*2.2. Neutron Scattering in Fission Chamber*

Three neutron detectors were applied in the experiment [5] (Figure 2). The ionization chamber used for FF counting is shown in Figure 3. Both fissile materials 252Cf and 235U were placed in the same chamber.

The MCNP code was used for the simulation of neutron scattering in the environment. Preliminary data analysis of the experimental results had shown that the experimental PFNS has very strong angular-energy dependence. At the same time, the MCNP simulation calculates an isotropic angular distribution. More careful analysis of the model used in the

calculations had shown that the simplification was achieved in the geometry; namely, 235U and 252Cf samples were placed in the same position in the center of the fission chamber.

**Figure 2.** Experimental set-up for the IRMM-2008 experiment [5].

**Figure 3.** Drawing of the fission ionization chamber. Cu, Ccf—cathodes with U and Cf neutron sources, A1, A2, G1, G2—cathodes and grids for U part of the ionization chamber, Acf—anode for Cf part [5].

After the correction of the MCNP input data, the angular effect appeared in the MCNP results (Figure 4) and disappeared in the corrected PFNS measured by detectors placed under different angles. The experimental spectra for different angles are in good agreement (inside experimental uncertainties (Figure 5)). This case demonstrates that the use of a simplified model of the experimental set-up (construction) may produce SDF. However, the accurate model of the experiment may remove this SDF.

**Figure 4.** Ratio of multiple scattering corrections for Cf- and U-sources calculated in the MCNP simulations.

**Figure 5.** Results of 235U PFNS measurements for three detectors after introducing the multiple scattering correction. They are shown as the ratios of the Maxwellian spectrum with the average energy <E> = 1.988 MeV.

#### *2.3. The Energy-Angular Distribution of Neutrons Relative to FF Flight Direction*

Fission neutrons have a very strong energy-angular correlation in the Laboratory System (LS) of coordinate relative to the FF flight direction. This is a well-known experimental fact, which has a simple theoretical justification: if most neutrons are emitted after full acceleration of the FF by the Coulomb field, they should have high translational velocity of FF in the LS. However, evaluated data libraries and all practical applications are based on the trivial assumption, "during the fission, neutrons with the same spectrum as the angular integrated spectrum are emitted". This is an incorrect simplification, which may stimulate strong SDF during the construction of the experimental set-up. This problem was discussed in several papers [8–10]. We would like to remind the reader of some results from [8].

The novel measurements of PFNS with registration of the angle between the flight direction of the fission fragment and neutron were performed at the PINP [11]. The registration of FF was performed in flat 2π geometry, with the azimuth angle fixed by "the belt" of FF counters and registration of neutrons by two neutron detectors located at the same plane.

This flat geometry was included in MC simulations. It was assumed that fission neutrons are emitted from fixed FF (single fragment) with Center of Mass (CM) energy Ev. The Maxwellian neutron spectrum for CM was used for calculation. Therefore, if we apply full integration (total 4π angle range), we should obtain the Watt distribution in the LS. The ratio of simulated spectra for flat geometry to the Watt distribution is shown in Figure 6. We see that the SDF for this geometry of measurements can be very strong. It increases the high energy part of the spectrum and average energy. In this simulation, we did not use the FF yields with their mass and kinetic energy distributions; therefore, this result cannot be used as the correction at the SDF. However, it demonstrates clearly that the limitation in the geometry of the measurements of neutron angular distributions relative to the FF flight direction may lead to the appearance of the SDF.

**Figure 6.** Distortion effect in the derived PFNS due to incomplete (angle selection) azimuth integration in [8].
