Definition of cross sections 1 - Moodle

The SLBW formula 8The SLBW equations (28) and (31) are function of the excitation energy e exc in the CM.However, most theoretical developments used in reactor physics are expecting crosssections defined in term of LAB-related quantities. We remember the expression of theexcitation energy E exc in the LAB as(37)E exc = A+1A e exc = 1 2 mV 2 R .In case where the target nuclide is initially at rest, E exc is equal to the initial energy of theneutron in the LAB. If we replace e exc by E exc in Eqs. (??) and (??), these equations remainvalid provided that we redifine LAB-related peak energy and resonance widths as(38)E 1 = A+1A e 1 and Γ x,1 = A+1A γ x,1 .Peak energy and resonance widths are measured and are reported in reference tables asLAB-defined values, similar to those defined in Eqs. (38). The neutron widths are reportedwith the statistical spin factor included, as g J Γ n,1 (E 1 ).ENE6101: Week 4 Cross sections – 31/37