8.1 Basic Concepts and Formulae
431
Table 8.2 Comparison of compound nucleus reactions and direct reactions
Compound nuclear
Feature
reactions
Direct reactions
Times involved
10
−14 –10
−16 s
∼10
−20 –10
−21 s
Dominance of
reaction
Low energy
High energy
Nature of reaction
Surface
phenomenon
Nuclear interior
Cross - section
∼Barn
∼Millibarn
Angular distribution Isotropic in the
CMS
Peaked in the forward
hemisphere
Location of peaks
Energy dependent
Orbital angular
momentum
dependent
Fig. 8.3 Kinematics
of a collision
Inverse reactions and the reciprocity theorem
σ (b → a)
σ (a → b)
=
(2I x + 1)(2I a + 1)
(2I y + 1)(2I b + 1)
.
p
2
a
p
2
b
(8.30)
At the same CM energy.
σ
l
S =
π
k 2 (2l + 1)|1 − η l |
2
(8.31)
σ
l
r =
π
k 2 (2l + 1)(1 − |η l |
2 )
(8.32)
The Breit – Wigner formulae – Reactions via compound nucleus formation.
σ S =
π -
λ
2
Γ
2
s .g
(E − E R ) 2 + (Γ/2) 2
(8.33)
σ r =
π -
λ
2
Γ R Γ S .g
(E − E R ) 2 + (Γ/2) 2
(8.34)
σ t = σ s + σ r =
π -
λ
2
Γ s Γ.g
(E − E R ) 2 + (Γ/2) 2
(8.35)