Ek uv v v2 uv Ehlmac Ek
Since in the non-relativistic energy range the total particle energy E ~ macc , we obtain for the relative change of the total energy:
Thus the energy loss and gain also are not the same for the oblique head-on and overtaking collisions.
Assuming that the cloud velocity distribution is isotropic, we shall average the particle energy change over all the possible realizations of the relative velocity of the particle and cloud:
where 9 is the angle between u and v. If x is the azimuthally angle of projection of u on a plane perpendicular to v, then
where AEk(p) is determined from Eq. 4.4.5 and
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