# Internal conversion

The excess energy of radioactive nuclei in excited states is usually relieved through gamma emission. However, if the wave function of an orbital electron is such that it can exist close to or in the nucleus, the excess energy can be transferred directly to the orbital electron. Hence, as an alternative to gamma emission, the excited nucleus may return to a lower state or to the ground state by ejecting an orbital electron. This is known as internal conversion and results in the emission of a mono-energetic electron. Following the internal conversion, outer orbital electrons fill the deeper atomic energy levels, leading to characteristic X-ray emission or, alternatively, to the emission of Auger electrons.

The internal conversion process can be described by:

${}_Z^A\!P_{}^*\rightarrow [{}_Z^A\!P]^*+ e^-$

The ratio of internal conversion to gamma emission photons is known as the internal conversion coefficient $\alpha$ where

$\alpha = {N_e \over N_{\gamma}}$

where $N_e$ is the number of de-excitations via electron emission and $N_{\gamma}$ the number of de-excitations via gamma emission. The kinetic energy Ee of the ejected electron is almost equal to the excitation energy E* less the binding energy of the orbital electron EB , i.e.

$E_e = E^* - E_B$

The internal conversion coefficent alpha depends on the atomic number and the excitation energy , i.e.

$\alpha \propto {Z^3 \over E^*}$

Internal conversion is more important in heavy nuclei in particular in the decay of low-lying excited states (small E*). Gamma emission predominated in light nuclei.

Example:

Tc97m in the Karlsruhe Nuclide Chart (preview of the 8th Edition)

Consider the decay of the isomeric state Tc97m (half-life 91 days). The box is mainly white indicating isomeric transition as the main decay mode and the small red triangle indicates electron capture to the daughter Mo97. The nuclide data shows Iγ (97) and e-. The symbol e- indicates that the converison coefficient is > 1 i.e. the state de-excites mainly by electron conversion rather than by gamma emission.

In addition, the fact that the energy of the isomeric transition is in backets i.e. (97) implies that gamma emission occurs in less that 1% of the de-excitations. Hence the electron conversion occurs is over 99% over the de-excitations. The actual conversion coefficient is not given in the chart, but can be obtained from the literature e.g nuclear Data sheets or from Nucleonica (see below).

Nucleonica references for the nuclide Tc97m.

The conversion coefficient is α = 311 i.e 311 times more conversion electrons than gamma photons. These conversion electrons are seen in the beta spectrum. This information can be found in the references in Nucleonica. Together with the original research papers, information is given on branching ratios etc.

Joseph Magill, Gerda Pfennig, Raymond Dreher, Zsolt Sóti, Karlsruhe Nuclide Chart, 8th Edition, 2012.

N. Nica, Nucl.Data Sheets 111(2010) 621, http://dx.doi.org/10.1016/j.nds.2010.03.001

J. E. Turner, Atoms, Radiation, and Radiation Protection, 2nd Edition, John Wiley, 1995.