## Friday, June 2, 2017

### Internal Conversion

In Chapter 17 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss nuclear decay.
Whenever a nucleus loses energy by γ-decay, there is a competing process called internal conversion. The energy to be lost in the transition, Eγ, is transferred directly to a bound electron, which is then ejected with a kinetic energy
T = EγB,
where B is the binding energy of the electron.
What is the energy of these ejected internal conversion electrons? Does the most important γ-emitter for medical physics, 99mTc, decay by internal conversion? To answer these question, we need to know the binding energy B. Table 15.1 of IPMB provides the energy levels for tungsten; below is similar data for technetium.

level     energy (keV)
K -21.044
LI   -3.043
LII   -2.793
LIII   -2.677
MI   -0.544
MII   -0.448
MIII   -0.418
MIV   -0.258
MV   -0.254

The binding energy B is just the negative of the energy listed above. During internal conversion, most often a K-shell electron is ejected. The most common γ-ray emitted during the decay of 99mTc has an energy of 140.5 keV. Thus, K-shell internal conversion electrons are emitted with energy 140.5 – 21.0 = 119.5 keV. If you look at the tabulated data in Fig. 17.4 in IPMB, giving the decay data for 99mTc, you will find the internal conversion of a K-shell electron (“ce-K”) for γ-ray 2 (the 140.5 keV gamma ray) has this energy (“1.195E-01 MeV”). The energy of internal conversion electrons from other shells is greater, because the electrons are not held as tightly.

Auger electrons also come spewing out of technetium following internal conversion. These electrons arise, for instance, when the just-created hole in the K-shell is filled by another electron. This process can be accompanied by emission of a characteristic x-ray, or by ejection of an Auger electron. Suppose internal conversion ejects a K-shell electron, and then the hole is filled by an electron from the L-shell, with ejection of another L-shell Auger electron. We would refer to this as a “KLL” process, and the Auger electron energy would be equal to the difference of the energies of the L and K shells, minus the binding energy of the L-shell electron, or 21 – 2(3) = 15 keV. This value is approximate, because the LI, LII, and LIII binding energies are all slightly different.

In general, Auger electron energies are much less than internal conversion electron energies, because nuclear energy levels are more widely spaced than electron energy levels. For 99mTc, the internal conversion electron has an energy of 119.5 keV compared to a typical Auger electron energy of 15 keV (Auger electron energies for other processes are often smaller).

Another important issue is what fraction of decays are internal conversion versus gamma emission. This can be quantified using the internal conversion coefficient, defined as the number of internal conversions over the number of gamma emissions. Figure 17.4 in IPMB has the data we need to calculate the internal conversion coefficient. The mean number of gamma rays (only considering γ-ray 2) per disintegration is 0.891, whereas the mean number of internal conversion electrons per disintegration is 0.0892+0.0099+0.0006+0.0003+0.0020+0.0004 = 0.1024 (adding the contributions for all the important energy levels). Thus, the internal conversion coefficient is 0.1024/0.891 = 0.115.

The ideal isotope for medical imaging would have no internal conversion, which adds nothing to the image but contributes to the dose. Technetium, which has so many desirable properties, also has a small internal conversion coefficient. It really is the ideal radioisotope for medical imaging.