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.