NUMERICAL MENTHOD FOR LAYERD CYLINDRICAL CONFIGURATION

Abstract

For the purpose of investigating the physical processes of atomic and molecular systems placed in mediums, we consider a system of layered cylindrical structure. The Green function of cylindrical system is also more complicated then the one of spherical or planar system. It makes calculating the Green function of system more difficult because the Green function has an infinite sum of n-modes and an integral over the entire wave number. The process of numerical calculations requires handling arithmetic over- and under-flow of bessel and hankel functions of complex variables when variables and/or the order of functions are large. In addition, the expression of Green function has the C_i. These coefficients can approach the limit 0/0 or infinity/infinity, it making numerical calculations impossible. In this article, we propose the proceduce to transform T_i matrices in the recurrence-matrices relation to eliminate 0/0 and infinity/infinity forms of coefficients C_i. By doing so, it makes the values of the T_i-matrices no longer the same as their original values but the final result does not change the Green function of system. These transforms are general for any N-layers of cylindrical configuration.