Rutherford backscattering spectrometry is named after Lord Rutherford, a physicist sometimes referred to as the father of nuclear physics.  Rutherford supervised a series of experiments carried out by Hans Geiger and Ernest Marsden between 1909 and 1914 studying the scattering of alpha particles through metal foils.  While attempting to eliminate "stray particles" they believed to be caused by an imperfection in their alpha source, Rutherford suggested that Marsden attempt to measure backscattering from a gold foil sample.  According to the then-dominant plum-pudding model of the atom, in which small negative electrons were spread through a diffuse positive region, backscattering of the high-energy positive alpha particles should have been nonexistent.  At most small deflections should occur as the alpha particles passed almost unhindered through the foil. Instead, when Marsden positioned the detector on the same side of the foil as the alpha particle source, he immediately detected a noticeable backscattered signal.  According to Rutherford, "It was quite the most incredible event that has ever happened to me in my life.  It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."
Rutherford interpreted the result of the Geiger–Marsden experiment as an indication of a Coulomb collision with a single massive positive particle.  This led him to the conclusion that the atoms positive charge could not be diffuse but instead must be concentrated in a single massive core: the atomic nucleus.  Calculations indicated that the charge necessary to accomplish this deflection was approximately 100 times the charge of the electron, close to the atomic number of gold.  This led to the development of the Rutherford model of the atom in which a positive nucleus made up of Ne positive particles, or protons, was surrounded by N' orbiting electrons of charge -e to balance the nuclear charge.  This model was eventually superseded by the Bohr atom, incorporating some early results from quantum mechanics.
If the energy of the incident particle is increased sufficiently,  the Coulomb barrier is exceeded and the wavefunctions of the incident and struck particles overlap. This may result in nuclear reactions in certain cases, but frequently the interaction remains elastic, although the scattering cross-sections may fluctuate wildly as a function of energy and no longer be calculable analytically.  This case is known as "Elastic (non-Rutherford) Backscattering Spectrometry" (EBS).  There has recently been great progress in determining EBS scattering cross-sections,  by solving Schrödinger's equation for each interaction. However, for the EBS analysis of matrices containing light elements, the utilization of experimentally measured scattering cross-section data is also considered to be a very credible option.