The relative weakness of the two ratios could be attributed
to destruction of PAH, a lack of UV photons exciting PAH molecules or ionising
hydrogen gas, extremely high dust attenuation, or active galactic nucleus
contribution to the $L$(IR). Although we cannot determine the cause of the
decreases of the luminosity ratios, a clear correlation between them implies
that they are related with each other. The catalogue presented in our work will
be available at the AKARI archive web page.
