Determination of differential-cross-section moments from polarization-dependent product velocity distributions of photoinitiated bimolecular reactions

Abstract

We describe procedures for the measurement of the differential-cross-section moments of the velocity distribution of the state-selected products of photoinitiated bimolecular reactions using resonance-enhanced multiphoton ionization (REMPI) detection and some form of laboratory velocity selection such as time-of-flight mass spectrometry. The relative ionization probability of a single product molecule is presented in the form I=1+f(Θ,Φ,θε,θu,Aq(k)stf), where the angles Θ, Φ, and θε describe the orientation of the product’s laboratory velocity with the photolysis and probe laser polarizations, θu is the product laboratory scattering angle, and the Aq(k)stf are the stationary target frame (STF) differential-cross-section moments. The STF is a reference frame defined by the laboratory velocity and the scattering plane. From the ionization probability, I, we derive a method to measure all five parameters with k⩽2, the differential cross section, 1/σ(dσ00/dΩr), and the four polarization parameters A1(1)stf, A0(2)stf, A1(2)stf, and A2(2)stf [where the Aq(k)stf are equal to the polarization-dependent differential cross sections normalized by the differential cross section, (dσkqstf/dΩr)/(dσ00/dΩr)]. The five parameters can be determined using only one rotational branch and several experimental geometries. We present simulations that show the effects of product polarization on experimental signals, and we discuss the effectiveness and limitations of inverting the measured signals to the Aq(k)stf.