Question: Who discovered the scattering of which Thomson scattering is just the low energy limit ?

Context paragraphs:
Elastic scattering: Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics.  In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified (by interaction with other particles and/or potentials).  Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not.  Generally, elastic scattering describes a process where the total kinetic energy of the system is conserved.  During elastic scattering of high-energy subatomic particles, linear energy transfer (LET) takes place until the incident particle's energy and speed has been reduced to the same as its surroundings, at which point the particle is "stopped."

Inelastic scattering: In chemistry, nuclear physics, and particle physics, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved (in contrast to elastic scattering).  In an inelastic scattering process, some of the energy of the incident particle is lost or increased.  Although the term is historically related to the concept of inelastic collision in dynamics, the two concepts are quite distinct; inelastic collision in dynamics refers to processes in which the total macroscopic kinetic energy is not conserved.  In general, scattering due to inelastic collisions will be inelastic, but, since elastic collisions often transfer kinetic energy between particles, scattering due to elastic collisions can also be "in"elastic, as in Compton scattering.

Quasielastic neutron scattering: Quasielastic neutron scattering (QENS) designates a limiting case of inelastic neutron scattering, characterized by energy transfers being small compared to the incident energy of the scattered particles.  In a more strict meaning, it denotes scattering processes where dynamics in the sample (such as diffusive dynamics) lead to a broadening of the incident neutron spectrum, in contrast to, e.g., the scattering from a diffusionless crystal, where the scattered neutron energy spectrum consists of an elastic line (corresponding to no energy transfer with the sample) and a number of well-separated inelastic lines due to the creation or annihilation of phonons with specific energies.

Ralph S. Phillips: Ralph Saul Phillips (23 June 1913 – 23 November 1998) was an American mathematician and academic known for his contributions to functional analysis, scattering theory, and servomechanisms.  He served as a Professor of mathematics at Stanford University.  He made major contributions to acoustical scattering theory in collaboration with Peter Lax, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent.  With Lax, he coauthored the widely referred book on scattering theory titled "Scattering Theory for Automorphic Functions".  Phillips received the 1997 Leroy P. Steele Prize for Lifetime Achievement.

Rutherford scattering: Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction.  It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model.  It is now exploited by the materials analytical technique Rutherford backscattering.  Rutherford scattering was first referred to as Coulomb scattering because it relies only upon static electric (Coulomb) forces, and the minimal distance between particles is set only by this potential.  The classical Rutherford scattering of alpha particles against gold nuclei is an example of "elastic scattering" because neither the alpha particles nor the gold nuclei are internally excited.  The Rutherford formula (see below) further neglects the recoil kinetic energy of the massive target nucleus.

UK Molecular R-matrix Codes: The term R-matrix can have several meanings, and was pioneered by Professor Philip Burke (winner of the Will Allis Prize for the Study of Ionized Gases Recipient in 2012).  In this case it is used in computational quantum mechanics to study scattering.  The R-matrix method of modelling low energy scattering by positrons and electrons by atomic and or molecular targets is used commonly by researchers.  The CCPQ and CCP2 have supported various incarnations of the UK Molecular R-matrix project for almost 40 years.  The UK Molecular R-Matrix Group is actually a subgroup of CCP2, and their codes are maintained by Professor Jonathan Tennyson and his group of researchers.  Advances in research have shown that the UK Molecular R-matrix codes can be used to explain scattering problems involving light molecular targets.

Compton scattering: Compton scattering, discovered by Arthur Holly Compton, is the inelastic scattering

Thomson scattering: Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism.  It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency do not change as a result of the scattering.  This limit is valid as long as the photon energy is much less than the mass energy of the particle: formula_1, or equivalently, if the wavelength of the light is much greater than the Compton wavelength of the particle.

String phenomenology: String phenomenology is a branch of theoretical physics that attempts to construct realistic or semi-realistic models of particle physics based on string theory.  The term "realistic" is usually taken to mean that the low energy limit of string theory yields a model which bears a resemblance to the Minimal Supersymmetric Standard Model (MSSM).

Multiangle light scattering: Multiangle light scattering (MALS) describes a technique for measuring the light scattered by a sample into a plurality of angles.  It is used for determining both the absolute molar mass and the average size of molecules in solution, by detecting how they scatter light.  Collimated light from a laser source is most often used, in which case the technique can be referred to as multiangle laser light scattering (MALLS).  The insertion of the word “laser” was intended to reassure those used to making light scattering measurements with conventional light sources such as Hg-arc lamps that low angle measurements could now be made.  Until the advent of lasers and their associated fine beams of narrow width, the width of conventional light beams used to make such measurements prevented data collection at smaller scattering angles.  In recent years, since all commercial light scattering instrumentation use laser sources, this need to mention the light source has been dropped and the term MALS used throughout.

Supporting paragraphs: Thomson scattering Compton scattering
Answer: Arthur Holly Compton