Experimental Investigation of Multiplicity Correlation Between Prompt Neutrons and Photons in the Spontaneous Fission of $^{252}$Cf
Excited nuclear fragments are emitted during nuclear fission. The de-excitation of fission fragments takes place as sequential emission of neutrons followed by photons. Particle emission dissipates the intrinsic and rotational excitation energies of the fragment until a long-lived state is reached. Both the number of neutrons and the number of photons emitted during de-excitation are dependent on the initial excitation energy, angular momentum, and parity of the radiating fission fragment. A correlation between neutron and photon multiplicities following fission is thus expected. We perform linear regression analysis of the data collected by the Chi-Nu array at the LANSCE facility in Los Alamos National Laboratory. We have developed analytic expressions to determine the bias introduced by background sources and the misclassification of particles by our pulse shape discrimination capable organic scintillation detectors. Additionally, we have developed perturbative techniques to derive corrections to the binomial-response model. We use the perturbative techniques to correct the experimentally-determined neutron-photon correlations for the effects of photon-neutron pileup. We have experimentally determined an event-by-event covariance, $\text{cov}(N_n,N_\gamma)$, of $-0.33 \pm 0.05$ between the neutron and photon multiplicities emitted following the spontaneous fission of $^{252}$Cf. The result suggests the existence of a small event-by-event competition of neutron and photon emission in fission. We compare our result with previous analyses and model calculations.