Neutron angular correlations in spontaneous and neutron-induced fission

Background: Neutron emission is correlated in fission events because, on average, more than one neutron is emitted per fission. Measurements of these correlations, coupled with studies of more inclusive observables such as neutron multiplicity, provide sensitive information about the fission mechanism. Neutron-neutron angular correlations have been studied in both spontaneous fission of ${}^{252}\mathrm{Cf}$ and neutron-induced fission of ${}^{235}\mathrm{U}$. These correlations, until recently incalculable in most available simulations of fission, can now be calculated in event-by-event simulations of fission.

Purpose: Phenomenological studies of fission are of interest both for basic science and for practical applications. Neutron-neutron angular correlations are characteristic of the fissioning isotope and could be used in material identification.

Method: We use our model of complete fission events, freya, to first study the sensitivity of two-neutron angular correlations to the model inputs and then compare to available data. We also compare our simulations to neutron-fragment angular correlations.

Results: We find that the correlations calculated with freya are fairly robust with respect to the input parameters. Any strong deviations in the correlations result in poor agreement with measured inclusive neutron observables such as neutron multiplicity as a function of fragment mass and the neutron multiplicity distribution. The agreement of freya with the present set of correlation data is found to be good.

Conclusions: freya can be used to reliably predict neutron-neutron angular correlations and could then be used to identify materials.

Figure 1

The angular correlation between two neutrons emitted from ${}^{252}\mathrm{Cf}$(sf) as a function of the opening angle between the two neutrons, ${\theta }_{nn}$. The freya results are shown for neutron kinetic energies $E_n>0.5$ MeV. The results of different parameter choices in freya are compared to the default results: $c_S=1$, $Q_{\min }=0.01$ MeV, $x=1.3$, $e_0=10$ MeV, and $c=1$. (a) Parameters affecting photon emission are varied. The dashed red curve is with $c_S=0.1$, $Q_{\min }=0.01$ MeV while the dot-dashed green curve is with $c_S=1$, $Q_{\min }=1$ MeV. (b) The parameter affecting the relative excitation energy of the light fragment, $x$, is varied. The dot-dot-dashed red curve is the result for $x=1$, equal partition between the light and heavy fragments. The dot-dashed-dashed green curve shows the result when giving the light fragment even more energy, $x=1.6$, while the dashed blue curve shows a result with $x=0.75$, with more excitation given to the heavy than to the light fragment. (c) The parameter governing the level density is varied. The dashed magenta curve is with $e_0=8$ MeV while the dot-dashed maroon curve is with $e_0=12$ MeV. (d) The parameter governing thermal fluctuations is varied with $c=1.2$ (dashed turquoise curve) increasing the width of the fluctuation while $c=0.8$ (dot-dashed blue) decreases it.

Figure 2

The variation of $\nu \left(A\right)$ with the parameter governing the partition of the excitation energy between the two fragments, $x$, compared to data [25, 26, 27]. The default result, black stars, including bars representing the variance in $A$ for fragment $Z$, is shown by the magenta stars. The results with $x=1$ (solid red, upward-facing triangles), $x=1.6$ (solid green, downward-facing triangles), and $x=0.75$ (blue stars) do not show the variances.

Figure 3

The variation in the neutron multiplicity distribution obtained from varying the thermal fluctuations, $c$. The data [31] (violet squares) are compared to the default (labeled freya) result as well as that with $c=1.2$ (turquoise diamonds) and that with $c=0.8$ (blue stars). The corresponding result for a Poisson distribution with the same average multiplicity is shown by the red dashed curve.

Figure 4

The default freya calculations compared to ${}^{252}\mathrm{Cf}$(sf) two-neutron angular correlation data from [12] (red squares) and [7] (blue circles) for neutron kinetic energies greater than 0.7 MeV.

Figure 5

The default freya calculations compared to ${}^{252}\mathrm{Cf}$(sf) two-neutron angular correlation data from [7] for neutron kinetic energies greater than 0.425, 0.55, 0.8, 1.2, and 1.6 MeV.

Figure 6

The default freya calculations compared to ${}^{235}\mathrm{U}$($n_{\mathrm{th}},\text{f}$) two-neutron angular correlation data from [11] for neutron kinetic energies greater than 1.0 MeV (bottom), 1.75 MeV (center), and 2.5 MeV (top).

Figure 7

The default freya calculations shown for ${}^{252}\mathrm{Cf}$(sf) neutrons correlated with the light fragment, $A_L$. The neutrons emitted from the light fragment (dashed red) and those emitted from the heavy fragment (dot-dot-dashed blue) are compared to the correlation of all neutrons with the light fragment. All neutrons have a minimum kinetic energy of 0.5 MeV.

Figure 8

The default freya calculations compared to ${}^{252}\mathrm{Cf}$(sf) neutron–light fragment ($A_L$) angular correlation data from [2] (red squares) and [3] (blue circles). The minimum kinetic energy of the neutrons is 0.5 MeV.