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Quantum Monte Carlo: the helium atom

The helium atom consists of two electrons and a nucleus with charge Z=2 . The contribution to the potential energy due to the attraction from the nucleus is -\frac{2ke^2}{r_1}-\frac{2ke^2}{r_2}, and if we add the repulsion arising from the two interacting electrons, we obtain the potential energy V(r_1, r_2)=-\frac{2ke^2}{r_1}-\frac{2ke^2}{r_2}+ \frac{ke^2}{r_{12}}, with the electrons separated at a distance r_{12}=|\boldsymbol{r}_1-\boldsymbol{r}_2| .