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7 Nuclear Physics – I
Fig. 7.3 Concept of
differential cross-section
The unit of σ is a Barn (B). 1 Barn = 10
−24 cm
2
, 1mB = 10
−27 cm
2 and 1 μB =
10
−30 cm
2 . The unit of σ (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
+ 2γ cos θ
∗ )
3
2
|1 + γ cos θ ∗ |
σ (θ
∗ )
(7.11)
where γ = 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
σ g = π R
2
(7.12)
This is the projected area of a sphere of radius R.
Rutherford Scattering
σ (θ ) = [1.295(z Z/T )
2
/ sin
4 (θ/2)] mb/sr
(7.13)
σ (θ
, θ
= (π/4)R 0
2 [cot
2 (θ
/2) − cot
2 (θ
/2)]
(7.14)
represents the cross-section for particles to be scattered between angles θ
and θ
R 0 (fm) = 1.44z Z/T 0 (MeV)
(7.15)