1000 Solved Problems in Modern Physics

8.1 Basic Concepts and Formulae 431

Table 8.2Comparison 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. 8.3Kinematics
of a collision

Inverse reactions and the reciprocity theorem

σ(b→a)

σ(a→b)

=

(2Ix+1)(2Ia+1)

(2Iy+1)(2Ib+1)

.

p^2 a

p^2 b

(8.30)

At the same CM energy.

σSl=

π

k^2

(2l+1)| 1 −ηl|^2 (8.31)

σrl=

π

k^2

(2l+1)(1−|ηl|^2 ) (8.32)

The Breit – Wigner formulae– Reactions via compound nucleus formation.

σS=

πλ-^2 Γ^2 s.g

(E−ER)^2 +(Γ/2)^2

(8.33)

σr=

πλ-^2 ΓRΓS.g

(E−ER)^2 +(Γ/2)^2

(8.34)

σt=σs+σr=

πλ-^2 ΓsΓ.g

(E−ER)^2 +(Γ/2)^2

(8.35)