where r₁ and r₂ are the distances between the electrons and the nucleus, and r₁₂ is the distance between the two electrons.
where a_0 is the Bohr radius.
The two-electron atom, also known as the helium-like atom, consists of two electrons orbiting a nucleus with atomic number Z. The time-independent Schrödinger equation for this system is: quantum mechanics of one- and two-electron atoms pdf