Measurement of the normalized ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ cross section ratio from threshold to 30 MeV with the NIFFTE fission Time Projection Chamber

The normalized ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ cross section ratio has been measured using the NIFFTE fission Time Projection Chamber (fissionTPC) from the reaction threshold to $30\mathrm{MeV}$. The fissionTPC is a two-volume MICROMEGAS time projection chamber that allows for full three-dimensional reconstruction of fission-fragment ionization profiles from neutron-induced fission. The measurement was performed at the Los Alamos Neutron Science Center, where the neutron energy is determined from neutron time of-flight. The ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ ratio reported here is the first cross section measurement made with the fissionTPC, and will provide new experimental data for evaluation of the ${}^{238}\mathrm{U}(n,f)$ cross section, an important standard used in neutron-flux measurements. Use of a development target in this work prevented the determination of an absolute normalization, to be addressed in future measurements. Instead, the measured cross section ratio has been normalized to ENDF/B-VIII.$\beta 5$ at 14.5 MeV.

Figure 1

Past measurements of the ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ cross section ratio shown between 0.5 and 30 MeV [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. Data are compared to the ENDF/B-VIII.$\beta 5$ [28] evaluation, shown with the evaluated uncertainty. The uncertainty at $20\mathrm{MeV}$, the maximum value at which an uncertainty is given, is used for energies greater than that value. An expanded view of the data is shown in the inset, compared to the ENDF/B-VII.1 [29] and ENDF/B-VIII.$\beta 5$ evaluations, indicating a recent 40% change to the ${}^{238}\mathrm{U}(n,f)$ cross section at $1.2\mathrm{MeV}$.

Figure 2

Visualization of a fission event in the fissionTPC. The thin target allows for both fission fragments to be detected, one in each chamber. The gray disk represents the target holder, and has a 4 cm diameter. The two fission fragments have a common start vertex, but are displaced in the $z$ direction to force all voxels of charge into their respective volumes.

Figure 3

Visualization of a spallation event in the fissionTPC. Several light ions can be seen in a single volume all with a common vertex. The fissionTPC is capable of tracking each particle separately.

Figure 4

The $x\text{−}y$ spatial distribution of fission fragment vertices reconstructed by the fissionTPC. The upper half disk is the ${}^{238}\mathrm{U}$ deposit while the lower is the ${}^{235}\mathrm{U}$ deposit. Black lines indicate spatial selection cuts: the radial cut prevents backgrounds from actinide contamination on the cathode, while the cut bisecting the two deposits identifies which actinide has fissioned. Two adjacent missing pixels can be seen near the position $(-0.5,-0.4)$, so only $x>0$ data is considered for the analysis.

Figure 5

Length vs energy for particles observed in the fissionTPC with the LANSCE neutron beam impinging the device. ADC (analog-to-digital converter) channel refers to the uncalibrated particle energy recorded by the digitizers. Different particles have unique stopping power profiles in the drift gas, and length/energy cuts can be used to isolate specific particle types. Labels have been added to the different particle distributions.

Figure 6

nToF distribution of the combined ${}^{235}\mathrm{U}$ and ${}^{238}\mathrm{U}$ targets. The inset shows a Gaussian fit to the nToF photo-fission distribution, yielding a timing resolution of $2.03\left(2\right)$ ns FWHM.

Figure 7

Distribution of $\alpha$-particle track lengths emitted by the (a) ${}^{238}\mathrm{U}$ and (b) ${}^{235}\mathrm{U}$ targets. Track length is related to energy by the $\alpha$-particle stopping power.

Figure 8

Normalized distribution of recoil proton start vertices recorded during high-gain fissionTPC operation, representing the spatial distribution of neutrons incident on the actinide target. The distribution has been convolved with a Gaussian of $\sigma =0.3$ mm to reduce aliasing effects from ADC thresholds. The black curves outline the regions of actinide target deposit used for the cross section ratio determination, where only $x>0$ is considered due to inactive pad plane pixels. The aliased shape of the outline represents the binning of the target deposit histogram.

Figure 9

Normalized distributions of the beam flux and target activity for the ${}^{238}\mathrm{U}$ [(a) and (b)] and ${}^{235}\mathrm{U}$ [(c) and (d)] actinide deposits. Bin-by-bin multiplication of these distributions determines the beam and target overlap. Only $x>0$ is considered due to inactive pad plane pixels.

Figure 10

Determination of the wraparound correction in the ${}^{235}\mathrm{U}$ data. The nToF data (green), averaged in the low-energy tail region (magenta), are fit to determine the wraparound contribution (red line) to the nToF model (blue line). The nToF model consists of a logarithmic spline following the distribution of prompt neutron data.

Figure 11

The nToF data and wraparound correction after all micropulses are combined. The band around the red line represents the uncertainty of the wraparound fit, which was produced by propagating the fit covariances.

Figure 12

Selection cuts are applied to the energy vs length distribution of detected particles. There are two static cuts which remove background particles, and one dynamic cut (varied within the range shown by vertical red lines) which is used to determine residual uncertainties from the efficiency correction. ADC channel refers to the uncalibrated particle energy recorded by the digitizers.

Figure 13

Energy of observed fission fragments as a function of emission angle from the target [$cos\left(\theta \right)$; $cos\left(\theta \right)=1$ is emission perpendicular to the target]. ADC refers to the uncalibrated particle energy recorded by the digitizers. These distributions are compared for data [(a) and (b)] and simulation [(c) and (d)] for both isotopes. The two vertical bands represent the escape angle distributions of light and heavy fission fragments. These distributions are used to determine ${\epsilon }_{ff}$ via a fitting procedure with a Monte Carlo simulation. The data exclude $cos\left(\theta \right)>0.95$ to avoid electronics saturation effects. Different neutron energy ranges are displayed for the two actinides: ${}^{238}\mathrm{U}$ between 1.33 and 2.51 MeV and ${}^{235}\mathrm{U}$ between 0.16 and 0.42 MeV.

Figure 14

Representative roughness distribution of the actinide targets calculated with a fractal noise model. The axis units are arbitrary, but are common for all axes. The ratio of the height to the wavelength determines the surface normal distribution.

Figure 15

Calculated fission detection efficiency for ${}^{238}\mathrm{U}$ and ${}^{235}\mathrm{U}$.

Figure 16

The normalized ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ cross section ratio measured in this work, compared with the three most recent measurements and the ENDF/B-VIII.$\beta 5$ [28] evaluation shown with the evaluated uncertainty. In many cases, the uncertainty on the measured data is smaller than the symbol. The inset shows a comparison to the ENDF/B-VII.1 [29] and ENDF/B-VIII.$\beta 5$ evaluations near $1.2\mathrm{MeV}$. The lower plot shows the residual of the four data sets and ENDF/B-VIII.$\beta 5$, shown with the evaluated uncertainty.

Figure 17

The ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ correlation matrix measured in this work. At low neutron energy, the contaminant correction becomes the largest source of uncertainty, resulting in a large correlated region in the correlation matrix. The contaminant correction is a fixed value at all energies and, as the ratio becomes small at low energy, a large relative uncertainty results. The $z$ axis represents the value of the correlation matrix elements.

Figure 18

Uncertainty contributions to the ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ cross section ratio. At low neutron energy, the contaminant correction becomes the largest source of uncertainty, and statistical uncertainty is largest at high energy. The contaminant correction is a fixed value at all energies and, as the ratio becomes small at low energy, a large relative uncertainty is found.

Figure 19

The fission ratio of the left and right halves of the ${}^{235}\mathrm{U}$ target measured from this work.

Figure 20

The normalized ${}^{238}\mathrm{U}(n,f)/{}^{235}\mathrm{U}(n,f)$ cross section ratio measured in this work, compared with the three most recent measurements and to the ENDF/B-VIII.$\beta 5$ [28] evaluation shown with the evaluated uncertainty. The neutron energy range 1.6 to $3.4\mathrm{MeV}$ is shown, and the new data are seen to differ from ENDF/B-VIII.$\beta 5$ by $\sim 2.5\%$ at $2.4\mathrm{MeV}$.