Astroparticle Physics

353 Kinematics and Cross Sections“The best way to escape a problem is tosolve it.”Alan SaportaIn astroparticle physics the energies of participating particlesare generally that high, that relativistic kinematics mustbe used. In this field of science it becomes obvious that massand energy are only different facets of the same thing. Massis a particularly compact form of energy, which is related tothe total energy of a particle by the famous Einstein relationrelativistic kinematicsE = mc 2 . (3.1)In this equation m is the mass of a particle, which moveswith the velocity v, andc is the velocity of light in vacuum.The experimental result that the velocity of light in vacuumis the maximum velocity in all inertial systems leads tothe fact that particles with velocity near the velocity of lightdo not get much faster when accelerated, but mainly onlybecome heavier,relativistic mass increasem =m 0√1 − β 2 = γm 0 . (3.2)In this equation m 0 is the rest mass, β = v/c is the particlevelocity, normalized to the velocity of light, andγ =1√1 − β 2(3.3)is the Lorentz factor. Using this result, (3.1) can also be writtenasLorentz factorE = γm 0 c 2 , (3.4)where m 0 c 2 is the rest energy of a particle. The momentumof a particle can be expressed asp = mv = γm 0 βc . (3.5)Using (3.3), the difference