Partial stopping power and straggling effective charges of heavy ions in condensed matter

The stopping-power effective charge (SPEC) has been formulated in the Brandt-Kitagawa (BK) model. In the effective-charge theory, the stopping power of heavy ions can be obtained by scaling using the SPEC with a mean charge state. Based on the BK treatment for the statistical ion screening and the dielectric function, a formula for the straggling effective charge (SGEC) has been obtained. The SGEC, which is different from the SPEC, provides the scaling of collisional (without charge exchange) straggling in the effective-charge theory. To properly describe the stopping power and straggling of heavy projectiles in condensed matter, partial effective charges (PEC's) are introduced to describe the charge-state-dependent stopping power and straggling in a charge-state model. The partial stopping power and straggling of projectiles with a fixed charge state can be obtained by scaling to those of the bare nucleus with related PEC's. This allows the calculation of the total stopping power and straggling of heavy projectiles in a charge-state description including the charge-exchange effect.