(a) Find a quantitative expression for the thermal equilibrium concentration n = n+ = n– in the particle-antiparticle reaction A+ + A– = 0. The reactants may be electrons and positrons; protons and antiprotons; or electrons and holes in a semiconductor. Let the mass of either particle be M; neglect the spins of the particles. The minimum energy release when A+ combines with A– is ∆. Take the zero of the energy scale as the energy with no particles present.
(b) Estimate n in cm-3 for an electron (or a hole) in a semiconductor T = 300K with a ∆ such that ∆/τ = 20. The hole is viewed as the antiparticle to the electron. Assume that the particles are in the classical regime.
(c) Correct the result of (a) to let each particle have a spin of ½. Particles that have antiparticles are usually fermions with spins of ½.