Direct exchange integral

The triplet state is the lowest state and the energy difference between the two states is given by the direct exchange integral... 

The matrices J, K and B are direct, exchange and Breit interaction matrices, of which only the first is block diagonal. Their matrix elements are linear combinations of interaction integrals over G-spinors. 

The assumption of a constant exchange integral is justified, because experiments show only small differences when measuring along different crystallographic directions. When the angle between S and S is small Eq. (16) can be written... 

A virtually interference-free and reagentless approach is immobilizing the redox enzyme on a suitable electrode surface in such a way that the protein-integrated redox site can directly exchange electrons with the electrode (enzymes with direct electron transfer contact). 

Suppose now that Eq. (5-112) is integrated over the entire confining surface of an enclosure which has been subdivided into M finite area elements. Each of the M surface zones must then satisfy certain conservation relations involving all the direct exchange areas in the enclosure... 

Two arrays of direct exchange areas are now defined i.e., the matrix ss = IT, is the M X M array of direct surface-to-surface exchange areas, and the matrix sg= [Tg,] is the MxN array of direct gas-to-surface exchange areas. Here the scalar elements of ss and sg are computed from the integrals... 

The standard hemispherical monochromatic gas emissivity is defined as the direct volume-to-surface exchange area for a hemispherical gas volume to an infinitesimal area element located at the center of the planar base. Consider monochromatic transfer in a black hemispherical enclosure of radius ft that confines an isothermal volume of gas at temperature Tg. The temperature of the bounding surfaces is T. Let A2 denote the area of the finite hemispherical surface and dAi denote an infinitesimal element of area located at the center of the planar base. The (dimensionless) monochromatic direct exchange area for exchange between the finite hemispherical surface A2 and d then follows from direct integration of Eq. (5-116a) as... 

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