Astroparticle Physics and Cosmology by (Eds.) G. Senjanovic, A. Smirnov, G. Thompson

By (Eds.) G. Senjanovic, A. Smirnov, G. Thompson

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11)). It is only possible 18 1 Definition and orders of magnitude of principal quantities to speak of a particle temperature if the distribution in energy (velocity) is Maxwellian (short for a Maxwell-Boltzmann distribution); if not, in addition to the average energy of the particles, it is necessary to know the distribution in energy of these particles. We will see that, in a system in thermodynamic equilibrium, a single value T is sufficient to characterise the distribution of photons and particles at the same time.

69)) throughout the collision, hence: w0 = w0 . 69), where we have replaced wα and wβ by wα0 and wβ0 . 71) which shows that the velocities of the two particles, both before and after the collision, are anti-parallel in the CM frame (see also Appendix IV). 72) from which we can write the expression for the velocities of the particles in the CM frame: wα0 = mβ m α + mβ wαβ , wβ0 = − mα m α + mβ wαβ . 73) These various transformations allow us to completely determine the motion of the particles in the laboratory frame as the superposition of the rectilinear motion of the CM and the relative motion of the particles in this frame.

A system in TE is completely characterised by its temperature T and the density Nn of its heavy constituent particles. 4). Consider a system consisting of atoms (neutral and ionised) together with EM radiation (photons), this radiation being linked to the excited states of the atoms and ions as well as to the Coulomb interactions between charged particles (Bremsstrahlung, Sect. 1). This ensemble is in complete thermodynamic equilibrium if there are sufficient interactions between the various components of the system, such that each type of energy exchange process in a given energy direction (for example, increase of energy of the “particle” during the interaction) is statistically rigorously compensated by the same type of process in the inverse direction (loss of energy by the same type of particle in our example): this requirement of compensation (detailed balance) is called the principle of microscopic reversibility, or more simply, micro-reversibility.

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