What Is Particle scattering?

Particle scattering is the deflection or change in direction and energy of a particle as a result of interaction with a target particle, nucleus, or field. It is a foundational process in nuclear and particle physics, materials science, and electron microscopy, providing the primary experimental means for probing the structure of matter at atomic and subatomic scales. The phenomenon is described using quantum mechanics and electromagnetic theory, and the quantitative outcomes are expressed through cross-section formalisms that specify the probability of various scattering outcomes as a function of the incoming particle's energy and direction.

The modern understanding of atomic structure originated directly from scattering experiments: in 1911, Ernest Rutherford and his collaborators used the scattering of alpha particles off gold nuclei to demonstrate that atomic mass is concentrated in a small, dense nucleus, overturning the prevailing diffuse-charge model of the atom.

Elastic and Inelastic Scattering

Particle scattering is classified by whether kinetic energy is conserved in the collision. In elastic scattering, the total kinetic energy of the particles is conserved and the internal states of the target and projectile remain unchanged. The Rutherford formula describes elastic scattering of charged particles from a bare Coulomb potential, giving the differential cross-section as a function of scattering angle and projectile energy. At higher energies or for composite targets, quantum mechanical and relativistic corrections become necessary, leading to Mott cross sections that account for spin-orbit coupling. In inelastic scattering, energy is transferred to the internal degrees of freedom of the target, exciting nuclear or electronic states, and the projectile loses a corresponding amount of kinetic energy. Inelastic scattering cross-sections are often larger than elastic ones because of the additional interaction channels available at a given collision energy.

Scattering Cross-Sections and Measurement

The cross-section is the primary quantitative measure of scattering probability. The differential cross-section gives the probability per unit solid angle that a scattered particle emerges at a particular angle, while the total cross-section integrates over all scattering angles and represents the effective target area presented to the incoming beam. Transport cross-sections weight the differential cross-section by the momentum transfer and govern quantities like mean free path and electrical resistivity in solids. Measuring cross-sections requires a well-defined particle beam of known energy, a target of known composition and thickness, and position-sensitive detectors that count scattered particles by angle and energy. The NIST Electron Elastic-Scattering Cross-Section Database (SRD 64) provides calculated and tabulated differential and total elastic cross-sections for elements with atomic numbers from 1 to 96, for electron energies between 50 eV and 300 keV, supporting quantitative analysis in electron spectroscopy and microprobe techniques.

Scattering in Electron Microscopy and Material Analysis

Scanning electron microscopy relies on the scattering of a focused electron beam by atoms in a specimen to produce signals used for imaging and chemical analysis. When the beam electrons interact with target atoms, they produce backscattered electrons through large-angle elastic collisions, secondary electrons through inelastic excitation of near-surface atoms, and characteristic X-rays through inner-shell ionization. The contrast in a scanning electron micrograph arises largely from variations in elastic backscattering yield, which depends on atomic number. NIST research on scanning electron microscopy and electron scattering uses Monte Carlo simulations of electron scattering to develop model-based measurement software that improves dimensional metrology at the nanoscale. Knowledge of elastic scattering cross-sections is also central to quantitative analysis by Auger electron spectroscopy and X-ray photoelectron spectroscopy.

Applications

Particle scattering has applications in a wide range of fields, including:

• Nuclear structure research using alpha-particle and neutron scattering at research reactors and accelerator facilities
• Scanning electron microscopy for surface imaging and elemental analysis of materials and semiconductor devices
• Rutherford backscattering spectrometry for thin-film composition and depth profiling
• Radiation shielding design, using scattering cross-sections to model particle transport through materials
• Protein structure determination by small-angle X-ray and neutron scattering