be "inelastic scattering". Target recoil can be handled fairly easily. We still consider the situation described above, with particle 2 initially at rest in the laboratory frame. The above results all apply in the center of mass frame. In the lab frame, denoted by a subscript L, the scattering angle for a general central potential is where . For , . For a heavy particle 1, and , that is, the incident particle is deflected through a very small angle. The final kinetic energy of particle 2 in the lab frame, , is F is between 0 and 1, and satisfies , meaning it is the same if we switch the particle masses. The energy ratio maximizes at F for a head-on collision with and thus . For , . It maximizes at 1 for , which means that in a head-on collision with equal masses, all of particle 1's energy is transferred to particle 2. For , or a heavy incident particle, and approaches zero, meaning the incident particle keeps almost all of its kinetic energy. For any central potential, the differential cross-section in the lab frame is related to that in the center-of-mass frame by To give a sense of the importance of recoil, we evaluate the head-on energy ratio F for an incident alpha particle (mass number ) scattering off a gold nucleus (mass number ): . In the opposite case of gold incident on an alpha, F has the same value, as noted above. For the more extreme case of an electron scattering off a proton, and . See also Rutherford backscattering spectrometry References Textbooks External links E. Rutherford, The Scattering of α and β Particles by Matter and the Structure of the Atom, Philosophical Magazine. Series 6, vol. 21. May 1911 Scattering Foundational quantum physics Ernest Rutherford