372 7 Nuclear Physics – I
Fig. 7.3Concept of
differential cross-section
The unit ofσis a Barn (B). 1 Barn= 10 −^24 cm^2 ,1mB= 10 −^27 cm^2 and 1μB=
10 −^30 cm^2. The unit ofσ(θ, φ) is Barn/Steradian, where steradian (sr) is the unit of
solid angle.
Relation between the differential cross-sections in the LS and CMS
σ(θ)=(1+γ^2 + 2 γcosθ∗)(^32)
| 1 +γcosθ∗|
σ(θ∗) (7.11)
whereγ=m 1 /m 2
Note that the total cross-section is the same for both LS and CMS because the
occurrence of the total number of collisions is independent of the description of the
process.
Geometric cross-section
σg=πR^2 (7.12)
This is the projected area of a sphere of radiusR.
Rutherford Scattering
σ(θ)=[1.295(zZ/T)^2 /sin^4 (θ/2)] mb/sr (7.13)
σ(θ′,θ′′=(π/4)R 02 [cot^2 (θ′/2)−cot^2 (θ′′/2)] (7.14)
represents the cross-section for particles to be scattered between anglesθ′andθ′′
R 0 (fm)= 1. 44 zZ/T 0 (MeV) (7.15)