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Furthermore, if the beam is moving at velocity v toward a stationary target for a duration of t, then N_{B} = n_{B}vtA, where n_{B} is the number density of the beam. Thus, = P/L_{int} , where P = N/N_{T} is the transition probability per target particle, L_{int} = n_{B}vt is the integrated (over time, in unit of barn b = 10^{24} cm^{2}) luminosity of the incident beam. 

Figure 01o Scattering Cross Section [view large image] 
It is the P and L_{int} measured in experiments to obtain , which is in turn used to check out the theoretical formulation. 
Figure 01p Partial Wave Scattering 
Figure 01q Scattering Zones [view large image] 
See Fabulous Formulas for a portrait of the spherical coordinates, and the expression for ^{2}. Also see some forms of the Legendre Polynomial. 
Figure 01r Decay Width 
Figure 01r shows the decay width of the Z boson in weak interaction decay at about 91 Gev with a lifetime of 1/ ~ 2.5x10^{25} sec (see "Physics of W and Z Bosons", and natural unit conversion to cgs). 