Long-ranged potential

With this convention, we can now classify energy transfer processes either as resonant, if IA defined in equation (A3.13.81 is small, or non-resonant, if it is large. Quite generally the rate of resonant processes can approach or even exceed the Leimard-Jones collision frequency (the latter is possible if other long-range potentials are actually applicable, such as by pennanent dipole-dipole interaction). 

A final point to remember is that the simulation with the smallest deviation from the X-ray structure (0.25 angstrom switch) is probably the least realistic of the entire set of simulations that were truncated near 7.5 angstroms, which implies that a simulation should not be judged by this value alone. It is hoped that from these simulations that better methods for handling the truncation of long range potentials can become more universal. 

LeRoy, R. J., and Bernstein, R. B. (1970), Dissociation Energy and Long-Range Potential of Diatomic Molecules from Vibrational Spacings of Higher Levels, J. Chem. Phys. 52, 759. 

A very interesting field of research covers the spectroscopy of van der Waals molecules in search of more detailed information about the long range potential and the polarizability. Raman spectra of van der Waals dimers in argon have been observed and a vibrational frequency shift for I2-molecules from 213 cm" to 197 cm has been measured for I2 -Ar-complexes. 

Eq. (92) represents the difference betw n two long range potentials both having a Coulombic — 1/r behavior and it therefore decays faster than Coulombic. In the approximation ASi — As, the potential W reduces to the Slater potential Vx.scr and only the first term survives in Eq. (92). If we apply this same... 

All the preceding mechanisms of the carrier packet spread and transit time dispersion imply that charge transport is controlled by traps randomly distributed in both energy and space. This traditional approach completely disregards the occurrence of long-range potential fluctuations. The concept of random potential landscape was used by Tauc [15] and Fritzsche [16] in their models of optical absorption in amorphous semiconductors. The suppressed rate of bimolecular recombination, which is typical for many amorphous materials, can also be explained by a fluctuating potential landscape. 

Thus, whereas the asymptotic Friedel oscillations in eqn (6.84) have their phase fixed with respect to the underlying lattice for a given valence Z, the oscillations of the long-range potential are electron density or atomic volume sensitive through the phase shift a3 which from eqs (6.97) and (6.99) is given by... 

The MCQDT could probably be extended to include long-range potentials other than Coulomb, for instance, dipole potentials. 

From the various possible closures, the mean spherical approximation (MSA) [189] has found particularly wide attention in phase equilibrium calculations of ionic fluids. The Percus-Yevick (PY) closure is unsatisfactory for long-range potentials [173, 187, 190]. The hypemetted chain approximation (HNC), widely used in electrolyte thermodynamics [168, 173], leads to an increasing instability of the numerical algorithm as the phase boundary is approached [191]. There seems to be no decisive relation between the location of this numerical instability and phase transition lines [192-194]. Attempts were made to extrapolate phase transition lines from results far away, where the HNC is soluble [81, 194]. 

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