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{\Large \bf Quantum pair potentials for strongly correlated plasmas}\\[2ex]

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{\large A.V.~Filinov$^1$, M.~Bonitz$^1$, and W.~Ebeling$^2$}

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$^{1}$FB Physik, Rostock University, D-18051 Rostock, Germany\\
$^2$Institut f\"ur Physik, Humboldt-Universit{\"a}t Berlin\\
Invalidenstrasse 110 D-10115 Berlin

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%\centerline{\large Abstract}
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\noindent

The pair interaction between charged particles is modified on small distances of the
order of the particle quantum wave length. In particular, this effect removes the
classical singularity of the attractive Coulomb potential. Such potentials which have
previously been derived by Kelbg and co-workers~[1,2]
and others~ capture the basic quantum diffraction effects and
are exact in the weak coupling limit. Moreover, using path integral Monte Carlo (PIMC)
methods, they can be extended to strongly coupled plasmas which include
bound states [3]. We investigate the accuracy of the Kelbg potential as well
as the off-diagonal Kelbg potential by comparison with accurate
solutions of the off-diagonal two-particle Bloch equations.
Results for the energies of an electron-proton pair
and pair distribution functions are presented. A significant
improvement is achieved by correcting the potential value at zero
particle separation by introducing a single temperature-dependent parameter. This allows
to extend the applicability of effective potentials to strongly coupled plasmas.
The resulting semi-analytical expression is very useful for efficient PIMC and molecular
dynamics simulations of quantum plasmas.

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\noindent [1] G.~Kelbg, Ann. Physik, {\bf 12}, 219 (1963);
{\bf 13}, 354; {\bf 14}, 394 (1964).

\noindent [2] W.~Ebeling, H.J.~Hoffmann, and G.~Kelbg,
Contr. Plasma Phys.
{\bf 7}, 233 (1967) and references therein.

\noindent [3] V.~Filinov, M.~Bonitz, W.~Ebeling, and V.E.~Fortov,
Plasma Physics and Controlled Fusion {\bf 43}, 743-759 (2001)


%\noindent [3] H.~Wagenknecht, W.~Ebeling, and A.~F\"orster,
%Contrib. Plasma Phys. {\bf 41}, 15 (2001).

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