An analytical formulation of isotope fractionation due to self-shielding

Isotope fractionation due to photochemical self-shielding is believed to be responsible for the enrichment of inner solar system planetary materials in the rare isotopes of carbon, nitrogen, and oxygen relative to the Sun. Self-shielding may also contribute to sulfur isotope mass-independent fractionation in modern atmospheric sulfates, although its role in the early Earth atmosphere has not yet been convincingly established. Here, I present an analytical formulation of isotopic photodissociation rate coefficients that describe self-shielding isotope signatures for 3 and 4-isotope systems broadly representative of O and S isotopes. The analytic equations are derived for idealized molecular spectra, making an analytic formulation tractable. The idealized spectra characterize key features of actual isotopologue spectra, particularly for CO and SO₂, but are applicable to many small molecules and their isotopologues. The analytic expressions are convenient for evaluating the magnitude of isotope effects without having to pursue involved numerical solutions. More importantly, the analytic expressions illustrate the origin of particular isotope signatures, such as the previously unexplained large mass-dependent fractionation associated with photodissociation of optically-thick SO₂. The formulation presented here elucidates the origin of some of these important isotopic fractionation processes.

Oscillator strengths and integral cross sections of the ÃA2″1← X̃1A1 excitation of ammonia studied by fast electron impact

The vibrationally resolved generalized oscillator strengths of the first and strongest singlet excitation ÃA2″1← X̃¹A₁ of ammonia have been determined at an impact electron energy of 1500 eV with an energy resolution of 80 meV. The comprehensive comparison of the present results with the previous experimental and theoretical ones shows that the high-energy limit, where the first Born approximation holds, has been reached at an impact electron energy of 1500 eV in K² < 1 a.u., while it is still not satisfied in the K² > 1 a.u. even at 1500 eV. It is also observed that the minimum position of the generalized oscillator strength of the vibronic state shifts toward the larger squared momentum transfer with the increasing vibrational quantum number. By extrapolating the generalized oscillator strength to the zero momentum transfer, the optical oscillator strength of the ÃA2″1 state has been obtained, which gives an independent cross check to the previous results. The integral cross sections of the ÃA2″1 state have been obtained systematically from the threshold to 5000 eV with the aid of the BE-scaling method.

HCl and DCl: a case study of different approaches for determining photo fractionation constants

The photoabsorption cross sections of HCl and DCl are calculated using the reflection principle and time dependent wavepacket propagation methods. The absorption cross sections are compared to high precision experimental absorption cross sections from the literature and the different results given by the methods are discussed. The results of the calculations emphasize the important roles that photodissociation dynamics and the change in transition dipole moment with internuclear distance play in isotopic fractionation. The wave number dependent fractionation constants have been determined. The process fractionation constant has been calculated in the Venusian atmosphere where photo-fractionation leads to enrichment in deuterium through loss of hydrogen to space. At an altitude of 70 km the process fractionation constant was found to be epsilon(p) = -344 per thousand and epsilon(p) = -256 per thousand for the experimental and the reflection principle methods, respectively. At the top of the atmosphere the process fractionation constant was evaluated to be epsilon(p) = -32 per thousand, epsilon(p) = -20 per thousand and epsilon(p) = -40 per thousand using the experimental data, the wavepacket and the reflection principle methods, respectively. Using the Rayleigh distillation formula it is concluded that HCl at the top of the Venusian atmosphere is fractionated (enriched in D) relative to the bulk composition prior to photolysis.