Stopping Power (particle Radiation) - Electronic, Nuclear and Radiative Stopping

Electronic, Nuclear and Radiative Stopping

Electronic stopping refers to the slowing down of a projectile ion due to the inelastic collisions between bound electrons in the medium and the ion moving through it. The term inelastic is used to signify that energy is lost during the process (the collisions may result both in excitations of bound electrons of the medium, and in excitations of the electron cloud of the ion as well). Linear electronic stopping power is identical to unrestricted linear energy transfer.

Since the number of collisions an ion experiences with electrons is large, and since the charge state of the ion while traversing the medium may change frequently, it is very difficult to describe all possible interactions for all possible ion charge states. Instead, the electronic stopping power is often given as a simple function of energy which is an average taken over all energy loss processes for different charge states. It can be theoretically determined to an accuracy of a few % in the energy range above several hundred keV per nucleon from theoretical treatments, the best known being the Bethe formula. At energies lower than about 100 keV per nucleon, it becomes more difficult to determine the electronic stopping theoretically.

Graphical presentations of experimental values of the electronic stopping power for many ions in many substances have been given by Paul. The accuracy of various stopping tables has been determined using statistical comparisons.

Nuclear stopping power refers to the elastic collisions between the projectile ion and atoms in the sample (the established designation "nuclear" may be confusing since nuclear stopping is not due to nuclear forces, but it is meant to note that this type of stopping involves the interaction of the ion with the nuclei in the target). If one knows the form of the repulsive potential between two atoms (see below), it is possible to calculate the nuclear stopping power . In the stopping power figure shown above for protons in aluminum, nuclear stopping is negligible except at the lowest energy. Nuclear stopping increases when the mass of the ion increases. In the figure shown here, nuclear stopping is larger than electronic stopping at low energy. For very light ions slowing down in heavy materials, the nuclear stopping is weaker than the electronic at all energies.

Especially in the field of radiation damage in detectors, the term "non-ionizing energy loss" (NIEL) is used as a term opposite to the linear energy transfer (LET), see e.g. Refs. Since per definition nuclear stopping power does not involve electronic excitations, NIEL and nuclear stopping can be considered to be the same quantity in the absence of nuclear reactions.

The total non-relativistic stopping power is therefore the sum of two terms: . Several semi-empirical stopping power formulas have been devised. The model given by Ziegler, Biersack and Littmark (the so called "ZBL" stopping, see next chapter), implemented in different versions of the TRIM/SRIM codes, is used most often today.

At extremely high ion energies, one also has to consider radiative stopping power which is due to the emission of bremsstrahlung in the electric fields of the particles in the material traversed. For electron projectiles, radiative stopping is always important. At high ion energies, there may also be energy losses due to nuclear reactions, but such processes are not normally described by stopping power.

Close to the surface of a solid target material, both nuclear and electronic stopping may lead to sputtering.