370 7 Nuclear Physics – I
The solid angle forθ 1 =0 andθ 2 =θis
Ω=
∫
dΩ=∫θ02 πsinθdθ= 2 π(1−cosθ)The maximum solid angleΩ= 4 π(forθ=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
massm 1 moving with velocityu 1 in the LS be scattered by the target particle of mass
initially at rest and be scattered at angleθwith velocityv 1. The target particle recoils
with velocityv 2 at angleφthe angles being measured with the incident direction
(Fig. 7.2). The corresponding angles in the CMS will be denoted byθ∗andφ∗.
Fig. 7.2Scattering angle and recoil angle in the LS and CMS