Finite Temperature Densities via the SFunction Method with Application to Electron Screening in Plasmas
Abstract
A new approach to the Green'sfunction method for the calculation of equilibrium densities within the finite temperature, KohnSham formulation of density functional theory is presented, which extends the method to all temperatures. The contour of integration in the complex energy plane is chosen such that the density is given by a sum of Green's function differences evaluated at the Matsubara frequencies, rather than by the calculation and summation of KohnSham singleparticle wave functions. The Green's functions are written in terms of their spectral representation and are calculated as the solutions of their defining differential equations. These differential equations are boundary value problems as opposed to the standard eigenvalue problems. For large values of the complex energy, the differential equations are further simplified from second to firstorder by writing the Green's functions in terms of logarithmic derivatives. An asymptotic expression for the Green's functions is derived, which allows the sum over Matsubara poles to be approximated. The method is applied to the screening of nuclei by electrons in finite temperature plasmas. To demonstrate the method's utility, and to illustrate its advantages, the results of previous wave function type calculations for protons and neon nuclei are reproduced. The method is also used to formulate a new screening model for fusion reactions in the solar core, and the predicted reaction rate enhancements factors are compared with existing models.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1997
 Bibcode:
 1997PhDT.........3W
 Keywords:

 Physics: Astronomy and Astrophysics, Physics: Atomic, Physics: Condensed Matter