IV. The triplets of helium

Abstract

Heisenberg’s theory of the helium atom, following his famous principle of “resonance,” accounted satisfactorily for the ortho- and para- states. His more detailed treatment of the triplets, besides giving ground for minor criticisms, necessarily had to be derived from Schrödinger’s equation , with a somewhat incongruous electronic “spin” grafted upon it. The present work uses Dirac’s recent theory, in which the spin effects grow more naturally from the fundamental equations. Calculations which are in dependent of the spin, such as the approximate energy-levels and the ortho-para separations, are the same on either theory. We deal here with spin effects, such as the fine structure of the triplets and intercombinations between ortho- and para- states. The fundamental equations, the perturbation theory which is used, and the perturbing spin energy, have been discussed fully elsewhere. The present paper, after a short recapitulation of the general theory, gives in detail the calculations whose results alone were quoted in the other. §§ 4–7 work out the structure of the helium triplets with one excited election. The resulting spin separations are different from Heisenberg’s, but in equally good agreement with experiment. At the same time, the correct first approximations to the wave-functions are found, and they are used in § 8 to verify the ordinary classification and selection rules.