Fine Structure of the metastable a 3 Σ u + state of the helium molecule

The original article written by Lichten, McCusker, and Vierima reported the measurement of the fine structure of the v=0 vibrational state of the a 3 Σu + metastable state of He2 by a molecular beams-magnetic resonance (MBMR) machine from the afterglow of a pulsed helium plasma discharge. By fitting the measured zero field intervals in the N=1 and N=3 rotational levels, the author deduced the spin-spin interaction constant λ and spin-rotation interaction constant γ of these corresponding rotational levels. In this paper we follow the steps to get the same results, skipping the process of doing the real experiment. Introduction It had been more than half a century since the discovery of the helium band spectrum by Curtis and Goldstein 1 when the article was written. The existence of stably bound, excited states of He2 had been confirmed along with the existence of a metastable a 3 Σu + state, which raised the possibility of measuring the fine structure in helium molecule. However a definite claim of such a measurement was absent until the authors of this article made a breakthrough by means of a molecular beam-magnetic resonance (MBMR) technique. In this paper we first briefly talk about the structure of helium molecule and the experimental setup, then follow the steps of making theoretical estimates and reproducing the interaction constants from experimental measurement. The Structure of helium molecule The ground state of helium molecule He2, X 1 Σg + , consists of four electrons filling two lowest atomic orbitals 1sA and 1sB, forming a closed shell. Under linear combination of atomic orbitals (LCAO) approximation, four electrons occupy the two lowest molecular orbitals (MO) σg1s and σu1s, which are