differentialkorsssektioner

Differential cross‑sections are a fundamental quantity in particle and nuclear physics that describe how often a particular reaction or scattering process occurs as a function of kinematic variables, most commonly the scattering angle or momentum transfer. While the total cross‑section gives the overall probability of a reaction occurring, the differential cross‑section, denoted generally as dσ/dΩ or dσ/dt, reveals how this probability is distributed over the final state phase space. The unit of a differential cross‑section is typically square centimetres per steradian (cm²/sr) when expressed per solid angle, reflecting the conversion from a probability per unit area to a density over angular distribution.

In practice, experimentalists measure the angular or energy distribution of outgoing particles and fit these data with theoretical models that predict the shape of dσ/dΩ. For example, Rutherford scattering of alpha particles from heavy nuclei gives a characteristic 1/(sin⁴(θ/2)) angular dependence, which reproduces the classical Coulomb potential. Quantum mechanical scattering from short‑range potentials, such as in nucleon–nucleon collisions, often requires partial‑wave analysis where the differential cross‑section is expanded in Legendre polynomials.

The differential cross‑section also appears in reaction rates for astrophysical processes, where integration over energy or momentum transfer yields macroscopic quantities such as opacity or reaction rate coefficients. In high‑energy collider experiments, detector angular coverage in pseudorapidity (η) and azimuth (φ) is designed to capture the differential distributions of produced particles, which are essential for testing perturbative quantum chromodynamics and probing new physics.

Mathematically, a differential cross‑section is obtained by dividing the infinitesimal number of events dN occurring within an infinitesimal element of phase space dΦ by the product of the incident flux J and the target number density n: dσ = dN/(J n dΦ). Integration over the full phase space recovers the total cross‑section σ. Proper treatment of units, normalization, and acceptance corrections is crucial for precise determination of differential cross‑sections and for meaningful comparison between theoretical predictions and experimental measurements.