Geometriefactor

Geometriefactor, often translated as geometrical factor, is a term used in experimental physics to describe a detector’s geometric acceptance. It combines the effective area of a detector with its angular acceptance to relate an incoming particle flux to the observed event rate. In many contexts the geometriefactor is written as G and has units of area times solid angle (for example, m^2 sr).

Definition and formula. If a detector has a face area A and responds to particles arriving from a range of directions described by a solid angle Ω, and the local incidence is described by angle θ relative to the detector normal, the geometric factor can be written as G = ∫_A ∫_Ω cos θ dΩ dA. For a detector with uniform response over a symmetric angular range, this reduces to G = A ∫_Ω cos θ dΩ. A common simple case is a planar detector of area A accepting particles within a cone of half-angle θ_max, giving G = A ∫_0^{2π} ∫_0^{θ_max} cos θ sin θ dθ dφ = A π sin^2 θ_max.

Relation to flux and rate. The geometric factor is used to convert a particle flux Φ (per unit area per unit solid angle) into an observed rate R, often written as R = Φ G ε, where ε represents the detector efficiency. If Φ is isotropic, G provides the detector’s effective sensitivity to that flux.

Applications and context. The geometriefactor is widely used in cosmic-ray, gamma-ray, and particle-physics experiments to characterize detector acceptance, compute effective area, and normalize observed counts to physical fluxes. It is distinct from detection efficiency, which accounts for the probability of an event being recorded after interactions.

See also. Detector acceptance, effective area, solid angle, flux.