Relation of charge-changing cross sections to relative population of charge states for fast heavy ions

Abstract

The relations between charge-changing cross sections sigma ij and the relative populations phi i(x) of states i=1, N are analysed. An analytic solution for the vector phi (x) is given for any number N of states in terms of eigenvalues and eigenvectors of a matrix M of the cross sections. Another solution for phi (x) is given in terms of successive multiple squarings of the matrix M, then acting on phi (0). The manifolds of ratios of various sigma ij which lead to the same equilibrium distribution phi ( infinity ) are examined along with the question of the sensitivity of phi (x) data in various cases for determining various sigma ij. The inclusion of excited states in the matrix is discussed, as well as the minor effect of complex eigenvalues.