Multipole radiation

(physics) Electromagnetic radiation which has characteristics equivalent to those of radiation generated by an oscillating electric or magnetic multipole, and is made up of photons of well-defined angular momentum and parity. Internal conversion electrons, or positron-electron pairs having similar characteristics, emitted from an atom when the nucleus makes a transition between two energy states.

Standard patterns of radiation distribution about their source. The term radiation applies primarily to the transport of energy by acoustic, elastic, electromagnetic, or gravitational waves, and extends to the transport of atomic or subatomic particles (as represented by quantum-mechanical wave functions). See also Electromagnetic radiation; Gravitational radiation; Quantum mechanics; Sound; Wave motion.

Each multipole pattern reflects the source's geometrical shape (or the shape of a source component). These geometrical features stand out clearly for the static electric potentials generated by fixed charges as shown by the small set of monopole, dipole, and quadrupole charges (see illustration), elements of all multipoles being named (in terms of powers of 2) 2^l-poles, with l equal to any nonnegative integer. A monopole (l = 0) acoustic wave radiates from a perfectly spherical bubble with oscillating radius; higher multipoles would arise from bubble distortions. So-called transverse waves, elastic or electromagnetic (including light), have only l ≥ 1 components, gravitational waves only l ≥ 2. The angular distributions, in azimuth (ϕ) and colatitude (θ), of 2^l-pole waves have amplitudes distributed in directions (θ, ϕ) in proportion to the spherical harmonic functions Y_l^m (θ, ϕ). The index m is a positive or negative integer whose absolute value is equal to less than l. See also Coordinate systems; Dipole; Spherical harmonics.

Static electric potentials generated by fixed multipoles. (a) Monopole (l = 0). (b) Dipole (l = 1). (c) Quadrupole (l = 2).

The multipolarity index l also represents the number of angular momentum quanta ℏ (Planck's constant divided by 2π) radiated together with each energy quantum hν (phonon, photon, graviton, and so forth). Detection and measurement of received energy quanta, together with measurement of their detection rate and mapping of their directionaldistribution, generally serve to diagnose the mechanics of the radiationsource. Energy and momentum conservation underlie this analysis; so does theconservation of angular momentum which states that the initial angular momentumof the source equals the vector sum of the final angular momentum of the sourceand the angular momentum of the radiation. The quantitativeimplications of this vector relation are studied by the branch of quantumtheory called angular momentum algebra. The balancing of parity, that is, ofeach variable's sign reversal (or persistence) under reflection throughthe source's center, also contributes to the analysis of experimentaldata. Further, more complex angular-momentum considerations play a role in theanalysis of the behavior of spin-carrying particles. See also Angular momentum; Conservation laws (physics); Graviton; Phonon; Selection rules (physics); Spin (quantum mechanics).