Impacts of Hawking Radiation from Primordial Black Holes in Critical
  Collapse Model on the Light Element Abundances
  We study the photodisintegration process triggered by the nonthermal
electromagnetic Hawking radiation from primordial black holes (PBHs) in
critical collapse model. We consider the simplest case that all PBHs formed at
a single epoch stemming from an inflationary spectrum with a narrow peak, and
an extended mass distribution is obtained due to critical phenomena of
gravitational collapse. The presence of a low-mass tail of critical collapse
mass function could lead to an enhancement of energetic photon emissions from
Hawking radiation of PBHs. Nuclear photodisintegration rates are calculated
with a nonthermal photon spectrum derived by solving the Boltzmann equation
iteratively. The exact spectrum is much different than that based on an
often-used analytical bended power-law spectrum and it is found to
significantly depend on the adopted PBH mass functions. With the newest
observational limit on the $^3$He abundance in Galactic H II regions, the
updated $^3$He constraints on PBH mass spectrum in the horizon mass range
$10^{12} - 10^{13}$ g are derived. Our results for the first time show that
$^3$He constraints on the critical mass function are about one order of
magnitude severer than the monochromatic one although the fraction of PBHs in
the low-mass tail region is relatively small. The $^6$Li elemental abundance is
also enhanced significantly for the critical mass function. More precise
measurement of $^6$Li abundance is highly desirable to provide a promising
constraint on PBHs in the future. For monochromatic mass function, we provide
the analytical bounds for photodisintegration and hadrodissociation from PBH
radiation, and we report discrepancies between our updated $^3$He constraints
and the previous results.
