Resulting ansatz

The above results in

$$ {\cal R}_T \propto \exp{(r_{ij}/2)}, $$

for anti-parallel spins and

$$ {\cal R}_T \propto \exp{(r_{ij}/4)}, $$

for anti-parallel spins. This is the so-called cusp condition for the relative motion, resulting in a minimal requirement for the correlation part of the wave fuction. For general systems containing more than say two electrons, we have this condition for each electron pair \( ij \).

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