Impact of Extended Charge Distribution on Energy-Loss Straggling of Heavy Ions

The energy-loss straggling of partially ionized heavy ions is determined by the stochastic fluctuations of the energy loss in atomic collisions remaining in a fixed charge state, (collisional straggling) and by the influence of charge-state fluctuations (charge-exchange straggling) [1, 2]. Besides the charge-changing cross sections the charge-exchange straggling depends critically on the differences between the partial stopping powers of ions in different charge states, and small modifications can influence the variance of the energy loss (Ω) considerably. Therefore, new measurements of energy-loss straggling for few-electron uranium ions penetrating different solids at (200-1000) MeV/u were performed with the fragment separator FRS using the same method as already described in ref.[1] and the theory of partial stopping powers was improved. To determine the difference in stopping number (∆LZ−n) between an ion of nuclear charge (Ze) carrying (n) electrons with a realistic charge distribution and a point-like system of charge (Z − n)e, the method described in ref.[3] for a homogenously charged nucleus was extended to a realistic charge distribution as given by the relativistic quantum-mechanical probability density of 1sstate electrons [4, 5]. As the de Broglie wavelength of a scattered target electron in the rest frame of the projectile is comparable to the radius of the K-shell of an uranium ion in the considered energy range, the electron will probe the true charge distribution of the projectile and scattering will be different from that pertaining to a point charge. In Fig.1 one can clearly see that perturbation theory underestimates the difference ∆LZ−1 by far for high energies. Towards lower velocities close collisions contribute less to the total stopping power and the difference decreases.