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Finite Temperature Jastrow Factor

The VDM method can be improved by including correlations that are missed in an Hartree-Fock type ansatz. This is usually done in form of a Jastrow factor f(R,R') as shown in Eq. 3.79,

\begin{displaymath}
f({\bf R},{\bf R}') = \exp \left \{ -\frac{1}{2}{\sum_{i<j}u(r_{ij})+u(r'_{ij})} \right\}
\quad.
\end{displaymath} (263)

The Jastrow factor can be calculated at zero temperature using the RPA (see Ceperley and Alder (1981)), then generalized to finite temperature and approximately expressed in the form (Pollock, 2000),
$\displaystyle u(r)$ $\textstyle =$ $\displaystyle \frac{A}{r} \left( 1- e^{-B\,r} \right)
\quad,$ (264)

where $r$ is the separation of the pair of particles. The coefficients $A$ and $B$ depend on density $n$, inverse temperature $\beta $, and on the type of interacting particles. They are derive that the fulfill the cusp condition at any temperature. The coefficients for a pair of electrons is given by,
$\displaystyle A_{ee}$ $\textstyle =$ $\displaystyle c t
\quad\quad,\quad\quad c=2 \sqrt{r_s^3/3}
\quad\quad,\quad\quad t=\tanh \left( \beta/c \right)\quad,$ (265)
$\displaystyle B_{ee}$ $\textstyle =$ $\displaystyle \sqrt{ 2/ A_{ee}}
\quad.$ (266)

For an electron and an ion of charge $Q$, they read,
$\displaystyle A_{ei}$ $\textstyle =$ $\displaystyle - \frac{Qc}{t} \; \left( 1-e^{-\beta t/c} \right)$ (267)
$\displaystyle B_{ei}$ $\textstyle =$ $\displaystyle \sqrt{ -4Q / A_{ei}}
\quad.$ (268)


next up previous contents
Next: Debye Model Up: Path Integral Monte Carlo Previous: Variational Interaction Terms   Contents
Burkhard Militzer 2003-01-15