Theoretical solutions of stopping power in cylindrical many-electron systems

Using several kinds of mathematical formulae of the modified Bessel function, and taking into account the uncertainty principle at mathematically singular point for inelastic interactions between a projectile and electron, we develop the theory of stopping power for cylindrical many-electron systems. Addition theorem, the formula of Wronskian and integral formulae of the modified Bessel function perform important roles in solving complex integral equation of stopping power discussed here. For a cylindrical free electron gas, we derive the theoretical solution of stopping power analytically. We also show the equipartion rule of contributions due to surface plasmon mode to stopping power for random systems.