## Screened Relativistic (SR) Non Ionizing Energy Loss (NIEL) Calculator

An expression for the Mott cross section of electrons and positrons on nuclei with Z up to 118

Radiation Physics and Chemistry, Volume 90, September 2013, Pages 39–66

M.J. Boschini^{a,b}, C. Consolandi^{a}, M. Gervasi^{a,c}, S. Giani^{d}, D. Grandi^{a}, V. Ivanchenko^{d}, P. Nieminem^{e}, S. Pensotti^{a,c}, P.G. Rancoita^{a}, M. Tacconi^{a,c}

^{a} Istituto Nazionale di Fisica Nucleare, INFN Milano-Bicocca, Milano, Italy^{b} CINECA, Segrate, MI, Italy)^{c} Department of Physics, University of Milano Bicocca, Milano, Italy^{d} CERN, Geneva, 23, CH-1211, Switzerland^{e} ESA, ESTEC, AG Noordwijk, Netherlands

In the present work, an improved numerical solution for determining the ratio, *R*^{Mott}, of the unscreened Mott differential cross section (MDCS) with respect to Rutherford's formula is proposed for the scattering of electrons and positrons on nuclei with 1≤*Z*≤118. It accounts for incoming lepton energies between 1 keV and 900 MeV. For both electrons and positrons, a fitting formula and a set of fitting coefficients for the ratio *R*^{Mott} on nuclei are also presented. The found average error of the latter practical interpolated expression is typically lower than 1% also at low energy for electrons and lower than 0.05% for positrons for all nuclei over the entire energy range. Both the improved numerical solution and the interpolated practical expression were found in good agreement with the partially available previous calculations.

Keywords: Mott cross section; Electron interaction on nuclei; Unscreened nuclear Coulomb potential

13th ICATPP Conference on Astroparticle, Particle, Space Physics and Detectors for Physics Applications, Villa Olmo (Como, Italy), 3–7 October, 2011.

M.J. Boschini^{1,2} , C. Consolandi^{∗,1} , M. Gervasi^{1,3} , S. Giani^{4} , D. Grandi^{1} , V. Ivanchenko^{4} , P. Nieminem^{5} , S. Pensotti^{3} , P.G. Rancoita^{1} and M. Tacconi^{1}

^{1} INFN-Milano Bicocca, P.zza Scienza,3 Milano, Italy^{2} CILEA, Via R. Sanzio, 4 Segrate, MI-Italy^{3} Milano Bicocca University, P.zza della Scienza, 3 Milano, Italy^{4} CERN, Geneva, 23, CH-1211, Switzerland^{5} ESA, ESTEC, AG Noordwijk (Netherlands)

The treatment of the electron–nucleus interaction based on the Mott differential cross section was extended to account for effects due to screened Coulomb potentials, finite sizes and finite rest masses of nuclei for electrons above 200 keV and up to ultra high energies. This treatment allows one to determine both the total and differential cross sections, thus, subsequently to calculate the resulting nuclear and non-ionizing stopping powers. Above a few hundreds of MeV, neglecting the effect due to finite rest masses of recoil nuclei the stopping power and NIEL result to be largely underestimated. While, above a few tens of MeV, the finite size of the nuclear target prevents a further large increase of stopping powers which approach almost constant values.

ICATPP Conference on Cosmic Rays for Particle and Astroparticle Physics, Villa Olmo (Como, Italy), 7–8 October, 2010

M.J. Boschini^{1,2} , C. Consolandi^{∗,1} , M. Gervasi^{1,3} , S. Giani^{4} , D. Grandi^{1 }, V. Ivanchenko^{4} , S. Pensotti^{3} , P.G. Rancoita^{∗∗,1} , M. Tacconi^{1}^{1} INFN-Milano Bicocca, P.zza Scienza,3 Milano, Italy^{2} CILEA, Via R. Sanzio, 4 Segrate, MI-Italy^{3} Milano Bicocca University, Piazza della Scienza, 3 Milano, Italy^{4} CERN, Geneva, 23, CH-1211, Switzerland

In the space environment, instruments onboard of spacecrafts can be affected by displacement damage due to radiation. The differential scattering cross section for screened nucleus–nucleus interactions - i.e., including the effects due to screened Coulomb nuclear fields -, nuclear stopping powers and non-ionization energy losses are treated from about 50 keV/nucleon up to relativistic energies.

GEANT4-BASED APPLICATION DEVELOPMENT FOR NIEL CALCULATION IN THE SPACE RADIATION ENVIRONMENT

ASTROPARTICLE, PARTICLE AND SPACE PHYSICS, DETECTORS AND MEDICAL PHYSICS APPLICATIONS. Proceedings of the 11th Conference. Held 5-9 October 2009 in Villa Olmo, Como, Italy

M.J. BOSCHINI^{1,2} , C. CONSOLANDI^{∗,1,3} , M. GERVASI^{1,3} , S. GIANI^{4} , D. GRANDI^{1} , V. IVANCHENKO^{4} , P.G. RANCOITA^{1} .

^{1} INFN-Milano, Pizza Scienza,3 Milano, Italy^{2} CILEA, Via R. Sanzio, 4 Segrate, MI-Italy^{3} Milano Bicocca University, P.zza della Scienza, 3 Milano, Italy^{4} CERN, Geneva, 23, CH-1211, Switzerland

In the space radiation environment, instruments undergo radiation damage. For testing their reliability one has to know the fluxes of energetic particles and has to be able to quantify their energy deposition. The Geant4 toolkit, via its multilevel approach, enables physicists to reproduce the space radiation environment. In this work we report the results obtained with an improved implementation of the already existing single scattering model allowing the simulation of the recoil of high energy ions. This gives the possibility to calculate the Coulomb scattering contribution to the Non-Ionizing Energy Loss (NIEL) for the complete energy range of interest. Moreover the Galactic Cosmic Ray fluxes of the ISO model 15390 have been introduced in Geant4.