When a cross section is specified as the differential limit of a function of some final-state variable, such as particle angle or energy, it is called a differential cross section (see detailed discussion below).

Cross sections in classical physics Definition B χ Consider a beam of particles, approaching a target at rest with velocity v∞. Describe the target by a potential centered at the origo. Due to different impact parameters B, different particles of the beam are scattered at different angles χ. Define cross section dσ(χ) = dN(χ)/n with

The impact of the measured differential cross-sections as a function of lepton $\eta$ on the determination of these functions is studied using a profiling technique. Comments: 45 pages in total, author list starting page 28, 9 figures, 2 tables, submitted to EPJC.

The differential cross section, written \(d \sigma / d \Omega\) is the fraction of the total number of scattered particles that come out in the solid angle \(d \Omega\), so the rate of particle scattering to this detector is \(n d \sigma / d \Omega, \text { with } n\) the beam intensity as defined above.

The differential cross section, which is an area, multiplied by the flux, gives you the number of particles per unit time that are crossing at differential cross section area.