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
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.
| 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.