Gamma Emission and Internal Conversion

Overview

The decay from an excited state in a nucleus to levels in the same nucleus can be achieved by a) gamma emission, and b) internal conversion. In the former, the excess energy is carried out by a photon, while in the latter, the excess energy is carried out by an orbiting electron.

The gamma energy is basically equal to the level energy difference (neglecting the recoil energy), while the electron energy is equal to the level energy difference minus the electron binding energy:

     E_γ=E_{initial level} - E_{final level}

     E_electron=E_{initial level} - E_{final level} - E_{electron binding energy}

Multipolarity

The energy available for the decay is known as β decay Q-value. For transitions between nuclear ground states it is calculated as:

    β- decay Q-value=Mass(Z,N) - Mass(Z+1,N-1)

    β+ decay Q-value=Mass(Z,N) - Mass(Z-1,N+1)- 2×Mass(electron)

    Electron Capture Q-value=Mass(Z,N) - Mass(Z-1,N+1)- Binding Energy(electron)

Numerical values can be obtained from the web application QCalc.

Internal Conversion

The electron binding energy and the internal conversion probability depend on the orbit the electron occupied before the ejection. For instance, the atomic K orbit is the tightest bound, that is, it has the largest binding energy. It is also the one with the lowest value of angular momentum, which means it has the highest probability of finding the electron close to the nucleus, and as a result has the highest probability of conversion electron.

For each transition between levels, there is a gamma energy, E_γ, a gamma probability, P_γ, as well as an array of electron energies and probabilities E_i, P_i, where the index i indicates the atomic shell i. Each element of the array is tagged as "CE-i", for instance, "CE-K" means it is the conversion electron from the K-shell.

The total conversion coefficient, which is a function of the gamma multipolarity, is defined as:

     α=P_{internal conversion} / P_γ

and is equal to the sum of the individual conversion coefficients:

     α=Σ α_i / P_γ=Σ P_i / P_γ

Chart Region

α values range from very small, that is transition dominated by gamma emission, to very large, when gamma emission is negligible. The codes HSICC and BRICCcan be used to obtain numerical values.

Gamma emission and internal conversion are highly dependent on the angular momentum and parity differences between the initial and final levels. The larger the spin difference the less likely the probability per unit time (rate) of decay.

The majority of known nuclear levels have very short half-lives, smaller than 1 nano-second. The term "Isomeric Transition" (IT) is often used for gamma emission and electron conversion from a level with half-life larger than a given value, typically 1 nano-second.

For a gamma ray with energy E_γ, multipolarity M_λ/E_λ, conversion coefficient α, de-exciting a level with half-life T_1/2, the partial half-life is given by:

     T_γ=T_1/2 / [I_γ(1+α)]

where I_γ is the gamma ray intensity normalized so that the sum of all intensities for the transitions de-exciting the same level is equal to one.

The reduced transition probability in Weisskopf units is defined as:

     B(M_λ,E_λ)=T_γ/T_W

where T_W is the Weisskopf single-particle estimate of the half-life. Its definition can be found in page iii of the Nuclear Data Sheets policies.

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