Fractional index

Data relating to radionuclide deposition (fallout) within a few miles of the Danny Boy, Sedan, and Palanquin nuclear cratering shots are examined for evidence of fractionation. The fractionation index is computed for several fission-product mass chains produced in each event. For the three events studied only Danny Boy showed unambiguous evidence of fractionation in the early fallout, and the degree of fractionation was small. In Danny Boy there was only a factor of four difference between most enriched and most depleted species, compared with the factors of several hundred that have been observed in many late time samples of airborne debris. If this small amount of fractionation proves to be true in general for cratering shots, predictions of early-fallout gamma-radiation patterns will be simplified. 

The fractionation index U is calculated for each measured fission product at each tray location in the fallout field as follows ... 

As a rough check on the magnitude of the indices in Table I, a theoretical estimate of the fractionation index for unfractionated fission products can be calculated as follows. The index has the units kiloton-hr./ft.2 roentgens if we use the most probable value of 2500 roentgens /hr. for 1 kiloton/sq. mile over Nevada Test Site terrain for unfractionated fission products, we obtain (since 1 square mile = 2.78 X 107 ft.2)... 

Fig. 3. Relationship between unit cell (mesh) vectors of a LEED pattern and unit mesh vectors of the corresponding surface structure, x = Integral-index LEED spots (due to substrate) x = fractional-index LEED spots (due to overlap) O = (2v/3 x 2N/3)R30° overlayer lattice (mesh) Grid = substrate mesh A, B = unit cell (mesh vectors of LEED pattern a, b = unit mesh vectors of overlayer structure I = unit mesh vectors of substrate LEED pattern and i = unit mesh vectors of substrate surface.

This is a set of equations applicable to z = 1,..., C, where C is the total number of components. Equation 12.17 is one form of the Fenske equation (Fenske, 1932) for a total reflux distillation column. The number of stages A, is the minimum required to achieve the separation corresponding to component flow rates and and bottoms rate B. In this equation, N, the number of stages, is also known as the fractionation index. 

A fractional index, therefore, represents a root of the particular number affected with that exponent. Similarly,... 

Qj mass fraction (index 1 for solvent, index 2 for polymer)... 

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