A coalescence model was employed to form deuterons (d), tritons (t), and helium-3 ( \(^3{\textrm{He}}\) ) nuclei from a uniformly-distributed volume of protons (p) and neutrons (n). We studied the ratio \(N_\textrm{t}N_\textrm{p}/N_\textrm{d}^2\) of light nuclei yields as a function of the neutron density fluctuations. We investigated the effect of finite transverse momentum ( \(p_{\textrm{T}}\) ) acceptance on the ratio, in particular, the “extrapolation factor” (f) for the ratio as a function of the \(p_{\textrm{T}}\) spectral shape and the magnitude of neutron density fluctuations. The nature of f was found to be monotonic in \(p_{\textrm{T}}\) spectra “temperature” parameter and neutron density fluctuation magnitude; variations in the latter are relatively small. We also examined f in realistic simulations using the kinematic distributions of protons measured from the heavy-ion collision data. The nature of f was found to be smooth and monotonic as a function of the beam energy. Therefore, we conclude that extrapolation from limited \(p_{\textrm{T}}\) ranges does not create, enhance, or reduce the local peak of the \(N_\textrm{t}N_\textrm{p}/N_\textrm{d}^2\) ratio in the beam energy. Our study provides a necessary benchmark for light nuclei ratios as a probe for nucleon density fluctuations, an important observation in the search for the critical point of nuclear matter.
