Coulomb coupling parameter

In most plasmas of interest Fe(i) 1, which means they are ideal. In a dusty plasma (Fridman Ketmedy, 2004) with a dust particle density n, charge Z e, and temperature 7d, the non-ideality parameter (which is also called the Coulomb coupling parameter) is... 

Another interesting application of the total energy approach involves superconductivity. For conventional superconductors, the 1957 theory of Bardeen, Cooper and Schrieffer [26] has been subject to extensive tests and has emerged as one of the most successful theories in physics. However, because the superconducting transition temperature Tc depends exponentially on the electron-phonon coupling parameter X and the electron-electron Coulomb parameter p, it has been difficult to predict new superconductors. The sensitivity is further enhanced because the net attractive electron-electron pairing interaction is proportional to X-p, so when these parameters are comparable, they need to be determined with precision. 

Considering now the low energy or low temperature behaviour of this system, it follows immediately that the phase diagram is the same as for the one-cutoff model (3,12) with the only difference that the parameters are the new bare couplings g",0 + gt c and g"lc + glfrt. Since the Coulomb coupling is... 

Fig. 1. Errors of calculated fiee ion transition energies with respect to experimental values. Open squares sfss CGWB-AIMP calculations with A = 1. Open circles sfss CGWB-AIMP with A = 0.9. Full circles a -1000 cm empirical correction is added to the spin-free state shifting parameters 8( P) and 8( l). Dotted line stands for Dirac-Coulomb coupled-cluster calculations from Ref. [66].

Equation (3.71) contains a coupling parameter A, which takes values from 0 to 1. A value of zero corresponds to a system where there is no Coulomb repulsion Uxc between the electrons (i.e. the Kohn-Sham non-interacting reference state). As A increases to 1 the interelectronic Coulomb repulsion is introduced until A = 1, which corresponds to the real system with full interactions. For all values of A the electron density is the same and equal to the density of the real system. It is not practical to perform this integral anal) ically and so it must be approximated. The simplest approximation is a linear interpolation ... 

Fig. 2. Bounds on the Coulomb hole size / required for the iteration function G to be a contraction map are shown. The gradient condition (ii) leads to the result (34) where L(/) is plotted here (broken line). For sufficiently large coupling parameters F > Fcut/ the largest root /min of L = F sets a non-trival lower bound f on ttie initial sequence term. The corresponding solution I given by (24) is also indicated (solid line) as well as an upper bound (dotted line) presented by the non-negativity condition on the renormalisation factor...

The Coulomb interaction between the re-electrons is neglected. The standard tra/is-polyacetylene parameters are ta=2.5 eV for the hopping amplitude in the undimcrizcd chain, u-4. cV/A for the electron-phonon coupling, and K= 21 eV/A2 for the spring constant [1,4, 8]. 

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