Measurement of the ${}^{239}\mathrm{Pu}(n,f)$ prompt fission neutron spectrum from 10 keV to 10 MeV induced by neutrons of energy 1–20 MeV

Although the prompt fission neutron spectrum (PFNS) is an essential component of neutron-driven systems that has been measured for decades, there are still multiple glaring unknowns regarding the PFNS of major actinides in the fission neutron incident energy range, specifically with regard to multichance fission and pre-equilibrium neutron emission processes. The only impactful experimental ${}^{239}\mathrm{Pu}$ PFNS measurements included in recent nuclear data evaluations were measured over a limited outgoing neutron energy range at thermal and 1.5-MeV average incident neutron energy, while other potentially impactful measurements have been shown to contain errors that resulted in either large uncertainty increases or in complete exclusion from nuclear data evaluation. We report here a measurement of the ${}^{239}\mathrm{Pu}$ PFNS over a wide range of incident neutron energy (1–20 MeV) and three orders of magnitude in outgoing neutron energy (0.01–10 MeV) resulting from the Chi-Nu experiment at the Los Alamos Neutron Science Center. These results are the combination of separate PFNS measurements in the same experimental area, one using a Li-glass and the other a liquid scintillator detector array. Covariances between all PFNS data points from each detector and within each incident energy range were generated between all other data in both detector arrays and within all other incident neutron energy bins, yielding a single covariance matrix for all 1300 PFNS data points reported here. These covariances are based on a thorough assessment of systematic bias and uncertainties associated with the measurement, PFNS extraction technique, combination of data from each detector type, and other aspects of the analysis. The existence of covariances between PFNS data points in different incident neutron energy ranges yielded covariances between average PFNS energy values at each incident energy to be reported here as well, which allowed for firm statements to be made regarding a shape of a purely experimental mean PFNS energy trend for the first time. Although minor PFNS shape differences exist between the results reported here and recent nuclear data evaluations, the ENDF/B-VIII.0 and JEFF-3.3 PFNS evaluations agree reasonably well with the present results from 1-to 10-MeV incident neutron energy, which spans the well-measured 1.5-MeV incident neutron energy PFNS from Lestone and Shores as well as the onset of second-chance fission. However, while the pre-equilibrium component of the PFNS above 12-MeV incident neutron energy roughly agrees in position and magnitude with ENDF/B-VIII.0 and JEFF-3.3, clear differences relating to the relative magnitude of third-chance fission PFNS features are present in the PFNS shape and in the mean PFNS energy trends.

Figure 1

The neutron flux at the Chi-Nu target position based on an MCNP calculation of neutron emission from the tungsten spallation target following irradiation with the nominal proton beam at WNR is shown here. Note that attenuation along the target flight path reduces the low-energy flux compared to what is shown in this calculation.

Figure 2

An example PPAC integral spectrum is shown here. This is the observed spectrum from a single PPAC volume after the analyses described in Secs. 3a and 4a.

Figure 3

A rendering of the Chi-Nu Li-glass detector array is shown here. Beam enters from the lower-left of this figure. The PPAC fission counter is at the center of the array.

Figure 4

A rendering of the Chi-Nu liquid scintillator detector array is shown here. Beam enters from the lower-left of this figure. The PPAC fission counter is at the center of the array.

Figure 5

The mean PFNS energy as a function of laboratory detection angle with respect to the incident neutron beam for the incident energy of $E_n^{\mathrm{inc}}=2-3\mathrm{MeV}$ is shown here for the present measurement (black diamonds) and the corresponding MCNP6 simulation (red circles). For this incident neutron energy bin the fragments are emitted close to isotropically in the center-of-mass frame and there is very little motion of the center of mass. Therefore, the pattern observed in this figure is primarily a result of the PPAC angular efficiency. See the text for a discussion.

Figure 6

The distribution of neutron energies from time of flight as a function of fragment emission angle generated via the methods described in Sec. 2d.

Figure 7

An example spectrum of the number of fissions observed as a function of time within a macropulse for three micropulses. See the text for a description of the two varieties of wraparound. The exponential extrapolation of the low-energy wraparound is shown as the blue dashed line with the uncertainty band shown as the shaded region. The relative time is defined such that pulse 1 begins at approximately $0\mu \mathrm{s}$.

Figure 8

Number of neutron detections as a function of time within a macropulse for a ${}^6\mathrm{Li}$-glass detector. The $y$-axis maximum is reduced well below the maximum number of counts to emphasize the changes in neutron detection rate. See the text for a discussion.

Figure 9

Top: A kinematic spectrum for neutrons determined to be part of a valid double coincidence. Bottom: A spectrum of the measured data (black, solid line) and the random coincidence background spectrum (red, dashed line) for incident neutron energy $E_n^{\mathrm{inc}}=2.0-3.0\mathrm{MeV}$, which corresponds to an average incident energy of $\langle E_n^{\mathrm{inc}}\rangle =2.514\mathrm{MeV}$. Counts per bin are plotted versus an outgoing neutron energy calculated from the time of flight from the PPAC to the ${}^6\mathrm{Li}$-glass neutron detector, assuming a straight-line path. See the text for a discussion of both figures.

Figure 10

The Chi-Nu Li-glass response matrix including a ${}^{239}\mathrm{Pu}$ PPAC is shown here. This matrix was calculated with MCNP X-PoliMi.

Figure 11

Number of neutron detections as a function of time within a macropulse for liquid scintillator data. The $y$-axis maximum is reduced to emphasize the changes in neutron detection rate. See the text for a discusion.

Figure 12

An example of a liquid scintillator PSD spectrum is shown here. The gate for neutrons is shown as the area bounded by the red line.

Figure 13

Top: A kinematic spectrum for neutrons determined to be part of a valid double coincidence. Bottom: A spectrum of the measured data (black, solid line) and the random coincidence background spectrum (red, dashed line) for an incident neutron energy of $E_n^{\mathrm{inc}}=2.0-3.0\mathrm{MeV}$, which corresponds to an average incident energy of $\langle E_n^{\mathrm{inc}}\rangle =2.514\mathrm{MeV}$. See the text for a discussion of both figures.

Figure 14

The Chi-Nu liquid scintillator response matrix including a ${}^{239}\mathrm{Pu}$ PPAC is shown here. This matrix was calculated with MCNP X-PoliMi.

Figure 15

The unnormalized correlation matrix associated with both the Li-glass and liquid scintillator PFNS for $E_n^{\mathrm{inc}}=1.0-2.0\mathrm{MeV}$ is shown here. This matrix and those all other $E_n^{\mathrm{inc}}$ ranges reported in the work result directly from the covariance in Eqs. (23) and (24).

Figure 16

The correlation matrices shown here result from the individual normalization of the combined Li-glass-liquid scintillator PFNS at each incident energy following the procedure described in Ref. [28] and extending it to multiple incident energies. See the text for a discussion and description of the $E_n^{\mathrm{inc}}$ bins. The normalized correlation matrix associated with both the Li-glass and liquid scintillator PFNS for $E_n^{\mathrm{inc}}=1.0–2.0\mathrm{MeV}$ is shown in panel (a), and the combined normalized correlation matrix for the Li-glass and liquid scintillator data across all incident neutron energies is shown in panel (b).

Figure 17

Shown here are a set of representative relative uncertainties from each uncertainty source incorporated into the PFNS results shown in this work. Solid and dashed lines of the various colors correspond to liquid scintillator and Li-glass uncertainties, respectively.

Figure 18

Shown here are the various paths that can lead to fission for the ${}^{239}\mathrm{Pu}+n$ system with the approximate incident neutron energy ranges for which they occur. Note that the chosen fission fragments are only one of the many possible combinations of fission fragment pairs. This figure is a reproduction of Fig. 1 from Ref. [53]. The various processes involving prefission neutron emission allow different nuclei to undergo fission and can create unique features in the measured spectra. Numbers of neutrons and fission fragment identities are approximate.

Figure 19

Shown here are comparisons of the present PFNS results with the spectra from Lestone and Shores [16] and Chatillon et al. [20] as well as the ENDF/B-VIII.0 [15] and JEFF-3.3 [76] evaluations at the relevant incident neutron energies. The band for each evaluation trend represents the 1-$\sigma$ uncertainty limit. Note that the evaluation spectra are evaluated at a single $E_n^{\mathrm{inc}}$ value and the other experiment spectra are integrated over different $E_n^{\mathrm{inc}}$ ranges. See the text for a discussion. (a) The PFNS for $E_n^{\mathrm{inc}}=1.0–2.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =1.54\mathrm{MeV}$, (b) The PFNS for $E_n^{\mathrm{inc}}=2.0–3.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =2.51\mathrm{MeV}$, (c) The PFNS for $E_n^{\mathrm{inc}}=3.0–4.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =3.50\mathrm{MeV}$, and (d) The PFNS for $E_n^{\mathrm{inc}}=4.0–5.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =4.53\mathrm{MeV}$.

Figure 20

Shown here are comparisons of the present PFNS results with the spectra from Chatillon et al. [20] and the ENDF/B-VIII.0 [15] and JEFF-3.3 [76] evaluations for $E_n^{\mathrm{inc}}$ ranges corresponding to a combination of first- and second-chance fission. The band for each evaluation trend represents the 1-$\sigma$ uncertainty limit. Note that the evaluation spectra are evaluated at a single $E_n^{\mathrm{inc}}$ value and the other experiment spectra are integrated over different $E_n^{\mathrm{inc}}$ ranges. See the text for a discussion. (a) The PFNS for $E_n^{\mathrm{inc}}=5.0–5.5\mathrm{MeV}$, corresponding to an average incident neutron energy $E_n^{\mathrm{inc}}=5.25\mathrm{MeV}$, (b) The PFNS for $E_n^{\mathrm{inc}}=5.5–6.0\mathrm{MeV}$, corresponding to an average incident neutron energy $E_n^{\mathrm{inc}}=5.81\mathrm{MeV}$, (c) The PFNS for $E_n^{\mathrm{inc}}=6.0–7.0\mathrm{MeV}$, corresponding to an average incident neutron energy $E_n^{\mathrm{inc}}=6.50\mathrm{MeV}$, (d) The PFNS for $E_n^{\mathrm{inc}}=7.0–8.0\mathrm{MeV}$, corresponding to an average incident neutron energy $E_n^{\mathrm{inc}}=7.52\mathrm{MeV}$, (e) The PFNS for $E_n^{\mathrm{inc}}=8.0–9.0\mathrm{MeV}$, corresponding to an average incident neutron energy $E_n^{\mathrm{inc}}=8.54\mathrm{MeV}$, and (f) The PFNS for $E_n^{\mathrm{inc}}=9.0–10.0\mathrm{MeV}$, corresponding to an average incident neutron energy $E_n^{\mathrm{inc}}=9.46\mathrm{MeV}$.

Figure 21

Shown here are comparisons of the present PFNS results with the spectra from Chatillon et al. [20] and from the ENDF/B-VIII.0 [15] and JEFF-3.3 [76] evaluations for $E_n^{\mathrm{inc}}$ ranges corresponding to a combination of first-, second-, and third-chance fission as well as pre-equilibrium neutron emission preceding fission from $E_n^{\mathrm{inc}}=10-15\mathrm{MeV}$. The band for each evaluation trend represents the 1-$\sigma$ uncertainty limit. Note that the evaluation spectra are evaluated at a single $E_n^{\mathrm{inc}}$ value and the other experiment spectra are integrated over different $E_n^{\mathrm{inc}}$ ranges. See the text for a discussion. (a) The PFNS for $E_n^{\mathrm{inc}}=10.0–11.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =10.60\mathrm{MeV}$, (b) The PFNS for $E_n^{\mathrm{inc}}=11.0–12.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =11.61\mathrm{MeV}$, (c) The PFNS for $E_n^{\mathrm{inc}}=12.0–13.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =12.48\mathrm{MeV}$, (d) The PFNS for $E_n^{\mathrm{inc}}=13.0–14.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =13.56\mathrm{MeV}$, and (e) The PFNS for $E_n^{\mathrm{inc}}=14.0-15.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =14.53\mathrm{MeV}$.

Figure 22

Shown here are comparisons of the present PFNS results with the ENDF/B-VIII.0 [15] and JEFF-3.3 [76] evaluations for $E_n^{\mathrm{inc}}$ ranges corresponding to a combination of first-, second- , and third-chance fission as well as pre-equilibrium neutron emission preceding fission from $E_n^{\mathrm{inc}}=15-20.0\mathrm{MeV}$. The band for each evaluation trend represents the 1-$\sigma$ uncertainty limit. The data of Chatillon et al. were excluded from the ENDF/B-VIII.0 ${}^{239}\mathrm{Pu}$ PFNS evaluation for these incident energies, so they are not shown here. Note that the evaluation spectra are evaluated at a single $E_n^{\mathrm{inc}}$ value and the other experiment spectra are integrated over different $E_n^{\mathrm{inc}}$ ranges. See the text for a discussion. (a) The PFNS for $E_n^{\mathrm{inc}}=15.0–16.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =15.53\mathrm{MeV}$, (b) The PFNS for $E_n^{\mathrm{inc}}=16.0–17.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =16.60\mathrm{MeV}$, (c) The PFNS for $E_n^{\mathrm{inc}}=17.0–18.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =17.67\mathrm{MeV}$, (d) The PFNS for $E_n^{\mathrm{inc}}=18.0–19.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =18.59\mathrm{MeV}$, and (e) The PFNS for $E_n^{\mathrm{inc}}=19.0–20.0\mathrm{MeV}$, corresponding to an average incident neutron energy $\langle E_n^{\mathrm{inc}}\rangle =19.56\mathrm{MeV}$.

Figure 23

Shown here is an example pre-equilibrium peak angular distribution from ${}^{239}\mathrm{Pu}(n,f)$ for $E_n^{\mathrm{inc}}=19-20\mathrm{MeV}$. The measured data are shown as the black diamonds and a fit to the data using Kalbach-Mann systematics [84] and a maximum Legendre polynomial $l$ value of 2 is shown as the red shaded region. An independent Feshbach, Kerman, and Koonin calculation for inelastically scattered neutrons from ${}^{239}\mathrm{Pu}$ [78, 79] is shown as the blue line. Note that this figure is a reproduction of Fig. 5(f) in Ref. [53]. The reader is referred to Ref. [53] for the full presentation of these results.

Figure 24

Top: Shown here is the mean PFNS energy trend for the present results compared to the ENDF-B/VIII.0 [15], JEFF-3.3 [76], and JENDL-4.0 [85] evaluations shown as the red solid, blue dashed, and green dotted lines, respectively. The present results are shown as uncertainty bands only, with the net statistical uncertainty of the normalized PFNS results combined across Li-glass and liquid scintillator spectra shown as the smaller, red uncertainty band and the total uncertainty as the larger black uncertainty band. Note that each point on this plot corresponds to a PFNS distribution shown in Secs. 6a–6c. Bottom: The percentage uncertainty trends for the statistical and total uncertainties are shown here as the solid black and red dashed lines.

Figure 25

Shown here is the correlation matrix between the $\langle E\rangle$ points shown in Fig. 24. Note that the $z$-axis scale only goes down to 0.8, with white indicating a correlation of 0.9, implying that all $\langle E\rangle$ points are highly correlated.