A high-accuracy analytical method is broadly required to obtain reliable research results. Thus, prompt γ-ray analysis (PGA), one of the most accurate non-destructive analytical methods, has been employed in various fields. However, the measurement accuracy of PGA is also known to degrade in hydrogenous samples. The degradation is caused by variation in the measurement sensitivity (counts per milligram) following the change in neutron energy due to scattering with hydrogen nucleus. Number of scatterings is well known to depend on the hydrogen content in a sample. However, considering multiple scatterings, hydrogen density, which has not been taken into account as yet, may also lead to the accuracy degradation. Here, we show the effect of the hydrogen density in PGA by evaluating the measurement sensitivity of samples with the same hydrogen content and different densities. We find that the measurement sensitivity varies by more than 30% depending on the hydrogen density even at the same hydrogen content. The variation is a particularly serious problem for PGA requiring a few percent accuracy in most cases. Additionally, although the variation is apparently observed in hydrogenous samples, the similar phenomenon can occur in other nuclides with a large scattering cross section; it may affect nuclear cross-section measurements using neutrons in such fields as astrophysics and nuclear energy.