Internal conversion coefficient determination

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. 

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. 

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. 

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 internal conversion coefficient for Fe has been accurately determined from the transmission integral (seeO Eqs. (25.11), (O 25.30), and (O 25.31)) by using a series of iron absorbers all having the same thickness of iron atoms but the enrichment in Fe varied by a factor of as much as 37 (Hanna and Preston 1965). 

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. 

Consider the reaction used as the basis for Illustrations 10.1 to 10.3. Determine the volume required to produce 2 million lb of B annually in a plug flow reactor operating under the conditions described below. The reactor is to be operated 7000 hr annually with 97% conversion of the A fed to the reactor. The feed enters at 163 C. The internal pipe diameter is 4 in. and the piping is arranged so that the effective reactor volume can be immersed in a heat sink maintained at a constant temperature of 160 °C. The overall heat transfer coefficient based on the... 

Natural gas is reacted with steam on an Ni-based catalyst in a primary reformer to produce syngas at a residence time of several seconds, with an H2 CO ratio of 3 according to reaction (9.1). Reformed gas is obtained at about 930 °C and pressures of 15-30 bar. The CH4 conversion is typically 90-92% and the composition of the primary reformer outlet stream approaches that predicted by thermodynamic equilibrium for a CH4 H20 = 1 3 feed. A secondary autothermal reformer is placed just at the exit of the primary reformer in which the unconverted CH4 is reacted with O2 at the top of a refractory lined tube. The mixture is then equilibrated on an Ni catalyst located below the oxidation zone [21]. The main limit of the SR reaction is thermodynamics, which determines very high conversions only at temperatures above 900 °C. The catalyst activity is important but not decisive, with the heat transfer coefficient of the internal tube wall being the rate-limiting parameter [19, 20]. 

The question remains as to when the various diffusion effects really influence the conversion rate in fluid-solid reactions. Many criteria have been developed in the past for the determination of the absence of diffusion resistance. In using the many criteria no more information is required than the diffusion coefficient DA for fluid phase diffusion and for internal diffusion in a porous pellet, the heat of reaction and the physical properties of the gas and the solid or catalyst, together with an experimental value of the observed global reaction rate (R ) per unit volume or weight of solid or catalyst. For the time being the following criteria are recommended. Note that intraparticle criteria are discussed in much greater detail in Chapter 6. 

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