Nuclear structure

A nuclear level scheme represents nuclear energy levels and transitions among them. Gamma ray energies constrain pairwise differences; emission counts and coincidence measurements help resolve different schemes having the same difference multiset.

For a complete ensemble of downward nuclear de-excitation cascades, let $F_i$ be the direct population of excited level $i$ and $C_{i\to j}$ the total number of transitions from $i$ to $j$. Conservation of population gives the displayed outward-minus-inward formula. A negative $F_i$ rules out a proposed scheme under the assumed complete transition inventory. Gamma ray counts equal transition counts only when unreported internal conversion and other competing paths can be neglected or corrected. Summing over all excited levels cancels internal transitions and leaves the transitions into the ground state.

Nuclear de-excitation is a transition from a higher to a lower nuclear energy level. It can transfer energy to an emitted gamma ray or to an atomic Electron through internal conversion, among other channels when thresholds permit.

Internal conversion transfers nuclear excitation energy directly to a bound atomic Electron, which is emitted, rather than to a real gamma ray. Photon counts alone then underestimate the number of nuclear transitions unless the conversion contribution is included.

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.

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.