Neutron-neutron angular correlations in spontaneous fission of ${}^{252}\mathrm{Cf}$ and ${}^{240}\mathrm{Pu}$

Background: Angular anisotropy has been observed between prompt neutrons emitted during the fission process. Such an anisotropy arises because the emitted neutrons are boosted along the direction of the parent fragment.

Purpose: To measure the neutron-neutron angular correlations from the spontaneous fission of ${}^{252}\mathrm{Cf}$ and ${}^{240}\mathrm{Pu}$ oxide samples using a liquid scintillator array capable of pulse-shape discrimination. To compare these correlations to simulations combining the Monte Carlo radiation transport code MCNPX with the fission event generator FREYA.

Method: Two different analysis methods were used to study the neutron-neutron correlations with varying energy thresholds. The first is based on setting a light output threshold while the second imposes a time-of-flight cutoff. The second method has the advantage of being truly detector independent.

Results: The neutron-neutron correlation modeled by FREYA depends strongly on the sharing of the excitation energy between the two fragments. The measured asymmetry enabled us to adjust the FREYA parameter $x$ in ${}^{240}\mathrm{Pu}$, which controls the energy partition between the fragments and is so far inaccessible in other measurements. The ${}^{240}\mathrm{Pu}$ data in this analysis was the first available to quantify the energy partition for this isotope. The agreement between data and simulation is overall very good for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ and ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$.

Conclusions: The asymmetry in the measured neutron-neutron angular distributions can be predicted by FREYA. The shape of the correlation function depends on how the excitation energy is partitioned between the two fission fragments. Experimental data suggest that the lighter fragment is disproportionately excited.

Figure 1

Photograph of the 77 liquid scintillator array on low mass floor.

Figure 2

Energy calibration of the 77 liquid scintillators using a ${}^{137}\mathrm{Cs}$ source. The energy spectra is given for each channel number.

Figure 3

Pulse-shape discrimination for one of the liquid scintillators. The regions of neutron (magenta or light gray outline) and photon (black outline) identification are shown. From a PSD classifier perspective, they can be referred to as the neutron and photon acceptance regions.

Figure 4

Acceptance of neutron pulses as a function of scintillation light output and averaged over all detector channels. Bars indicate the dispersions around the means, from channel-to-channel variations.

Figure 5

Distribution of time intervals between counts in adjacent detectors.

Figure 6

Distribution of time intervals between counts for the ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ source measured with a subset of the liquid scintillator array. A light output threshold of 100 keVee is applied.

Figure 7

Measured (black) and simulated (red or light gray) pulse height distributions produced by a ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ source recorded by the scintillators.

Figure 8

Average neutron detection efficiency as a function of kinetic energy, for a scintillation light output threshold of 100 keVee.

Figure 9

MCNPX 2.7.0 model of the liquid scintillator array. Scintillators are in yellow (light gray), PMTs in green (dark gray).

Figure 10

Our two-neutron angular correlation for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ as a function of the angular separation. The open circles are based on 30 minutes of data taking and were adjusted for neutron acceptance. The Gagarski [4] and Pozzi [5] results are shown by the filled circles and stars, respectively. From the top to the bottom curves: 1600, 1200, 800, 550, and 425 keV.

Figure 11

The ratio of two-neutron angular correlations for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ in a small detector relative to a large detector. Ratio arbitrarily set to 1 at ${90}^{\circ }$. The ratio shows the sensitivity of the correlations to the detector size based on FREYA simulations.

Figure 12

The two-neutron angular correlation for ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$ as a function of the angular separation before cross-talk correction and for several light output thresholds. The data points are based on 23 h of data taking and were adjusted for neutron acceptance.

Figure 13

Fraction of coincidences attributed to neutron cross talk as a function of the detector separation angle and for several light output thresholds.

Figure 14

The cross-talk and neutron acceptance corrected two-neutron angular correlation for ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$ as a function of the angular separation and for several light output thresholds. The full circles, squares, and triangles are based on 23 h of data taking. The Marcath [6] measurements are shown with stars.

Figure 15

The cross-talk and neutron acceptance corrected two-neutron angular correlation for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ as a function of the angular separation and for several light output thresholds.

Figure 16

The cross-talk and neutron acceptance corrected two-neutron angular correlation for ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$ as a function of the angular separation and for several light output thresholds. FREYA calculations with $x=1.1$, 1.2, 1.3, and 1.4 are also shown.

Figure 17

The two-neutron angular correlation for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ and ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$ as a function of the angular separation, for several neutron kinetic energies. These curves were obtained by running FREYA in standalone mode, without transporting the neutrons and photons to the detectors. A value of $x=1.3$ was used for ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$.

Figure 18

The cross-talk and neutron acceptance corrected two-neutron angular correlation for ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$ as a function of the angular separation and for several light output thresholds. Simulations with $x=1.3$ are shown, see Eq. (7).

Figure 19

Acceptance of neutron pulses as a function of scintillation light output and averaged over all detector channels. Bars indicate the dispersions around the means, from channel-to-channel variations.

Figure 20

The cross-talk and neutron acceptance corrected two-neutron angular correlation for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ as a function of the angular separation, for several neutron kinetic energies. The neutron kinetic energy is determined from the neutron time-of-flight using a spontaneous fission photon trigger. FREYA simulations are also shown for the same kinetic energies.

Figure 21

The cross-talk and neutron acceptance corrected two-neutron angular correlation for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ as a function of the angular separation, using either light output threshold (LO) or time-of-flight ($E_{\text{kin}}$) as a neutron filter.

Figure 22

The cross-talk and neutron acceptance corrected two-neutron angular correlation for ${}^{240}\mathrm{Pu}\left(\mathrm{sf}\right)$ as a function of the angular separation. The neutron kinetic energy is determined from the neutron time-of-flight using a spontaneous fission photon trigger. FREYA simulations are also shown for the same kinetic energies.