Definition of cross sections 1 - Moodle

Formation of a compound nucleus 4A decay channel is open only if the three following laws are observed: conservation ofenergy, linear and angular momentum of the nuclide-nucleus pair. The first two laws havealready been studied in Week 3. The conservation of angular momentum is written(12)J = I +K +L whereI , K = angular momentum of the target nucleus A ZX in its ground state and of the neutronJ = angular momentum of the compound nucleus A+1ZX in its excited stateL = orbital angular momentum of the nuclide-nucleus pair in the CM.The classical definition of the orbital angular momentum of the nuclide-nucleus pair aboutthe origin of the CM is L = m(r n −r CM )×v n +mA(r A −r CM )×v A .Using relations in week 3 and defining the e z –directed axis as perpendicular to the planewhere the particles are moving, this equation simplifies to(13)L = ∆RV R m 0 e zwhere ∆R is the distance between the lines of definition of vectors v n and v A in the CM andm 0 is the reduced mass of the neutron defined as m 0 = mAA+1 .ENE6101: Week 4 Cross sections – 13/37