Asymptotic form of the mean spherical approximation for the internal energy of the classical one-component plasma

Abstract

The mean spherical approximation for the internal energyU of the classical one-component plasma is solved exactly in the limit γ ≫ 1, where γ is the usual Coulomb coupling parameter. The result${{\beta U} \mathord{\left/ {\vphantom {{\beta U} {N = - \tfrac{9}{{10}}\Gamma + {\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 6$}}\sqrt 3 \Gamma ^{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}} + \Gamma ^{{1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-\nulldelimiterspace} 6}} /15\sqrt 3 2^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} + 0(\Gamma ^{ - {1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-\nulldelimiterspace} 6}} )}}} \right. \kern-\nulldelimiterspace} {N = - \tfrac{9}{{10}}\Gamma + {\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 6$}}\sqrt 3 \Gamma ^{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}} + \Gamma ^{{1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-\nulldelimiterspace} 6}} /15\sqrt 3 2^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} + 0(\Gamma ^{ - {1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-\nulldelimiterspace} 6}} )}}$ is consistent with DeWitt's empirical analysis of the mean spherical approximation.