1 Irradiation Damage Calculation with Angular Distribution Shengli Chen 1,3,* , David Bernard 1 , Pierre Tamagno 1 , Jean Tommasi 1 , Stéphane Bourganel 2 , and Gilles Noguère 1 1 CEA, Cadarache, DEN/DER/SPRC/LEPh, 13108 Saint Paul Les Durance, France 2 CEA, Saclay, DEN/DM2S/SERMA/LPEC, 91191 Gif sur Yvette, France 3 Université Grenoble Alpes, I-MEP2, 38402 Saint Martin d'Hères, France * Corresponding author: shengli.chen@cea.fr Abstract The operating lifetime of a reactor is determined by the irradiation damage which is quantitatively accounted by the number of Displacement per Atom (DPA). The DPA rate is conventionally computed with DPA cross sections in reactor applications. However, the Gauss-Legendre Quadrature (GLQ) method used in current processing codes such as NJOY is shown unable to ensure the convergence of DPA cross sections due to the discontinuity of the damage energy versus the emission angle. The GLQ- based Piecewise Integration (GLQPI) is proposed to ensure the numerical convergence. The integration based on the GLQPI is shown suitable to compute DPA. On the other hand, even if high-order Legendre polynomials are important to describe the anisotropic angular distribution, 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 56 Fe within 0.5% overestimation for fission reactors, while 4 orders are required for fusion reactors. In the case of neutron inelastic scatterings-induced DPA, only the first order Legendre polynomial is sufficient for both fission and fusion reactors. Keywords: DPA, angular distribution, Gauss-Legendre quadrature, 56 Fe 1. Introduction The 21 st Conference of the Parties to the UN framework convention on climate change (COP21) builds upon the convention of a significant reduction in the emission of greenhouse gases. Nuclear power is and will be one of the most important energies due to its high efficiency and low CO2 emission. However, the irradiation environment changes the properties of materials. For example, the designed service life of Pressurized Water Reactors (PWRs) and the potential extension of operating lifetime are based on the irradiated performance of the Reactor Pressure Vessel (RPV). The irradiation leads to the decrease of the rupture strain for metals. The investigations of irradiation effect on materials are of significance. When an atom in a material is knocked-on by a kinematic particle, a vacancy and a corresponding interstitial are formed in the lattice. In addition, the Primary Knock-on