Astroparticle Physics

48 3 Kinematics and Cross Sectionswhere N A is the Avogadro number, i.e., the number ofnucleons per g, and σ N is the cross section per nucleon.The number of particles penetrating a target x unaffectedby interactions isN = N 0 e −x/λ .How many collisions happen in a thin target of thicknessx (N A = 6.022 × 10 23 g −1 , σ N = 1b,N 0 = 10 8 , x =0.1g/cm 2 )?3. The neutrino was discovered in the reaction¯ν e + p → n + e + ,where the target proton was at rest. What is the minimumneutrino energy to induce this reaction?4. The scattering of a particle of charge z on a target ofnuclear charge Z is mediated by the electromagnetic interaction.Work out the momentum transfer p b , perpendicularto the momentum of the incoming particle foran impact parameter b (distance of closest approach)!For the calculation assume the particle track to be undisturbed,i.e., the scattering angle to be small.5. The scattering of an electron of momentum p on a targetnucleus of charge Z was treated in Problems 4 underthe assumption that the scattering angle is small. Workout the general expression for the transverse momentumusing the Rutherford scattering formulatan ϑ 2 = Zr ebβ 2 , (3.62)where ϑ is the scattering angle.