Barkas effect in stopping power and energy-loss straggling for dressed projectiles

C. D. ARCHUBI, I. ABRIL, R. GARCÍA MOLINA, N. R. ARISTA

Forth Worth, Texas

Conferencia; 22nd International Conference on the Application of Accelerators in Research and Industry (CAARI 2012); 2012

The deviation in the stopping power from the quadratic dependence on projectile charge predicted by the Bethetheory [1], called Barkas effect, was first experimentally measured by Barkas and co-workers [2] as a difference in thepenetration range for positive and negative pions in matter. During the last four decades an important collection oftheoretical studies has been developed to explain the Barkas effect. However, all these analysis were made assuming bareprojectiles. On the other hand, it is well known that the degree of ionization of a projectile depends on its velocity [3].Therefore, the effect of the bound electrons in the energy loss of an ion must be considered at low and intermediatevelocities.In this work we evaluate the Barkas effect in the stopping power and the energy-loss straggling for dressedprojectiles moving in a free electron gas. The projectile trajectories were calculated by a numerical simulation, where thepotential is described by a sum of two Yukawa potentials related to the screening of the projectile by the electron gas andthe binding electrons. Then, following the classical model of the transport cross section [4], we calculate the Barkas factorfor H, He, Li and C projectiles in an Al target in a wide velocity range. Applying a scaling law analogous to that proposedby Lindhard [5] for bare projectiles, we conclude that the Barkas factor increases with the degree of ionization for low andintermediate velocities.[1] H. Bethe, Ann. Phys. 5 (1930) 325.[2] W.H. Barkas et al. Phys. Rev. 101 (1956) 778; Phys. Rev. Lett. 11 (1963) 26.[3] W. Brandt, M. Kitagawa, Phys. Rev. B 25 (1982) 5631.[4] N.R. Arista, P.L. Grande, A.F. Lifschitz, Phys. Rev. A 70 (2004) 042902.[5] J. Lindhard, Nucl. Instr. and Meth. 132 (1976) 1.