Ortho helium

Hylleraas, E. A., Z. Physik 54, 347, "Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium/ Explicit inclusion of r12. Scaling procedure. Open shell idea (Is, Is") introduced. 

A less grandiose but more specific verification of the principle comes from the study of the helium spectrum. This contains two sets of terms which do not combine. So completely independent are they that at one time they were ascribed to two modifications, known respectively as ortho-helium and para-helium. The para terms are singlet and the ortho terms triplet. The normal or ground state of the atom belongs to the para system. This state of affairs first becomes explicable in terms of the symmetry of the wave functions. 

The states with the higher statistical weight are called ortho (as with the triplet states of ortho-helium). Thus ortho-hydrogen has the odd numbers of rotational quanta and para-hydrogen the even numbers. 

Perspective on Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium" 180... 

Ground State as Well as the Lowest Term of Ortho-Helium. 

A NEW CALCULATION OF THE ENERGY OF HELIUM IN THE GROUND STATE AS WELL AS THE LOWEST TERM OF ORTHO-HELIUM... 

I will not give the precise details of the calculations, since they are fairly uninteresting and since we will encounter similar calculations for ortho-helium. 

We will now also attempt to compute the ground term of the eigenvalue problem (8) with the boundary condition V = 0 for = 0, i.e. the lowest term of ortho-helium. The exact eigenfunction of the unperturbed problem [deleting the perturbational term in Eq. (5) or 7 of Eq. (8)]... 

The lowest term of ortho-helium corresponds to the wave number 38 455 cm , and, therefore, measured in 4Rh and adding the energy of the ion it has the value... 

We note the small influence of the coordinate u = ri2 on the eigenvalue of ortho-helium, in opposition to the situation in para-helium. This is completely understandable. For t = 0, and therefore also for u = 0, the function becomes equal to zero because of antisymmetry. This largely accounts for the effect that the two electrons strive to be as far as possible from each other. 

In ortho-helium the precision has not been driven that far, but here the lowest eigenvalue, as obtained by simple means, definitely points to an absolute agreement between the theoretical and the experimental value. 

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