Coulomb oscillations as a remedy for the helium atom

TL;DR

This paper revisits the old Bohr-Sommerfeld theory for the helium atom, showing that correct orbit choices and the exclusion principle can yield accurate energies and insights into spectral features, challenging the notion that the orbit concept is fundamentally flawed.

Contribution

It demonstrates that semiclassical Coulomb oscillations with proper orbit selection can accurately predict helium atom energies and explain spectral features, reviving and extending classical ideas.

Findings

Calculated helium ground-state energy rivals quantum results.

Revealed Bohr's triplet energy as a forbidden state.

Provided a visual explanation for helium spectral features.

Abstract

The largest failure of the old, Bohr-Sommerfeld quantum theory was with the helium atom. It brought about the theory's demise. I show that this failure does not originate, as commonly believed, with the orbit concept per se. Instead, it was caused by the wrong choice of orbits, compounded by ignorance of the exclusion principle. Choosing semiclassical electron oscillations through the He nucleus, I calculate a singlet ground-state energy that rivals in accuracy with quantum-mechanical results. The same method reveals Bohr's historic energy value as the forbidden triplet ground state--a result beyond the reach of quantum mechanics. At the qualitative level, the concept of Coulomb oscillations visually explains the major features in the He double spectrum in terms of crossed or parallel orbit orientation.