Background: Organic scintillators are widely used for neutron detection in both basic nuclear physics and applications. While the proton light yield of organic scintillators has been extensively studied, measurements of the light yield from neutron interactions with carbon nuclei are scarce. Purpose: Demonstrate a new approach for the simultaneous measurement of the proton and carbon light yield of organic scintillators. Provide new carbon light yield data for the EJ-309 liquid and EJ-204 plastic organic scintillators. Method: A 33~MeV $^{2}$H$^{+}$ beam from the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory was impinged upon a 3-mm-thick Be target to produce a high-flux, broad-spectrum neutron beam. The double time-of-flight technique was extended to simultaneously measure the proton and carbon light yield of the organic scintillators, wherein the light output associated with the recoil particle was determined using $np$ and $n$C elastic scattering kinematics. Results: The proton and carbon light yield relations of the EJ-309 liquid and EJ-204 plastic organic scintillators were measured over a recoil energy range of approximately 0.3 to 1~MeV and 2 to 5~MeV, respectively for EJ-309, and 0.2 to 0.5~MeV and 1 to 4~MeV, respectively for EJ-204. Conclusions: These data provide new insight into the ionization quenching effect in organic scintillators and key input for simulation of the response of organic scintillators for both basic science and a broad range of applications.
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