Cross section and neutron angular distribution measurements of neutron scattering on natural iron

New measurements of the neutron scattering double differential cross section of iron were carried out at the neutron time-of-flight facilities GELINA and nELBE. A neutron spectrometer consisting of an array of up to 32 liquid organic scintillators was employed, which was designed to measure the scattering differential cross section at eight scattering angles and to simultaneously determine the integral cross section via numerical quadrature. The separation of elastic from inelastic scattering was achieved by analyzing the time-of-flight-dependent light-output distributions to determine the scattered neutron energy. The method was validated by studying elastic scattering on carbon and it was proved to work well for the determination of the elastic cross section. Here, the possibility to extend it to inelastic scattering was investigated too. For these experiments a sample of natural iron was used and the results cover the incident neutron energy range from 2 to 6 MeV. Both the differential and the integral elastic cross sections were produced for ${}^{\mathrm{nat}}\mathrm{Fe}$, while for inelastic scattering, partial angular distributions for scattering from the first excited level of ${}^{56}\mathrm{Fe}$ could be determined.

Figure 1

Energy level structure of the iron isotopes. The energies (in MeV) of all excited states of ${}^{56}\mathrm{Fe}$ up to 3 MeV [55] are indicated. For comparison, the first levels of ${}^{54}\mathrm{Fe}$ [56], ${}^{57}\mathrm{Fe}$ [57], and ${}^{58}\mathrm{Fe}$ [58], and are indicated too.

Figure 2

Picture of the setup installed in the measurement station at ${108}^{\circ }$, 30 m distance from the GELINA neutron source. The neutron beam comes from the right; it first passes through the fission chamber, then hits the target at the center of the scintillator array. The fission chamber is mounted on a lead wall which is the last beam collimator.

Figure 3

T.o.f. distributions measured at GELINA [(a) and (b)] and nELBE [(c) and (d)] with an EJ301 detector [(a) and (c)] and an EJ315 detector [(b) and (d)] at $100.6^{\circ }$ (same detector at the same position at both facilities), different irradiation times (see Table 6).

Figure 4

Light output distributions (in equivalent electron energy deposition) for EJ301 [(a) to (d)] and EJ315 detectors [(e) to (f)] at different angles $\theta$. The measurements were carried out at GELINA, and correspond to the t.o.f. interval from 1086 to 1091 ns. If elastic scattering is considered, it corresponds to an incident neutron energy of 3.31–3.34 MeV. This value represents a lower limit: for any other nonelastic reaction, the same t.o.f. interval corresponds to higher energies. The measurements (meas) are compared with the detector response modeled for elastically scattered neutrons (el), for inelastic scattering from the first three levels of ${}^{56}\mathrm{Fe}$ (${\text{in}}_1, {\text{in}}_2$, and ${\text{in}}_3$ for the levels at 847, 2085, and 2658 keV respectively), and their sum ($\text{tot}=\text{el}+{\sum }_{i=1}^3{\text{in}}_i$).

Figure 5

Same as for Fig. 4 but for measurements at nELBE, for the t.o.f. interval from 343 to 344 ns, corresponding to an incident neutron energy for elastic scattering of 3.31–3.33 MeV. Panels (a) to (d) refer to EJ301 and panels (e) and (f) to EJ315 detectors.

Figure 6

Differential cross section $\frac{d\sigma }{d\mathrm{\Omega }}$ of elastic scattering on ${}^{\mathrm{nat}}\mathrm{Fe}$ as a function of the cosine of the scattering angle in the laboratory system $\theta$, for selected intervals of incident neutron energy $E$: (a) $E=$ 2.002–2.016 MeV, (b) $E=$ 2.894–2.919 MeV, (c) $E=$ 3.635–3.671 MeV, (d) $E=$ 4.455–4.503 MeV, (e) $E=$ 4.973–5.030 MeV, (f) $E=$ 5.521–5.587 MeV. The results of the measurements at GELINA and nELBE are compared with other experiments and the angular distribution reported in the ENDF/B-VIII library.

Figure 7

Differential cross section $\frac{d\sigma }{d\mathrm{\Omega }}$ of elastic scattering on ${}^{\mathrm{nat}}\mathrm{Fe}$ as a function of the neutron incident energy $E$: comparison of the measured values with the ENDF/B-VIII evaluation at the laboratory angles $\theta$. To improve the readability of the graphs, the experimental uncertainties are given every third point.

Figure 8

Angle-integrated cross section $\sigma$ of elastic scattering on ${}^{\mathrm{nat}}\mathrm{Fe}$ as a function of the incident neutron energy $E$: comparison with previous measurements (a), and with the ENDF/B-VIII evaluation averaged (“ENDF/B-VIII,avg”) according to the experimental energy resolution (b,c).

Figure 9

Differential cross section $\frac{d\sigma }{d\mathrm{\Omega }}$ of inelastic scattering from the first level of ${}^{56}\mathrm{Fe}$ as a function of the cosine of the scattering angle in the laboratory system ${\theta }_{\mathrm{LAB}}$, for selected intervals of incident neutron energy $E$: (a) $E=$ 2.493–2.513 MeV, (b) $E=$ 2.638–2.660 MeV, (c) $E=$ 3.248–3.278 MeV, (d) $E=$ 3.934–3.973 MeV, (e) $E=$ 4.552–4.601 MeV, (f) $E=$ 5.521–5.587 MeV. The results of the measurements at GELINA and nELBE are compared with other experiments and the angular distribution reported in the ENDF/B-VIII library.

Figure 10

Differential cross section $\frac{d\sigma }{d\mathrm{\Omega }}$ of inelastic scattering from the first level of ${}^{56}\mathrm{Fe}$ as a function of the neutron incident energy $E$: comparison of the measured values with the ENDF/B-VIII evaluation at the laboratory angles $\theta$. To improve the readability of the graphs, the experimental uncertainties are given every third point.