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\begin{equation*}
\Psi_2(\mathbf{r}_1, \mathbf{r}_2; \alpha, \beta) = \Psi_1(\mathbf{r}_1,\mathbf{r}_2;\alpha) \exp[J_\text{ee}(\mathbf{r}_1,\mathbf{r}_2;\beta) + J_\text{ep}(\mathbf{r}_1,\mathbf{r}_2;\beta)],
\end{equation*}
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