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We derive the upper limit on the dark matter (DM) fraction in primordialblack holes (PBHs) in the mixed DM scenarios. In this scenarios, a PBH canaccrete weakly interacting massive particles (WIMPs) to form a ultracompactminihalo (UCMH) with a density profile of $\rho_{\rm DM}(r)\sim r^{-9/4}$. Theenergy released from UCMHs due to dark matter annihilation has influence on thephotodissociation of $^{4}{\rm He}$, producing the $^{3}{\rm He}$ and the D. Byrequiring that the ratio $\rm (^3{He}+D)/H$ caused by UCMHs does not exceed themeasured value, we derive the upper limit on the dark matter fraction in PBHs.For the canonical value of DM thermally averaged annihilation cross section$\left<\sigma v\right>=3\times 10^{-26}\rm cm^{3}s^{-1}$, we find that theupper limit is $f_{\rm PBH} < 0.35(0.75)$ for DM mass $m_{\chi}=1(10)~\rm GeV$.Compared with other limits obtained by different astronomical measurements,although our limit is not the strongest, we provide a different way ofconstraining the cosmological abundance of PBHs.

Constraints on primordial black holes in the mixed dark matter scenarios using the ratio $\rm (^3{He}+D)/H$