Coulomb potential screened

The solutions to this approximation are obtained numerically. Fast Fourier transfonn methods and a refomuilation of the FINC (and other integral equation approximations) in tenns of the screened Coulomb potential by Allnatt [M are especially useful in the numerical solution. Figure A2.3.12 compares the osmotic coefficient of a 1-1 RPM electrolyte at 25°C with each of the available Monte Carlo calculations of Card and Valleau [ ]. 

The first density correction to the rate constant depends on the square root of the volume fraction and arises from the fact that the diffusion Green s function acts like a screened Coulomb potential coupling the diffusion fields around the catalytic spheres. 

Mehler EL, Guarnieri F (1999) A self-consistent, microenvironment modulated screened coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins. Biophys J 75 3-22. 

Of course, this result has to come out of the calculation and it will be obtained in Sections V-C and V-E. However, it is intuitively clear that a qualitatively correct result should come out of the static approximation using a screened coulomb potential (see... 

We shall, however, keep here the screened Coulomb potential (314) for describing the interionic interaction the most general case will be discussed in Section V-E. 

In the simplest model, the interactions with the solvent were completely neglected and the collective Coulomb interactions between the ions were imitated by a screened Coulomb potential the result is (see Eq. (321))... 

Camus et a/.34 explained their observations by a picture which has sometimes been called the frozen planet model. Qualitatively, the relatively slowly moving outer electron produces a quasi-static field at the inner electron given by l/rc2, and this field leads to the Stark effect in Ba+. The field allows the transitions to the n >n0Z and ,f 0 states and leads to shifts of the ionic energies. The presence of the njpn0f and n in0t resonances in the spectrum of Fig. 23.12 is quite evident. Camus et al. compared the shifts to those calculated in a fashion similar to a Bom-Oppenheimer calculation. With the outer electron frozen in place at ra they calculated the Ba+ energies, W,(rQ), and wavefunctions. They then added the energy W0(r0) to the normal screened coulomb potential seen by the outer electron. This procedure leads to a phase shift in the outer electron wavefunction... 

Mott describes the localized center in terms of an electron hole pair with a screened Coulombs potential... 

The electrical conductivities of several alkali metals dissolved in liquid ammonia are shown in Figure 1 (7, 119 15). The strong variation of the conductivity, a, with concentration has been most difficult to explain. This difficulty can be assessed by referring to a simple model of conductance, the Thomas-Fermi model of a screened Coulomb potential (19). This model has been used in describing semiconductors as well as in theories of metal-ammonia solutions (1). 

If we only consider the static case w = 0we can distinguish two limiting cases First, if the typical range rjj of the screened Coulomb potential Vc is much smaller than the mean electron distance, the potential can be assumed to be a delta distribution and Ttc can be approximated by... 

An early calculation on the effect of the screened Coulomb potential on the energy of the He atom was due to Rogers [183]. Lam and Varshni [184] calculated the ground state energy of the He atom as a function of the... 

This process describes the scattering of free carriers by the screened Coulomb potential of charged impurities (dopants) or defects theoretically treated already in 1946 by Conwell [74,75], later by Shockley [10] and Brooks and Herring [76,77]. In 1969, Fistul gave an overview on heavily-doped semiconductors [78]. A comprehensive review of the different theories and a comparison to the experimental data of elemental and compound semiconductors was performed by Chattopadhyay and Queisser in 1980 [79]. For nondegenerate semiconductors the ionized impurity mobility is given by [79] ... 

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