Average inner and outer radii in singly-excited 1snl states of the He atom

Average inner < r _< > and outer < r _> > radii are studied for 28 singly-excited 1 snl singlet and triplet states (0 ≤ l ≤ n ≤ 5) of the He atom. In all the cases, the average inner radius < r _< > is close to 0.75 bohr, which indicates that one of the two electrons behaves like the 1s electron in He⁺. On the other hand, an analysis of the average outer radius < r _> > shows that the other electron of the 1snl states behaves approximately like an snl electron in the hydrogen atom. The average outer radius < r _> > reflects more diffuse character of the singlet electron distribution. This paper is dedicated to the late Professor Serafin Fraga for his great contribution to quantum sciences. Contribution to the Serafin Fraga Memorial Issue.