Internal conversion coefficient

Uncertainty in last digit or digits is shown in parentheses. ICC = internal conversion coefficient. 

The iatensity of a conversion fine can be expressed relative to that of the associated y-ray as the internal-conversion coefficient (ICC), denoted as d. For example, is the ratio of the number of electrons emitted from the K atomic shell to the number of photons emitted. For the other atomic levels, the corresponding conversion coefficients are denoted by (X, The total conversion coefficient is a = n, where the sum iacludes all atomic... 

Table 12. Calculated Internal-Conversion Coefficients for y-Rays ...

In addition to the possible multipolarities discussed in the previous sections, internal-conversion electrons can be produced by an EO transition, in which no spin is carried off by the transition. Because the y-rays must carry off at least one unit of angular momentum, or spin, there are no y-rays associated with an EO transition, and the corresponding internal-conversion coefficients are infinite. The most common EO transitions are between levels with J = = where the other multipolarities caimot contribute. However, EO transitions can also occur mixed with other multipolarities whenever... 

Not all nuclear transitions of this kind produce a detectable y-ray for a certain portion, the energy is dissipated by internal conversion to an electron of the K-shell which is ejected as a so-called conversion electron. For some Mossbauer isotopes, the total internal conversion coefficient ax is rather high, as for the 14.4 keV transition of Fe (ax = 8.17). ax is defined as the ratio of the number of conversion electrons to the number of y-photons. 

Total internal conversion coefficient Recoil energy (in 10 eV)... 

The first Mossbauer measurements involving mercury isotopes were reported by Carlson and Temperley [481], in 1969. They observed the resonance absorption of the 32.2 keV y-transition in (Fig. 7.87). The experiment was performed with zero velocity by comparing the detector counts at 70 K with those registered at 300 K. The short half-life of the excited state (0.2 ns) leads to a natural line width of 43 mm s Furthermore, the internal conversion coefficient is very large (cc = 39) and the oi pj precursor populates the 32 keV Mossbauer level very inefficiently ( 10%). 

All these conflicts can now be resolved because of what appears to be a deflnitive experiment by Bocquet et al. (4), who directly measured the internal conversion coefficients of the transition from the first nuclear level to the ground state. They directly compared the L, M, N, and O conversion electron intensities in two different states—namely, in stannic oxide and white tin. They found that the 5s electron density is 30% smaller in stannic oxide than in white tin, and since the isomer shift of stannic oxide is negative with respect to white tin, AR is clearly positive. From these data, the Brookhaven group has calculated the value for AR/R for tin-119 as +3.3 X 10". ... 

To characterize this decay process and its competition with 7-ray emission, we define the internal conversion coefficient, a, by the relationship... 

One can define this ratio, the internal conversion coefficient, for electrons from the K shell only for electrons from the M shell only, and so on, giving rise to aK, aM, and so on. Since the total probability of decay must equal the sum of the probabilities of decay via various paths, we have... 

The internal conversion coefficient depends primarily on the density of the atomic electrons at the center of the nucleus, and thus it can be calculated using principles from atomic physics. Large tables and nomographs of internal conversion coefficients exist, such as those shown in Figure 9.6. 

Rough approximate formulas for the internal conversion coefficients are... 

Example Problem Use a standard reference such as the Table of Isotopes, 8th ed., 1996, to determine the internal conversion coefficients for each shell for the transition from the first excited state at 0.08679 keV (2+) in 160Dy to the ground state (0+). Then calculate the decay rates for internal conversion and for 7-ray emission. 

Figure 9.6 Calculated internal conversion coefficients for (a) electric transitions and (b) magnetic transitions. (From M. A. Preston, 1962, p. 307.) Copyright 1962 by Addison-Wesley Publishing Company. Reprinted by permission of Pearson Education.

A 64-d isomer of an even Z, and an odd nucleus with A 90 occurs at 105 keV above the ground state. The isomeric state decays 10% by EC and 90% by IT. If the internal conversion coefficient a = 50, what is the y-ray lifetime and the most likely multipolarity of the isomeric transition If this is a magnetic transition and the isomeric state has Jit = j, what is the Jit of the ground state ... 

Doppler velocity may provide a Mossbauer spectrum with a large increase in the signal to noise ratio compared to that obtained in the transmission mode. The type of radiation used to generate the scattered Mossbauer spectrum depends on the internal conversion coefficient a a large value of a, which favors the emission of X rays by the Mdssbauer isotope, makes X-ray detection appropriate, while a small value of a favors y-ray detection. 

From the internal conversion coefficients given in table 2, the following gammas were determined to be M1/E2 transitions in agreement with... 

The 130 keV State. The decay of the 130 keV state has been studied extensively, and several inconsistencies are being resolved. The results of different measurements of the mean life and decay mode of the 130 keV state are discussed by Fink and Benczer-Koller (8). The half-life of the state has been measured electronically, and the transition matrix element for excitation has been derived from Coulomb excitation data (12). The combination of the Coulomb excitation yield, the internal conversion coefficient (8) a = 1.76 =t= 0.19, and the branching ratio (8) PCo = 0.060 zb 0.008 for the crossover decay to ground, yields a half-life ti/2 = (0.414 0.014) ns in excellent agreement with a recent (15) Mossbauer determination of the line width, r = (4.4 zb 0.4) mm/sec, equivalent to t1/2 = (0.49 0.05) ns. Wilenzick et al. (15) do not indicate the thickness of the Pt absorber used. 

Figure 5. Experimental values (9) of 0DW for various values of the internal conversion coefficient vs. temperature. The solid line was obtained from the analysis of specific heat measurements and other thermodynamic data (7).

Sources for activity calibration These sources enable a direct calibration of y-ray spectrometers, for radionuclides for which standards are available. Moreover, with the kits of y-ray sources, the efficiency/energy curve can be plotted in this case, knowledge of decay scheme parameters of the radionuclides involved is needed (y branching ratio, internal conversion coefficient, etc.). 

Gamma-ray sources for efficiency measurements as standard sources are characterised in terms of photon emission flux in 4tc sr, expressed in s, for each specified gamma-ray. The activity of the source is indicated. When an activity standard is used to determine the efficiency of a y-ray spectrometer as a function of photon energy, certain decay scheme parameters are required (gamma branching ratio, internal conversion coefficient, etc.). In this case, the calibration uncertainty is the combination of the uncertainty on the activity of the standard and of the uncertainties on the parameters of the decay scheme. 

It should not be forgotten that the excited absorber nuclei re-emit the y-ray within 10 s. However, if the internal conversion coefficient is high, correspondingly fewer y-rays will be emitted. More important, however, the re-emission is not directional but takes place over the full 4.-r solid angle. Consequently the number of secondary events recorded at the detector in a collimated transmission experiment are few and are usually neglected. 

The internal conversion coefficient a must be small so that the y-transition has a high probability of producing a y-photon rather than a conversion electron. This will also increase the absorption cross-section Uq (equation... 

Careful comparative measurements of the intensity of resonance in the absorption and scattering modes can be used to determine the effective cross-section and hence from equation 1.18 the internal conversion coefficient. 

The 37T5-keV transition is from the / = f + excited state to the / = f-1-ground state, the multipolarity being pure Ml. The first measurements used a source of chemically separated "Sn electroplated as 8-tin onto copper, and absorbers of Sb metal and SbjOs [24]. Isotopic enrichment of absorbers was not required to obtain a significant absorption with both source and absorber at 80 K. The tin source matrix was used in most of the early work, although "Sn/SnOa has also been used with success [26]. A third source is Ca SnOs, which by analogy with the same sources used in Sn work (see Chapter 14.1) is likely to have the narrowest line and highest recoil-free fraction of the three [27, 28]. Detailed comparative data are not available, but experiments are usually made with the source and absorber at 80 K in all cases. Linewidths close to the natural width (2-1 mm s ) can be obtained with an InSb absorber and a "Sn/jS-Sn source [29]. The recoil-free fraction of a "Sn/SnOj source is 0-32 at 80 K and 0-16 at room temperature [26]. The internal conversion coefficient derived from the same measurements is Or 10. 

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