Gamma-decay multipolarity and lifetimes

A real emitted photon has no angular-momentum monopole mode. For a transition between nuclear spins, the multipole rank must satisfy the angular-momentum triangle and be at least one. Electric multipoles change parity by a factor set by that rank; magnetic multipoles have the opposite parity factor. For example, a two-plus to zero-plus transition can emit an electric quadrupole photon, while a one-minus to zero-plus transition can emit an electric dipole photon.

A zero-to-zero transition cannot emit a single real gamma photon because no nonzero photon angular momentum can couple the two spins. An electric monopole nuclear transition can instead transfer energy to an atomic electron or, if energetically possible, create an electron–positron pair. This distinction prevents the absence of a gamma branch from being mistaken for a stable excited level. Mixed photon multipolarities are possible when more than one rank and type satisfy the same spin-parity constraints.

For a fixed multipole rank, the radiative rate contains a photon-energy power of twice the rank plus one multiplied by a reduced nuclear transition strength. This follows from the electromagnetic multipole matrix element and photon phase space. It explains why low-energy high-multipole transitions can be slow. Comparing rates at different energies is meaningful only if the transition strengths and multipole types are specified; the energy power alone is not a complete prediction for unrelated nuclei.

Single-particle Weisskopf estimates provide conventional reference scales for electromagnetic strength, not precise universal rates. Collective motion can strongly enhance some electric quadrupole transitions, while changes of nuclear configuration can hinder otherwise permitted transitions. Thus a measured lifetime plus branching information can reveal a reduced strength, but inferring multipolarity from lifetime alone is generally ambiguous. Angular distributions, correlations, polarization, and internal-conversion data provide additional independent evidence.

All outgoing transition rates contribute to the total level rate. Internal conversion competes with photon emission without changing the nuclear final state, while separate branches may feed other final levels. The total lifetime is therefore the inverse sum of rates, not the inverse of a measured photon intensity. A branching fraction and the conversion coefficient are needed to extract the radiative partial rate for one transition from a level lifetime.

For a freely recoiling nucleus, the photon energy is also slightly smaller than the nuclear level-energy difference, because the daughter recoil carries momentum and energy. This correction matters in precision spectroscopy and differs from the Doppler shift of a moving source. In a bound solid, recoil can be shared with the lattice and recoilless emission may occur under appropriate conditions. None of these recoil considerations replaces the spin-parity selection rules; they address energy and momentum sharing rather than the allowed electromagnetic tensor rank.