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Electron Bremsstrahlung
If is the energy spectrum of cosmic electrons in units of / , the photons of energy
produced by electrons of energy are:

(1.15) 
where we used:

(1.16) 
with :

(1.17) 
is the constant of fine structure, is the classical electron radius.
The Gaunt factor for bare nuclei is:
and for neutral atoms is:
The Bremsstrahlung gammaray emissivity of interstellar matter is therefore:

(1.18) 
The radiation lost bu Bremsstrahlung of a relativistic electron of energy moving through a medium formed by Hydrogen atoms is :

(1.19) 
It shows a flat energy spectrum up to energy
.
The photon spectrum is then:

(1.20) 
The integration of the (1.19) on leads to the energy emitted (therefore lost) by the electron :

(1.21) 
For a distribution of electrons with spectrum
we get:

(1.22) 
Therefore the index of photon spectrum of electron spectrum have the same value.
Next: Inverse Compton
Up: The physical processes producing
Previous: The cross section
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Andrea Giuliani
20050121