Critical energy for electrons and positrons

An electron (positron) loses energy by bremsstrahlung at a rate very nearly proportional to its energy, while collision losses (ionization and excitation) vary only slowly. The bremsstrahlung stopping power asympotically approaches X₀E, where X₀ is the radiation length in the material and E is the particle's energy. (See the Review of Particle Physics for a figure showing the difference.)

"Critial energy" is variously defined as the energy at which the collision loss rate equals the bremsstrahlung rate (in the EGS4 code, for example) or the energy at which the collision loss rate equals X₀E (Rossi). (See the Review of Particle Physics for a figure illustrating the difference.) Apparently the second form more accurately describes transverse shower development, and that is what we use here.

Comparison:

mmm	mmmmmmm	mmmmmmmmmmm	mmmmmmmmmmm
Z	Element	EGS4 method	Rossi method
3	Lithium	149.06	149.06
14	Silicon	40.05	40.19
29	Copper	19.63	19.42
47	Silver	12.57	12.36
82	Lead	7.79	7.43

In high energy physics E nearly always refers to the total energy. T = E - M is the kinetic energy, more appropriate for energies not large compared with the particle mass. Rossi uses E for the kinetic energy. The values reported in our tables are kinetic energies.