Rotational line strengths for the photoionization of diatomic molecules

Abstract

We derive an expression for the probability that a diatomic molecule AB(n,v,N) in the electronic state n, vibrational state v, and rotational level N yields upon photoionization AB+(n+,v+,N+), where we assume Hund’s case (b) coupling. Our result is formally equivalent to the previous work of Buckingham, Orr, and Sichel [Phil. Trans. Roy. Soc. London, Ser. A 268, 147 (1970)] but differs substantially in that we use spherical tensor methods, which provide insight into the photoionization dynamics in terms of the contribution of different multipole moments. The total interaction term is given by the tensor product of the electric dipole moment operator T(1,μ0) and the multipole moment tensor T(l,m) describing the photoelectron in the lth partial wave. The interaction term is further simplified into a sum of reduced multipole moments T(k,p), where k=l±1 and p=μ0+m. For an isotropic distribution of initial states, the transition probability is given by P(N,N+)=1/3∑k Sk(N,N+)‖μ̄(k,q)‖2, where the factor of 1/3 arises from the use of a beam of polarized light, Sk(N,N+) is a generalized rotational line strength factor, and ‖μ̄(k,q)‖2=‖μl=k+1(k,q) ‖2+‖μl=k−1(k,q)‖2 is the sum of the squares of reduced multipole moment matrix elements. The summation over k is restricted to even values for a (±)↔(±) transition and to odd values for a (±)↔(∓) transition. Thus, for an unpolarized molecular sample, the integrated photoelectron intensity associated with an N→N+ transition is the incoherent sum of the multipole moments that contribute to this transition, and each such contribution is an incoherent sum over l=k+1 and l=k−1. If the molecular sample is polarized (aligned and/or oriented), then the expression for the N→N+ integrated photoelectron intensity becomes a coherent sum over different k values with the same l value. Moreover, if the photoelectron distribution is angle resolved, then the expression for the N→N+ transition probability is a coherent sum over l values with the same k value when the molecular sample is unpolarized and cannot be separated into incoherent parts when the molecular sample is polarized. The expression for P(N,N+) has been used to fit the results of the photoionization of H2 and NO. In both cases, the fit obtained, which required only one or two adjustable parameters, respectively, agrees well with the experimental data. This treatment may be readily extended to photoionization of polyatomic molecules and to molecules that follow different angular momentum coupling cases.