Cross Section for Energy Transfer between Two Moving Particles

Abstract

The classical cross section ${\sigma }_{\Delta E}$, for producing a specified energy transfer $\Delta E$ in the collision of two particles 1,2 having arbitrary masses and velocities ${\mathbf{v}}_1$,${\mathbf{v}}_2$ in the laboratory system, is derived. The effective average (for fixed speeds $v_1$,$v_2$) of ${\sigma }_{\Delta E}$ over all directions of the particle velocities ${\mathbf{v}}_1$ and/or ${\mathbf{v}}_2$ is then computed. These results are required in the classical calculations of atomic-collision cross sections via the procedures recently proposed by Gryzinski. The method will yield the average of any function $F(v,V,cos\theta )$ over all directions of the particle velocities, where v=${\mathbf{v}}_1$-${\mathbf{v}}_2$, V is the velocity of the center of mass, and $\theta$ is the angle between v and V.