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7 Nuclear Physics – I
The solid angle for θ 1 = 0 and θ 2 = θ is
Ω =
d Ω =
θ
0
2 π sin θ d θ = 2 π(1 − cos θ)
The maximum solid angle Ω = 4π (for θ = π)
Kinematics of scattering
Relations between velocities, angles etc. in the Lab system (LS) and centre
of mass system (CMS)
In the centre of mass system the total momentum of particles is zero. Let a particle of
mass m 1 moving with velocity u 1 in the LS be scattered by the target particle of mass
initially at rest and be scattered at angle θ with velocity v 1 . The target particle recoils
with velocity v 2 at angle ϕ the angles being measured with the incident direction
(Fig. 7.2). The corresponding angles in the CMS will be denoted by θ
∗ and ϕ
∗ .
Fig. 7.2 Scattering angle and recoil angle in the LS and CMS