Correlations between energy and $\gamma$-ray emission in ${}^{239}\mathrm{P}\mathrm{u}(n,\mathrm{f})$

We study $\gamma$-ray emission following ${}^{239}\mathrm{P}\mathrm{u}(n,\mathrm{f})$ over an incident neutron energy range of $2<E_i<40$ MeV. We present the first experimental evidence for positive correlations between the total angular momentum generated in fission and the excitation energy of the compound nucleus prior to fission. The $\gamma$-ray multiplicity increases linearly with incident energy below the 2\textsuperscript{nd}-chance fission threshold with a slope of $0.085\pm 0.010$ MeV${}^{-1}$. This linear trend appears to hold for the average excitation energy of the compound nucleus between $9<⟨E_x⟩<19$ MeV. Most of the multiplicity increase comes from an enhancement around a $\gamma$-ray energy of 0.7 MeV, which we interpret as stretched quadrupole $\gamma$ rays that indicate an increase in total fission-fragment angular momentum with excitation energy.