ABSTRACT
FIGURE 2.1 Elastic collision diagram between two unequal masses as seen in the laboratory reference frame with reference to CM reference frame scattering angles.
(2.2)= θ + φM v M v cos M v cos1 0 1 1 2 2
(2.3)= θ − φ0 M v sin M v sin1 1 2 2 Equations (2.1)–(2.3) can be solved in various forms; for example, transpos-
ing the first term on the right to the left side in Equations (2.2) and (2.3), squaring and adding, will eliminate ϕ, giving
(2.4)( ) ( ) ( )= + − θM v M v M v 2M v v cos2 2 2 1 0 2 1 1 2 12 0 1 Substituting Equation (2.4) into Equation (2.1) to eliminate v2, one finds the
ratio of the particle’s velocity after and before the collision:
(2.5)
=
+ θ ±
+ θ + −
+
v v
M M M
cos M M M
cos M M M M
Equation (2.5) can be used with Equation (2.4) to determine v2 and E2, and it can be used with Equation (2.2) to find the angle of recoil, ϕ, of the scattered target atom.
