Optical theorem

The optical theorem relates the imaginary part of a scattering amplitude in the forward direction to the total cross section, connecting interference in a wave to all scattering outcomes.

Scattering amplitude: A complex quantity encoding the strength and phase of a wave or particle scattering process. The theorem extracts the total cross section from one specific value of this quantity.
Differential cross section: A scattering cross section specified per unit solid angle. Integrating this angular distribution gives the total cross section in the theorem.
Wolfgang Pauli: An Austrian-born theoretical physicist who made foundational contributions to quantum mechanics and quantum field theory. Pauli’s work helped establish the theorem’s role in quantum scattering theory.
Neutron scattering: The use of neutron beams to probe the structure and dynamics of matter through scattering. Forward amplitudes can determine total neutron interaction cross sections.
Kramers–Kronig relations: Integral relations connecting the real and imaginary parts of a causal response function across frequency. They link response components across frequencies, while the optical theorem links a forward amplitude to a cross section.
Forward scattering: Scattering in which the outgoing particle or wave travels in the same direction as the incident one. The theorem uses the amplitude at zero scattering angle.
Scattering angle: The angle between the incident direction and the outgoing direction of a scattered wave or particle. The forward amplitude is evaluated at zero scattering angle.
Max Born: A German physicist who developed the probabilistic interpretation of the quantum wavefunction and contributed to scattering theory. Born’s scattering framework supplied a setting for quantum versions of the relation.
Nuclear scattering: The scattering of particles by atomic nuclei, used to study nuclear interactions and structure. The theorem connects measured forward amplitudes with total reaction cross sections.
Born approximation: A perturbative method that estimates a scattering amplitude using the incident wave and interaction potential. The approximation calculates amplitudes; the optical theorem tests whether they satisfy probability conservation.

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