Spherically symmetric models for x-ray damage and the movement of electrons produced in non-spherically symmetric targets such as bio-molecules

This paper develops spherically symmetric models as well as a more accurate model for the calculation of the damage and the movement of free and quasi-free electrons which are produced from the irradiation of x-ray free electron lasers (XFELs). The behaviour of free and quasi-free electrons is studied for targets with various shapes such as spheres and ellipsoids by treating the space distribution of free and quasi-free electrons. Furthermore, the limits of the application of spherically symmetric models to various shapes are discussed. The spherically symmetric model developed here is also applied to a bio-molecule. The results obtained are useful for the analysis of the three-dimensional structures of large bio-molecules in the experiments of XFELs.