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The light output function of a φ50.8 mm×50.8 mm BC501A scintillation detector was measured in the neutron energy region of 1 to 30 MeV by fitting the pulse height (PH) spectra for neutrons with the simulations from the NRESP code at the edge range. Using the new light output function, the neutron detection efficiency was determined with two Monte-Carlo codes, NEFF and SCINFUL. The calculated efficiency was corrected by comparing the simulated PH spectra with the measured ones. The determined efficiency was verified at the near threshold region and normalized with a Proton-Recoil-Telescope (PRT) at the 8-14 MeV energy region.