Gamma decay ($E_{\gamma }\simeq E_i-E_f$)

Gamma decay is electromagnetic nuclear de-excitation by photon emission. It preserves mass number and atomic number, while changing the nuclear state. Angular momentum and parity constrain the allowed radiation multipoles. The gamma ray topic is broader than this nuclear process.

Named for Victor Weisskopf, a Weisskopf estimate is a benchmark electromagnetic nuclear transition strength based on a simple single-particle size model. It supplies a scale against which enhancement or hindrance is measured, rather than a universal rate. The partial rate contains both the photon-energy power $E_{\gamma }^{2L+1}$ and the actual reduced nuclear strength. Electric and magnetic multipoles at different energies cannot be universally ranked by order alone.^[ref]

For a prompt nuclear level fed in a steady decay cascade, incoming and outgoing transition populations balance. Quoted photon intensities must represent efficiency-corrected emission counts; internal conversion, alternative particle decays and unobserved feeds must either be included or explicitly excluded. Equal photon counts suggest a serial cascade, while a feed intensity equal to the sum of two branches suggests splitting. intensities alone do not determine the chronological order of equal-count lines.

To leading order neglecting nuclear recoil, a measured gamma ray has energy equal to the difference between the upper and lower nuclear energy levels. For a freely recoiling atomic nucleus initially at rest, four-momentum conservation instead giveswhere $M_u$ and $M_l$ are the rest masses of the upper and lower nuclear states. Some transition energy becomes daughter kinetic energy, so high-precision level reconstruction must account for nuclear recoil.

Reconstructing a nuclear gamma ray radiation spectrum amounts to assigning measured photon energies to differences between ordered nuclear energy levels with such corrections where needed. Cascade energy sums constrain the graph, while population-flow balances constrain its orientation and feeding. Experimental central energies need not close exactly; a weighted least squares energy-network fit uses their uncertainties consistently. Multiple graphs can satisfy the same radiation spectrum when coincidence or lifetime information is absent.

A real photon emitted in gamma decay carries a radiation multipole of integer angular momentum $L\ge 1$. The triangle rule gives the displayed range. An electric multipole $EL$ requires ${\pi }_f/{\pi }_i=(-1{)}^L$, while a magnetic multipole $ML$ requires ${\pi }_f/{\pi }_i=(-1{)}^{L+1}$. There is no real single-photon $E0$ decay; an electric monopole transition can instead proceed through internal conversion or, above threshold, pair creation. In the long-wavelength regime $kR\ll 1$, increasing $L$ usually strongly suppresses the rate, but nuclear transition matrix elements and collective enhancement can make an allowed lower multipole weaker than a higher one.

An absent otherwise-fast gamma transition can support a spin assignment that forbids it. It is not an absolute selection rule: a nuclear reduced matrix element may be small even when angular momentum and parity allow the mode. Meaningful limits require detection thresholds, branching normalization and competing-channel information. Assuming ordinary unhindered strengths can yield a useful conventional assignment, but that assumption must be distinguished from strict observed-line constraints.

If a cascade determines only absolute spin differences relative to a known reference spin, reflection of all inferred spins around that reference can preserve the same multipole pattern. Nonnegative-spin constraints, independently known spins, angular correlations or polarization measurements may break the ambiguity. A set of line energies and lowest-multipole labels need not do so.