Binäre SLATER‐Summen und Verteilungsfunktionen für quantenstatistische Systeme mit COULOMB‐Wechselwirkung. II

Abstract

In part 1 of this paper the SLATER-sums of two charged particles were expanded in TAYLOR-series with respect to the distance between the particles. Using these expansions we calculate the binary 8LATER-SUmS for small values of r ( r Q d) A-thermal wavelength).In the case of r $1 the binary SLATER-SUmS can be approximated by the classical BOLTZ-MANN-factor. In the intermediate region r w 2 we get the binary SLATER-sums by interpolation. For high temperatures we obtain KELBG'S result. For special cases the binary SLATER-sums and the binary distribution functions are presented graphically and discussed.

The method of effective potentials in the quantum-statistical theory of plasmas

“…As a result of Kelbg's approximations (first order in e 2 ) the effective potential is not exact at r = 0. It may differ from the expression obtained from the hydrogen wave functions, which is known and given in the form of tables [4,6]. On the other hand, the first derivative of Kelbg's potential at r = 0 and the asymptotic r → ∞ are correct, in agreement with quantum mechanics.…”

“…The Rostock School in Quantum Statistics formed by Günter Kelbg concentrated on analytical calculations of thermodynamic functions based on effective potentials [2][3][4]. Several authors calculated the two-particle density matrix from the known wave functions including numerical approaches [5][6][7]. Zelener, Zamalin, Norman and Filinov gave first applications within the Monte Carlo formalism [8,9], Deutsch introduced useful approximations [10], Hansen, McDonald and Pollock [11] gave first applications to molecular dynamics, and Kleinert developed a variational approach [12].…”

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

“…In the quantum case all effectice potentials are always finite at T = 0, the new characteristic length is A. Several approximations for the quantum effective potentials are available [2,38,391.…”

First Principle Thermodynamic and Dynamic Simulations for Dense Quantum Plasmas

“…[27,28]) several potentials which are suited for Coulomb systems: i) the diagonal Kelbg potential [18,19], ii) the off-diagonal Kelbg potential iii) the improved diagonal Kelbg potential [29,30], iv) an effective potential obtained with the FeynmanKleinert variational principle [31] and v) the "exact" quantum pair potential derived from the two-particle density matrix [32][33][34]. For the improved diagonal Kelbg potential we have obtained a simple temperature dependent fit which accurately reproduces the "exact" pair potential in the whole temperature range.…”

“…[13][14][15][16][17], where a real quantum system is projected onto a classical one by means of including quantum and spin effects into effective interparticle interaction potentials. Such potentials have been derived by many authors, including Kelbg [18,19], Deutsch [20], Klakow, Toepffer and Reinhard [13] and others, e.g. [21][22][23][24][25][26].…”