# Internal conversion

Internal conversion is a radioactive decay process wherein an excited nucleus interacts electromagnetically with one of its electrons. This causes the electron to be emitted (ejected) from the atom.[1] Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, 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. Since no beta decay takes place during internal conversion, the element atomic number does not change, and thus (as is the case with gamma decay) no transmutation of one element to another takes place. However, since an electron is lost, an otherwise neutral atom becomes ionized. Also, no neutrino is emitted during internal conversion.

Internally converted electrons do not have the energetically spread spectrum characteristic of beta particles. The spread spectrum of beta particles results from the decay of a neutron into a proton, a beta particle (electron), and an electron antineutrino. Varying amounts of decay energy are carried off by the antineutrino during beta decay, resulting in the spectrum of beta electrons' energy. Internally converted electrons, however, carry a fixed fraction of the characteristic decay energy, hence they have a discrete energy. The energy spectrum of a beta particle thus plots as a broad hump, extending from essentially zero (a bound electron that doesn't even have enough energy to escape the atom) to a maximum decay energy value. By contrast, the energy spectrum of internally converted electrons plots as a single sharp peak.

## Mechanism

In the quantum mechanical mathematical model for the internal conversion process, the wavefunction of an inner shell electron penetrates the volume associated with the atomic nucleus. When this happens, the mathematics of quantum theory implies that there is a finite probability of the electron in an s atomic orbital being found 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 process of imparting energy from the nucleus to an orbital electron is a quantum process and may be seen as taking place by means of a virtual photon. In that sense the photon involved can be considered as a "virtual gamma ray", which appears as a feature in an equation that describes the process, rather than as a directly measurable emission. 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 interacting with the nucleus. However, the s state 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 LMN internal conversion). Ratios of K-shell to other L, M, or N shell internal conversion probabilities for various nuclides have been prepared.[2]

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

Although s electrons are more likely for IC processes due to their superior nuclear penetration with regard 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.

## When the process is expected

Internal conversion is favoured when the energy gap between nuclear levels is small, and is also the primary mode of de-excitation for 0+→0+ (i.e. E0) transitions.[3] The 0+→0+ transitions occur where an excited nucleus has zero spin. In such cases, the nucleus cannot rid itself of energy by emitting a single gamma ray, since this would violate conservation of angular momentum. Emission of two gamma rays (double gamma decay) is allowed (with the photons having opposite spins), but internal conversion solves the problem for zero spin nuclei more naturally, and for low energies of excitation, is the favored process.

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.[4] 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.

Internal conversion is also the predominant mode of de-excitation whenever the initial and final spin states are not zero, but are the same (but with other different quantum numbers). However, the multi-polarity rules for non-zero initial and final spin states do not necessarily forbid the competing de-excitation by emission of a single gamma ray, in such cases.

The tendency towards internal conversion in a nucleus which is also allowed to decay by gamma emission, can be expressed by the internal conversion coefficient, which is empirically determined by the ratio of de-excitations that go by the emission of conversion electrons, to those that go by gamma emission.

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 an excited state of the nucleus 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
I
has an internal conversion coefficient of $\alpha = 13.3$.

Internal conversion coefficients are observed to increase for increasing atomic number (Z) and decreasing gamma-ray energy. As one example, IC coefficients are calculated explicitly for 55
Fe
, 67
Ga
, 99mTc, 111
In
, 113mIn, 115mIn, 123
I
, 125
I
, 193mPt, 201
Tl
and 203
Pb
by Howell (1992) using Monte Carlo methods. (For 55
Fe
the IC coefficient is zero.)

The energy of the emitted gamma ray is regarded as a precise measure of the difference in energy between the excited states of the decaying nucleus. However, this is not true in the case of conversion electrons. 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

This internal conversion process is also not to be confused with the similar photoelectric effect, which also may occur with electron emissions associated with gamma radiation, in which an incident gamma photon emitted from a nucleus interacts with an electron, expelling the electron from the atom. Thus, gamma photoelectric-effect electron emission may also cause high-speed electrons to be emitted from radioactive atoms without beta decay. However, in internal conversion, the nucleus does not first emit an intermediate real gamma ray, and therefore need not change angular momentum or electric moment.

Also, electrons from the gamma photoelectric effect show a spread in energy, depending on how much energy has been imparted to the ejected electron by the gamma ray that interacts with it—an amount that is variable depending on the angle of gamma photon scattering from the electron. Further, a gamma ray is still emitted in photoelectric processes, but one that possesses a fraction of the energy compared to the gamma ray that left the nucleus. By contrast, in internal conversion, no gamma ray is emitted at all, and the electron energy is fixed at a single, typical value.

Auger electrons, which may also be produced after an internal conversion, arise from a mechanism that is different from that of internal conversion, but is analogous to it. Internal conversion electrons arise when an intense electric dipole field inside the nucleus accelerates an electron that has penetrated the nucleus and removes it from the atom. Auger electrons similarly arise when an electric field is produced within an atom's electron cloud due to loss of another electron, and this field again induces the acceleration and removal of yet another of the atom's atomic orbital electrons. Like IC electrons, Auger electrons also emerge in a sharp energy peak.

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.