The internal conversion coefficient may be empirically determined by the following formula: -
- α = # de-excitations via electron emission / # de-excitations via gamma-ray emission
There is no valid "conversion coefficient" for E0 transitions. There are theoretical calculations that can be used to derive internal conversion coefficients. Their accuracy is not generally under dispute, but it should be understood that since they depend on quantum mechanical models involving purely electromagnetic interactions between nuclei and electrons, there may be unforeseen effects which result in a conversion coefficient differing from one that is empirically determined. Internal conversion coefficients can be looked up from tables, but this is time-consuming. Computer programs have been developed (see the ICC Program (*http://ie.lbl.gov/programs/icc/icc.htm*)) which will present internal conversion coefficients quickly and easily. The three theoretical calculations of interest are the Rösel (see note 1), Hager-Seltzer (see note 2), and the Band (see note 3). The Hager-Seltzer calculations omit the M and higher-energy shells on the grounds (usually valid) that those orbitals have little electron density at the nucleus and can be neglected. To first approximation this assumption is valid, upon comparing several internal conversion coefficients for different isotopes for transitions of about 100 keV. The Band calculation assumes that the M shell may contribute to internal conversion to a non-negligible extent, and incorporates a general term (called "N+") which takes into account the small effect of any higher shells there may be, while the Rösel calculation works like the Band, but does not assume that all shells contribute and so generally terminates at the N shell. Note 1: F. Rösel, H.M. Fries, K. Alder, H.C. Pauli: At. Data Nucl. Data Tables 21 (1978) 91. Note 2: R.S. Hager and E.C. Seltzer, Nucl. Data Tables A4 (1968) 1. Note 3: I.M. Band, M.B. Trzhaskovskaya: Tables of the gamma–ray internal conversion coefficients for the K, L, M shells, 10<Z<104 (Leningrad: Nuclear Physics Institute, 1978). |