Selection rules for the photoionization of diatomic molecules

Abstract

In the photoionization of the diatomic molecule AB to yield AB⁺+e⁻ the photoelectron may be charatcterized by a partial wave expansion in terms of its orbital angular momentum quantum number l. For a given value of l, conservation of angular momentum implies that transitions can only occur for ΔJ=l+ (3)/(2) , l+ (1)/(2) , ... ,−l− (1)/(2) , −l− (3)/(2) , where ΔJ=J⁺−J is the change (half‐integer) in the total angular momentum (excluding nuclear spin) of the AB⁺ ion rovibronic level and the AB neutral rovibronic level. Other selection rules are ΔΩ=−λ+ (3)/(2) , −λ+ (1)/(2) , ... , −λ− (3)/(2) , and ΔM=−m_l+ (3)/(2) , −m_l+ (1)/(2) , ... , −m_l− (3)/(2) . In addition, for Hund’s case (a) and case (b) coupling, ΔS=S⁺−S=± (1)/(2) , ΔΣ=± (1)/(2) , and ΔΛ=−λ, −λ±1. Parity selection rules have been derived for transitions connecting levels described by one of the four coupling schemes, Hund’s case (a), case (b), case (c), and case (d). In particular, for a case (a)–case (a) transition, ΔJ−ΔS+Δp+Δs+l=odd, where the symbols have their traditional spectroscopic meanings. The parity label p=0,1 has been associated with the e, f label, from which it may be shown that (e/f )↔(e/f ) for ΔJ− (1)/(2) +l=odd and (e/f )↔( f/e) for ΔJ− (1)/(2) +l=even. It also follows that ±↔± for l odd and ±↔∓for l even. Moreover, Σ^± is connected to Σ^± in general, but Σ^± is only connected to Σ^∓ for l≥2 and λ=±1 (π wave). For homonuclear diatomics, the additional selection rules are (g/u)↔(g/u) for l=odd, (g/u)↔(u/g) for l=even, and (s/a)↔(s/a) but (s/a)↔/(a/s).