Classical Dynamics of Particles and Systems · Problem 9-33

Motion in a Noninertial Reference Frame — Marion & Thornton

Physics — Mechanics · scattering-cross-section

Problem

Show that

T_1/T_0

can be expressed in terms of

m_2/m_1 \equiv \alpha

and

\cos\psi \equiv y

\frac{T_1}{T_0} = (1 + \alpha)^{-2}\left(2y^2 + \alpha^2 - 1 + 2y\sqrt{\alpha^2 + y^2 - 1}\right)

Plot

T_1/T_0

as a function of

\psi

for

\alpha = 1, 2, 4

, and 12. These plots correspond to the energies of protons or neutrons after scattering from hydrogen (

\alpha = 1

), deuterium (

\alpha = 2

), helium (

\alpha = 4

), and carbon (

\alpha = 12

), or of alpha particles scattered from helium (

\alpha = 1

), oxygen (

\alpha = 4

), and so forth.