Electron conversion coefficient

Here a = Fe/Fo is the internal electron conversion coefficient for excited nucleus. 

A Co ( Fe) radioactive isotope with energy Ey 14.4 keV of controlled nuclear gamma transition 2 I, internal electron conversion coefficient a 9 for this nuclear transition and small activity Q = 10 Ci was used as a source of controlled Mossbauer radiation I. 

TABLE 22.1 Total Electron Conversion Coefficients (aj) for Some Transitions of Common Mossbauer Isotopes... 

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... 

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. 

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". ... 

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. 

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. 

The ratio of conversion electrons and y-ray photons emitted per unit time is called the conversion coefficient ... 

X and Xy are the partial decay constants (probabilities) of conversion (electron emission) and y-ray emission. The conversion coefficient a is the sum of the partial conversion coefficients of the K shell, L shell,... 

The energies of isomeric transition are only 49 and 37 keV, and the conversion coefficients are 1.6 and 300, respectively. The recoil energy due to emission of a 49 keV y-ray photon is only 0.016 eV (section 9.2). It is too low to break a C-Br bond (247 kJ 2.6 eV). The recoil energy due to emission of an electron from the Is orbital (0.45 eV) is also too small to break the C-Br bond. Actually, breaking of the C-Br bond due to isomeric transition of ° Br is observed, for instance, if butyl bromide labelled with ° Br is shaken with water. In this experiment the main fraction of °Br is found free of ° Br in the aqueous phase. Results of experiments with various compounds labelled with < Br are compiled in Table 9.2. The high retention in the case of solid (NH4)2[PtBr6] is due to the fact that in the solid state the missing electron is quickly substituted. 

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... 

Note that the solution of the problem of the incidence of an s-polarized EW onto a periodic density-modulated 2D electron system gives the same values for the polarization conversion coefficients = R ) in the TIR regime. This attests to a reciprocal character of the polarization conversion process for 0> Or,. 

If we denote the conversion coefficient as Oj, it is equal to the ratio of K-electrons ejected (which we may denote with to that of gamma quanta emitted (7 ) ... 

Ig and Ig are the respective nuclear spin quantum numbers of the excited and ground states of the nucleus and a is the internal conversion coefficient, i.e., a is the ratio of the number of conversion electrons to the number of y-ray photons emitted from a Mbssbauer atom. For a to be large we need Ey and a to be small. Oq must also be large compared with the cross-section for other absorption processes, e.g., photoelectric. 

The appropriate excited state of the resonant nucleus can be populated from (a) decay of a radioactive precusor, (b) nuclear reaction or (c) by excitation. Method (a) is most frequently employed because of its convenience. A typical example is shown in Fig. 2 for Co(57), which leads to the 14.41 keV first excited level of Fe(57) by electron capture. The internal conversion coefficient, a, for the 14.41 keV y-ray is 9.0. Therefore, only -10% of the nuclear decays originating from B produce the required 14.41 keV photon. 

The magnetic components can also be obtained by measurements of internal conversion electrons. Experimental methods of measurement of internal conversion electrons produced by Coulomb excitation have been developed by Huus and Bjerregaard and used by them to study the rare earth nuclei in some detail 2. This method has the advantage that the composition of a mixed y-ray can be determined from the magnitude of the conversion coefficient or from the KjL ratios, although it is still necessary to know the relative intensities of the transitions between the various states. 

The second term represents the analog of the repulsive term in the heat of formation in Miedema s model (Miedema et al., 1980). The sign of the coefficient Q follows from the contention that the mismatch in electron density at the Wigner-Seitz atomic cell boundaries (/i,, ) in transition metal alloys can be removed by means of s-d intra-atomic electron conversion. The s electrons reside predominantly in the outside regions of the atomic cell. Conversion of s-type electrons into d-type electrons will therefore result in a decrease of n. It follows then that P and Q are of opposite sign. 

According to the theory, the internal conversion coefficient decreases with increasing transition energy and increases with increasing atomic number and multipolarity of y-radiation. The coefficient a depends also on the electric or magnetic character of the radiation. Internal e conversion is possible between 0 states, too. If both K and L electron emissions are allowed energetically, the L electron emission is usually weaker (kl 0.1 Kk)- For 0 — 0" transitions see the review article by KibMi and Spear (2005). 

The so-called internal conversion coefficient (a) is defined as the ratio of the probability of electron emission (pe) to that of gamma emission (py) ... 

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