Superfluid $^4$He is a promising target material for direct detection of light ($<$ 1 GeV) dark matter. Possible signal channels available for readout in this medium include prompt photons, triplet excimers, and roton and phonon quasiparticles. The relative yield of these signals has implications for the sensitivity and discrimination power of a superfluid $^4$He dark matter detector. Using a 16 cm$^3$ volume of 1.75 K superfluid $^4$He read out by six immersed photomultiplier tubes, we measured the scintillation from electronic recoils ranging between 36.3 and 185 keV$_mathrm{ee}$, yielding a mean signal size of $1.12^{+0.02}_{-0.03}$ phe/keV$_mathrm{ee}$, and nuclear recoils from 53.2 to 1090 keV$_mathrm{nr}$. We compare the results of our relative scintillation yield measurements to an existing semi-empirical model based on helium-helium and electron-helium interaction cross sections. We also study the behavior of delayed scintillation components as a function of recoil type and energy, a further avenue for signal discrimination in superfluid $^4$He.
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