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The experimental searches for diffuse supernova neutrino background andproton decay in next-generation large liquid-scintillator (LS) detectors arecompetitive with and complementary to those in the water-Cherenkov detectors.In this paper, we carry out a systematic study of the dominant backgroundinduced by atmospheric neutrinos via their neutral-current (NC) interactionswith the $^{12}{\rm C}$ nuclei in the LS detectors. The atmospheric neutrinofluxes at the location of Jiangmen Underground Neutrino Observatory (JUNO) areused, as the JUNO detector is obviously a suitable representative for future LSdetectors. Then, we implement the sophisticated generators \texttt{GENIE} and\texttt{NuWro} to simulate the neutrino interactions with the carbon nuclei,and the package \texttt{TALYS} to deal with the deexcitations of final-statenuclei. Finally, the event rates for the production of additional nucleons,$\gamma$'s, $\alpha$'s, pions and kaons are obtained and categorized, and thesystematic uncertainty of the NC background represented by a variety ofdata-driven nuclear models is estimated. The implications of the NC backgroundfrom atmospheric neutrinos for the detection of diffuse supernova neutrinobackground and proton decay are also discussed.

Neutral-current background induced by atmospheric neutrinos at large liquid-scintillator detectors: I. model predictions