Spherical shells calculation steps

The microscopic static property that is usually of primary concern is the pair correlation function g(r). To calculate g(r), each molecule in turn is imagined to be at the center of a series of concentric spheres. The number of molecules in each spherical shell is divided by the volume of that shell, with attention being paid to periodic image locations of molecules outside the box. The results are averaged over all the molecules, and then over many time steps. The pair correlation function is usually calculated in this way only for distances less than the range of the potential r,. Verlet has provided a method for extending g(r) beyond r, using the direct correlation function determined from the Percus-Yevick equation. ... 

Burns and Curtiss (1972) and Burns et al. (1984) have used the Facsimile program developed at AERE, Harwell to obtain a numerical solution of simultaneous partial differential equations of diffusion kinetics (see Eq. 7.1). In this procedure, the changes in the number of reactant species in concentric shells (spherical or cylindrical) by diffusion and reaction are calculated by a march of steps method. A very similar procedure has been adopted by Pimblott and La Verne (1990 La Verne and Pimblott, 1991). Later, Pimblott et al. (1996) analyzed carefully the relationship between the electron scavenging yield and the time dependence of eh yield through the Laplace transform, an idea first suggested by Balkas et al. (1970). These authors corrected for the artifactual effects of the experiments on eh decay and took into account the more recent data of Chernovitz and Jonah (1988). Their analysis raises the yield of eh at 100 ps to 4.8, in conformity with the value of Sumiyoshi et al. (1985). They also conclude that the time dependence of the eh yield and the yield of electron scavenging conform to each other through Laplace transform, but that neither is predicted correctly by the diffusion-kinetic model of water radiolysis. 

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