# Internal conversion

### Internal conversion

Internal conversion is a radioactive decay process wherein an excited nucleus interacts electromagnetically with one of the orbital electrons of the atom. This causes the electron to be emitted (ejected) from the atom.[1][2] Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but not from the nucleus. For this reason, the high-speed electrons resulting from internal conversion are not beta particles, since the latter come from beta decay, where they are newly created in the nuclear decay process.

Internal conversion is possible whenever gamma decay is possible, except in the case where the atom is fully ionised. During internal conversion, the atomic number does not change, and thus (as is the case with gamma decay) no transmutation of one element to another takes place.

Since an electron is lost from the atom, a hole appears in an electron shell which is subsequently filled by other electrons. This process produces characteristic X-ray(s), Auger electron(s), or both. The atom thus emits high-energy electrons and X-ray photons, but none of these originate in the nucleus, which supplies only the needed energy.

Since primary electrons from internal conversion carry a fixed (large) fraction of the characteristic decay energy, they have a discrete energy spectrum, rather than the spread (continuous) spectrum characteristic of beta particles. Whereas the energy spectrum of beta particles plots as a broad hump, the energy spectrum of internally converted electrons plots as a single sharp peak (see example below).

## Contents

• Mechanism 1
• An example: the decay of 203Hg 2
• When the process is expected 3
• Similar processes 4
• References 6

## Mechanism

In the quantum mechanical mathematical model for the internal conversion process, the wavefunction of an inner shell electron (usually an s electron) penetrates the volume of the atomic nucleus. This means that there is a finite probability of finding the electron within the nucleus. When this happens, the electron may couple to an excited energy state of the nucleus and take the energy of the nuclear transition directly, without an intermediate gamma ray being first produced. The kinetic energy of the emitted electron is equal to the transition energy in the nucleus, minus the binding energy of the electron to the atom.

Most internal conversion (IC) electrons come from the K shell (the 1s state), as these two electrons have the highest probability of being within the nucleus. However, the s states in the L, M, and N shells (i.e., the 2s, 3s, and 4s states) are also able to couple to the nuclear fields and cause IC electron ejections from those shells (called L or M or N internal conversion). Ratios of K-shell to other L, M, or N shell internal conversion probabilities for various nuclides have been prepared.[3]

The atomic binding energy of the s electron must at least be supplied to that electron in order to eject it from the atom to result in IC; that is to say, internal conversion cannot happen if the decay energy of the nucleus is insufficient to overcome the binding energy. There are a few radionuclides in which the decay energy is not sufficient to convert (eject) a 1s (K shell) electron, and these nuclides, to decay by internal conversion, must decay by ejecting electrons from the L or M or N shells (i.e., by ejecting 2s, 3s, or 4s electrons) as these binding energies are lower.

Although s electrons are more likely for IC processes due to their superior nuclear penetration compared to electrons with orbital angular momentum, spectral studies show that p electrons (from shells L and higher) are occasionally ejected in the IC process.

After the IC electron has been emitted, the atom is left with a vacancy in one of its electron shells, usually an inner one. This hole will be filled with an electron from one of the higher shells, and consequently one or more characteristic X-rays or Auger electrons will be emitted as the remaining electrons in the atom cascade down to fill the vacancy.

## An example: the decay of 203Hg

Decay scheme of 203Hg
Electron spectrum of 203Hg, according to Wapstra et al., Physica 20 (1954) 169

The decay scheme on the left shows that 203Hg produces a continuous beta spectrum with maximum energy 214 keV, that leads to an excited state of the daughter nucleus 203Tl. This state decays very fast (within 2.8x10-10 s) to the ground state of 203Tl, emitting a gamma quantum of 279 keV.

The figure on the right shows the electron spectrum of 203Hg, measured by means of a magnetic spectrometer. You can see the continuous beta spectrum and also the K-, L-, and M-lines due to internal conversion. Since the binding energy of the K electrons in 203Tl amounts to 85 keV, the K line has an energy of 279 - 85 = 194 keV. Because of lesser binding energies, the L- and M-lines have higher energies. Because of the finite energy resolution of the spectrometer, the "lines" have a Gaussian shape of finite width.

## When the process is expected

Internal conversion (often abbreviated IC) is favoured whenever the energy available for a gamma transition is small, and it is also the primary mode of de-excitation for 0+→0+ (i.e. E0) transitions. The 0+→0+ transitions occur where an excited nucleus has zero-spin and positive parity, and decays to a ground state which also has zero-spin and positive parity (such as all nuclides with even numbers of protons and neutrons). In such cases, de-excitation cannot happen with emission of a single gamma ray, since this would violate conservation of angular momentum, so other mechanisms like IC predominate. This also shows that internal conversion (contrary to its name) is not a two-step process where a gamma ray would be first emitted and then converted.

Internal Conversion Coefficient for E1 transitions for Z = 40, 60, and 80 according to the tables by Sliv and Band, as a function of the transition energy.

The competition between internal conversion and gamma decay is quantified in the form of the internal conversion coefficient which is defined as \alpha = e/{\gamma} where e is the rate of conversion electrons and \gamma is the rate of gamma-ray emission observed from a decaying nucleus. For example, in the decay of the excited state at 35 keV of 125Te (which is produced by the decay of 125I), 7% of the decays emit energy as a gamma ray, while 93% release energy as conversion electrons. Therefore, this excited state of 125
Te
has an internal conversion coefficient of \alpha = 93/7 = 13.3.

For increasing atomic number (Z) and decreasing gamma-ray energy, internal conversion coefficients are observed to increase. As an example, calculated IC coefficients for electric dipole (E1) transitions, for Z = 40, 60, and 80, are shown in the figure.[4]

The energy of the emitted gamma ray is a precise measure of the difference in energy between the excited states of the decaying nucleus. In the case of conversion electrons, the binding energy must also be taken into account: The energy of a conversion electron is given as E = (E_i - E_f)-E_B, where E_i and E_f are the energies of the nucleus in its initial and final states, respectively, while E_B is the binding energy of the electron.

## Similar processes

Nuclei with zero-spin and high excitation energies (more than about 1.022 MeV) are also unable to rid themselves of energy by (single) gamma emission, but they do have sufficient decay energy to decay by internal pair creation.[5] In this type of decay, an electron and positron are both emitted from the atom at the same time, and conservation of angular momentum is solved by having these two product particles spin in opposite directions.

The internal conversion process should not be confused with the similar photoelectric effect. When a gamma ray emitted by the nucleus of an atom hits a different atom, it may be absorbed producing a photo electron of well-defined energy (This used to be called "external conversion"). In internal conversion, however, the process happens within one atom, and without a real intermediate gamma ray.

As an atom may produce an internal conversion electron in place of a gamma ray, an atom may produce an Auger electron in place of an x ray if an electron is missing from one of the electron shells. Like IC electrons, Auger electrons have a discrete energy, resulting in a sharp energy peak in the spectrum.

The electron capture process also involves an inner shell electron, which in this case is retained in the nucleus (changing the atomic number) and leaving the atom (not the nucleus) in an excited state. The atom missing an inner electron can relax by a cascade of X-ray emissions as higher energy electrons in the atom fall to fill the vacancy left in the electron cloud by the captured electron. Such atoms also typically exhibit Auger electron emission. Electron capture, like beta decay, also typically results in excited atomic nuclei, which may then relax to a state of lowest nuclear energy by any of the methods permitted by spin constraints, including gamma decay and internal conversion decay.

## References

1. ^ Loveland, Walter D. (2005). Modern Nuclear Chemistry. Wiley. p. 232.
2. ^ M.E. Rose: "Theory of Internal Conversion", in: Alpha-, Beta- and Gamma-Ray Spectroscopy, ed. by Kai Siegbahn, North-Holland Publishing, Amsterdam (1966), Vol. 2
3. ^ [3] Internal conversion branch tables]
4. ^ L. A. Sliv and I. M. Band, Table of Internal Conversion Coefficients, in: Alpha-, Beta- and Gamma-Ray Spectroscopy, ed. by Kai Siegbahn, North-Holland Publishing (1966), Vol. 2, Appendix
5. ^ [4] E0 rules