Oscillator Strength of the Na₂ ¹Σ—¹Σ Transitions

Abstract

WHILE the oscillator strengths (or ƒ-values) of various molecular electronic transitions are urgently required by astrophysicists, very few experimental or theoretical results are available. I have recently carried out a calculation for the ƒ-value of the ¹Σ—¹Σ transition of the sodium molecule based on the simple hydrogen-ion model. In this calculation the wave functions of the two states were represented by a simple linear combination of the appropriate atomic wave functions (these being taken as Slater-type functions with effective nuclear charge 2.2e and n^* = 3). Taking the internuclear distance as 3.36 a₀ (a₀ is the radius of first Bohr orbit) and the wave-length of the electronic transition as 6812 A., the ƒ-value was found to be 0.26, corresponding to a mean life-time of 1.7 × 10⁻⁸ sec. No experimental measurement of this life-time has yet been made, but the value would not be expected to be widely different from the value for the blue-green system (¹Σ — ¹Π), which has approximately the same intensity. The life-time of this system was measured by Hupfeld¹ and found to be 1.0 × 10⁻⁸ sec., which is of the same order as the theoretical result. Further results based on the hydrogen-ion and the hydrogen-molecule approximations will be reported in greater detail at a later date.