Calculation and verification of neutron irradiation damage with differential cross sections

The Displacement per Atom (DPA) rate is conventionally computed with DPA cross sections in reactor applications. The method of direct calculation with energy-angular distributions given in the Center of Mass (CM) frame is proposed and recommended in the present work. The methods for refining and verifying the calculations of DPA cross sections are proposed: (i) Gauss-Legendre-Quadrature-based Piecewise Integration (GLQPI) for ensuring the numeric convergence of integral over emission angle due to the discontinuity of integrand; (ii) verification of the convergence for trapezoidal integration over the secondary energy; (iii) interpolation of double-differential cross sections. For Fe-56 of JEFF-3.1.1, the current numeric integration over emission angle is shown not convergent, whereas the direct trapezoidal over the secondary energy and the direct interpolation of energy-angle-integrated damage are shown accurate. On the other hand, it is shown that the DPA cross sections are overestimated if isotropic angular distributions are assumed. However, the DPA cross section is not sensitive to the high-order Legendre polynomials because the former is an angle-integrated quantity. Numerical results of neutron elastic scattering show that 2 orders of Legendre polynomials can give the DPA rates of Fe-56 within 0.5% overestimation for fission reactors, while 4 orders are required for fusion reactors. For neutron inelastic scatterings-induced DPA, the first order Legendre polynomial is sufficient for both fission and fusion reactors.