Elastic Scattering

The final state of elastic scattering is described by sampling the differential scattering cross-sections \({\rm d} \sigma / {\rm d} \Omega\). Two representations are supported for the normalised differential cross-section for elastic scattering. The first is a tabulation of the differential cross-section, as a function of the cosine of the scattering angle \(\theta\) and the kinetic energy \(E\) of the incoming neutron.

\[{{\rm d} \sigma \over {\rm d} \Omega}~=~ {{\rm d} \sigma \over {\rm d} \Omega}\left(\cos{\theta,~E}\right)\]

The tabulations used are normalised by \(\sigma/(2\pi)\) so the integral of the differential cross-sections over the scattering angle yields unity.

In the second representation, the normalised cross-section are represented as a series of legendre polynomials \(P_l(\cos{\theta})\), and the legendre coefficients \(a_l\) are tabulated as a function of the incoming energy of the neutron.

\[{2\pi\over\sigma (E)}{{\rm d} \sigma \over {\rm d} \Omega}\left(\cos{\theta,~E}\right)~=~ \sum_{l=0}^{n_l} {2l+1\over 2}a_l(E)P_l(\cos{\theta})\]

Describing the details of the sampling procedures is outside the scope of this paper.

An example of the result we show in Fig. 117 for the elastic scattering of 15 MeV neutrons off uranium a comparison of the simulated angular distribution of the scattered neutrons with evaluated data. The points are the evaluated data, the histogram is the Monte Carlo prediction.

In order to provide full test-coverage for the algorithms, similar tests have been performed for ⁷²Ge, ¹²⁶Sn, ²³⁸U, ⁴He, and ²⁷Al for a set of neutron kinetic energies. The agreement is very good for all values of scattering angle and neutron energy investigated.

Fig. 117 Comparison of data and Monte Carlo for the angular distribution of 15 MeV neutrons scattered elastically off uranium (²³⁸U). The points are evaluated data, and the histogram is the Monte Carlo prediction. The lower plot excludes the forward peak, to better show the Frenel structure of the angular distribution of the scattered neutron.