energy gained by the moderating nuclei K 2f / K 1i is f = − f (elastic collision) m m One can also verify this result by substituting from Eq. ( . ). For deuterium m = m and we obtain f = / while f = / .
Almost % of the neutron’s energy is transferred to deuterium. For carbon f = . % and f = . %.
In practice, however, this number is smaller since head-on collisions are rare. If the initial velocities and final velocities of both the bodies are along the same straight line, then it is called a one-dimensional collision, or head-on collision. In the case of small spherical bodies, this is possible if the direction of travel of body passes through the centre of body which is at rest. In general, the collision is two- dimensional, where the initial velocities and the final velocities lie in a plane.
. . Collisions in Two Dimensions Fig. .
also depicts the collision of a moving mass m with the stationary mass m . Linear momentum is conserved in such a collision. Since momentum is a vector this implies three equations for the three directions { x, y, z }. Consider the plane determined by the final velocity directions of m and m and choose it to be the x-y plane.
The conservation of the z -component of the linear momentum implies that the entire collision is in the x-y plane. The x - and y- component equations are m v i = m v f cos θ + m v f cos θ ( . ) = m v f sin θ − m v f sin θ ( . ) One knows { m , m , v i } in most situations.
There are thus four unknowns { v f , v f , θ and θ }, and only two equations. If θ