Backward-forward reaction asymmetry of neutron elastic scattering on deuterium

A new measurement of the angular distribution of neutron elastic scattering on deuterium was carried out at the neutron time-of-flight facility nELBE. The backward-forward asymmetry of the reaction was investigated via the direct detection of neutrons scattered at the laboratory angle of ${15}^{\circ }$ and ${165}^{\circ }$ from a polyethylene sample enriched with deuterium. In order to extend the measurement to neutron energies below 1 MeV, ${}^6\mathrm{Li}$ glass scintillators were employed. The data were corrected for the background and the multiple scattering in the target, the events due to scattering on deuterium were separated from those due to carbon, and the ratio of the differential cross section at ${15}^{\circ }$ and ${165}^{\circ }$ was determined. The results, covering the energy range from 200 keV to 2 MeV, were found to be in agreement with the theoretical predictions calculated by Canton et al. [Eur. Phys. J. A 14, 225 (2002)] and by Golak et al. [Eur. Phys. J. A 50, 177 (2014)]. The comparison with the evaluated nuclear data libraries indicated CENDL-3.1, JEFF-3.2, and JENDL-4.0 as the evaluations that best describe the asymmetry of $n\text{−}d$ scattering. ENDF/B-VII.1 is compatible with the data for energies below 700 keV, but above the backward to forward ratio is higher than measured. ROSFOND-2010 and BROND-2.2 resulted to have little compatibility with the data.

Figure 1

Picture of the detector array.

Figure 2

Diagram of the experimental setup (horizontal plane passing through the center of the target).

Figure 3

Model of the detectors, the target, and the supporting aluminium frame implemented in MCNP5. Here the vertical $x\text{−}z$ plane passing through the center of the target is shown; an analogous figure is obtained when the $x\text{−}y$ plane is plotted, with the difference that there the distance $z$ is replaced by that along the $y$ axis. The distances $x$, $y$, and $z$ were actually measured, $d$ and the angle $\theta$ were computed accordingly. The exact values of $x$, $y$ or $z$, $d$, and $\theta$ are reported in Table 3.

Figure 4

Diagram of the data acquisition system. DET: Li-glass detector; ACC: accelerator reference signal; CFD: constant fraction discriminator; FPGA: field programmable gate array logic module; QDC: charge-to-digital converter; TDC: time-to-digital converter; SCALER: scaler module.

Figure 5

Example of raw data. The two-dimensional histograms show the counts as a function of the TDC time and QDC integrated charge recorded in almost 70 h of beam time, with the ${\mathrm{CD}}_2$ sample as neutron scatterer, from one of the detectors at ${15}^{\circ }$ and one at ${165}^{\circ }$.

Figure 6

Example t.o.f. histograms, one for a detector at ${15}^{\circ }$ and one at ${165}^{\circ }$, after the room background subtraction. The counts have been normalized with the monitor counts for proper comparison between the ${\mathrm{CD}}_2$, sample-out (SO) and graphite (C - carbon) measurements.

Figure 7

Experimental ${\mathrm{CD}}_2$ t.o.f. histograms (“data”), at ${15}^{\circ }$ and ${165}^{\circ }$, after the subtraction of the contribution of scattering in air, compared with the simulated ${}^6\mathrm{Li}(n,\alpha )$ reaction rate tallied in the detector sensitive volume (“simulation”). The “single collisions” lines are the simulation results when only neutrons arriving after a single collision on deuterium are considered.

Figure 8

Contribution of multiple scattering in the target (“m.sc.”), single scattering on deuterium (“$n\text{−}d$”) or on carbon (“$n$-C”), expressed in percentage of number of events as a function of the time of flight.

Figure 9

Same as Fig. 7 but for the carbon data. In this case the “single collisions” lines indicate the single collision on carbon.

Figure 10

Same as Fig. 8 but for the carbon data.

Figure 11

Rescaling factor for the MCNP results obtained for each detector (detectors at ${15}^{\circ }$: numbers 3, 4, 7, and 8 at ${165}^{\circ }$: 1, 2, 5, and 6), for the ${\mathrm{CD}}_2$ and graphite (C) runs. The parameter $b$ has an order of magnitude of ${10}^{-7}$ because the data were normalized by the monitor counts. The arithmetic average (avg) of all values is what was used to rescale the simulations to the data in Figs. 7, 9, and 12.

Figure 12

Experimental t.o.f. histograms (“data”) for the sample-out run, at ${15}^{\circ }$ and ${165}^{\circ }$, compared to the simulated ${}^6\mathrm{Li}(n,\alpha )$ reaction rate tallied in the glass volume (“simulation”).

Figure 13

Single scattering on deuterium events at ${15}^{\circ }$ and ${165}^{\circ }$, for every detector alone (${\mathrm{DET}}_i\left(E\right)$), and their average ($\mathrm{AVG}\left(E\right)$), as a function of the incident neutron energy $E$. The deviation from the average, expressed as $({\mathrm{DET}}_i\left(E\right)-\mathrm{AVG}\left(E\right))/{\sigma }_{{\mathrm{DET}}_i}\left(E\right)$, where $\sigma$ is the uncertainty on the measured events, is also plotted for each detector.

Figure 14

Calculated detection efficiency for detectors at ${15}^{\circ }$ and at ${165}^{\circ }$ as a function of the neutron energy incident on deuterium.

Figure 15

Comparison of the ratio $\frac{d\sigma }{d\mathrm{\Omega }}{{|}_{{165}^{\circ }}/\frac{d\sigma }{d\mathrm{\Omega }}|}_{{15}^{\circ }}$: experimental results versus the main evaluated libraries and the calculations of Canton et al.

Figure 16

Comparison the experimental t.o.f. spectra with the MCNP5 simulations obtained after using several different libraries for the deuterium cross section tables. These spectra are the sum of the counts coming from all detectors at same angle.

Figure 17

Ratio between the MCNP and the experimental t.o.f. histograms shown in Fig. 16. The grey area represent the t.o.f. interval considered when computing the rescaling factor for the comparison between data and simulation.