Astroparticle Physics

17.4 Chapter 4 3434.p b❅■ ✒❅✻ target (mass A,chargeZ)rz b✲ particle track pForce F = zeZe rr ,p b =∫ +∞−∞= zZe2βcr 2∫ +∞zZe 2 b dx|F b | dt =−∞ r 2 r βc∫ +∞b dx−∞ ( √ x 2 + b 2 ) = zZe23 βcbmomentum transferperpendicular to pd(x/b)(√1 + ( )) 3x 2b∫ +∞−∞= 2zZe2βcb= 2r em e cbβ zZ ,} {{ }=2where the classical electron radius is r e =e2m e c 2 .5. Previously the transverse momentum transfer was obtained to be (z = 1)p b = 2 Z r em e cbβ= 2p r eZbβ 2 ,where p = m e v was assumed (classical treatment). The transverse momentum transferis given by p b = p sin ϑ. Sincesin 2γ = 2sinγ cos γ = 2tanγ cos 2 γ =2tanγ1 + tan 2 γ ,one gets, using Rutherford’s scattering formula:r e Z/bβ 2p b = 2p1 + (r e Z/bβ 2 ) 2 .17.4 Chapter 41. φ = N AA σ A = N A σ N ,[N A ]=mol −1 ⎫⎪⎬[A] = gmol −1 ⇒ [φ] =(g/cm 2 ) −1 .[σ A ] = cm 2 ⎪ ⎭