Stopping Power and Range of Heavy Ions

The equations presented in Secs. 4.3-4.6 for energy loss and range of charged particles were derived with the assumption that the charge of the particle does not change as the particle traverses the medium. This assumption is certainly 

An excellent review of the subject is presented by Northcliffe and Lindhard, Scharff, and Schiott. The results are usually presented as universal curves in terms of two dimensionless quantities, the distance s and the energy e, first 

X = actual distance traveled flo = h /me = Bohr radius = 5.29 X 10 m Zj, Mj = charge and mass of incident particle Z2, M2 = charge and mass of stopping material The parameters N, Tq, and mc have been defined in Sec. 4.3. 

At high ion velocities, v VqZ, where Uq = e /h = orbital velocity of the electron in the hydrogen atom, the nuclear energy loss is negligible. The particle has an effective charge equal to Zj, and the energy loss is given by an equation of the form 

At velocities of the order of v VqZ, the ion starts picking up electrons and its charge keeps decreasing. The energy loss through nuclear collisions is still negligible. 

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