<p>The energy correlations of prompt fission neutrons have not yet been considered in the related coincidence and multiplication measurement techniques. To measure and verify the energy correlations, an experiment was performed with a total measurement duration of approximately 1200&#xa0;h. In the experiment, eight CLYC detectors and sixteen EJ309 liquid scintillation detectors were utilized, and the fission moment was tagged with the measured fission <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-rays. The relative ratios of the energy spectra of the neutrons correlated with different energy neutrons to the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(^{252}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>252</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Cf fission neutron energy spectra were obtained. The present results may be helpful for studying fission physics and nuclear technology applications.</p>