The equations for \( r \) and \( R \) can be separated via the ansatz for the wave function \( u(r,R) = \psi(r)\phi(R) \) and the energy is given by the sum of the relative energy \( E_r \) and the center-of-mass energy \( E_R \), that is $$ E^{(2)}=E_r+E_R. $$ We add then the repulsive Coulomb interaction between two electrons, namely a term $$ V(r_1,r_2) = \frac{\beta e^2}{|\mathbf{r}_1-\mathbf{r}_2|}=\frac{\beta e^2}{r}, $$ with \( \beta e^2=1.44 \) eVnm.