dNdE

dNdE (often written as dN/dE) denotes the differential number of events or particles as a function of energy. It describes how the yield varies with energy and is used to characterize energy spectra. N represents the relevant count (detected, produced, or observed), and E is the energy variable (for example photon energy or kinetic energy).

In experiments, dN/dE is estimated by binning data in energy and dividing by the bin width and by the exposure or efficiency. The observed distribution reflects the true spectrum convolved with the detector response; unfolding or modeling is often required to recover the underlying spectrum.

Relation to totals: The total number of events in an energy range is N = ∫ dN/dE dE. If a differential flux Φ(E) (per unit area, time, energy, and solid angle) describes a source, the expected counts scale as Φ(E) × A_eff(E) × T × Ω × ε(E).

Examples: In gamma-ray astronomy, dN/dE is the differential photon flux dΦ/dE. In cosmic-ray physics, spectra are often expressed as a power law dN/dE ∝ E^-γ, with γ the spectral index. Units depend on context and may be counts GeV^-1 or photons cm^-2 s^-1 GeV^-1.

Notes: The term dNdE is a shorthand used across disciplines; its precise meaning depends on the measurement setup, including exposure, area, solid angle, time, and efficiencies. It serves to compare theoretical predictions with data and to infer properties of sources and processes.