The spin-forbidden vacuum-ultraviolet absorption spectrum of 14N15N
A. N. Heays B. R. Lewis N. de Oliveira W. Ubachs




Department of Physics and Astronomy, and LaserLaB, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands

School of Earth & Space Exploration, Arizona State University, Tempe, AZ USA
NASA Astrobiology Institute, NASA Ames Research Center, Moffett Field, California, USA
Corresponding author: aheays@asu.edu

Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia



Synchrotron Soleil, Orme des Merisiers, St. Aubin, BP 48, 91192 Gif sur Yvette Cedex, France

Department of Physics and Astronomy, and LaserLaB, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands


  Photoabsorption spectra of ^14N^15N were recorded at high resolution with a vacuum-ultraviolet Fourier-Transform spectrometer fed by synchrotron radiation in the range 81 to 100 nm. The combination of high column density ([cm^-2]3e17) and low temperature ([K]98) allowed for the recording of weak spin-forbidden absorption bands exciting levels of triplet character. The triplet states borrow intensity from ^1Π_u states of Rydberg and valence character while causing their predissociation.
  New predissociation linewidths and molecular constants are obtained for the states C ^3Π_u(v=7,8,14,15,16,21), G ^3Π_u(v=0,1,4), and F ^3Π_u(v=0).
  The positions and widths of these levels are shown to be well-predicted by a coupled-Schrödinger equation model with empirical parameters based on experimental data on ^14N_2 and ^15N_2 triplet levels.


The spin-forbidden vacuum-ultraviolet absorption spectrum of ^14N^15N
    W. Ubachs
    December 30, 2023
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§ INTRODUCTION



The vacuum-ultraviolet (VUV) photoabsorption spectrum of molecular nitrogen is of importance to studies of terrestrial atmospheric physics,<cit.> planetary physics<cit.> and astrophysics.<cit.>
It is also of fundamental interest in molecular physics in view of the benchmark perturbation phenomena occurring in this diatomic molecule.
Early investigations of the dipole-allowed absorption spectrum of N_2 revealed the perturbations between singlet states of valence and Rydberg character,<cit.> giving rise to intensity-interference effects in the vibronic spectrum, even extending into details of the rotational fine structure.<cit.> Interactions between the singlet manifolds and the triplet manifolds, induced by spin-orbit coupling, were found to cause strong predissociation effects in the excited states, however, in most cases, still allowing for resolved rotational structure.<cit.>

Over the decades a large number of spectroscopic investigations of N_2 have been performed, focusing on the predissociation phenomenon, and using a variety of advanced techniques, ranging from tunable narrowband extreme ultraviolet (XUV) laser spectroscopy,<cit.> picosecond pump-probe experiments,<cit.> electron-impact excitation,<cit.> synchrotron absorption studies,<cit.> synchrotron fluorescence-excitation studies,<cit.> detection of dissociation products in charge-exchange studies,<cit.> as well as upon VUV-laser excitation,<cit.> and the spectroscopic study of infrared transitions within the triplet system.<cit.>


A framework of coupled-channel Schrödinger equations (CSE) was developed<cit.> to provide a description of the absorption spectrum of molecular nitrogen, including Rydberg-valence electrostatic interactions and singlet-triplet spin-orbit interactions. Through this description, a comprehensive explanation is provided for the spectral perturbations as well as the predissociation phenomena.<cit.>
Based on the CSE-framework, the full absorption spectrum and dissociation cross section of N_2 has been calculated,<cit.> as well as the electron-impact XUV emission spectrum.<cit.>
In principle, the CSE model is applicable to all isotopologues of nitrogen through mass scaling of the molecular parameters involved, and in some cases it has been applied to ^14N^15N and ^15N_2,<cit.> comparing with data from XUV laser excitation.
One application resulted in the calculation of the isotopically selective dissociation of nitrogen in the interstellar radiation field.<cit.>

The most complete investigation of the absorption spectrum of ^14N^15N was performed using VUV Fourier-Transform (FT) spectroscopy, analyzing in detail 25 singlet-singlet bands of this isotopologue<cit.> and identifying perturbations in the level structure of singlet states caused by a parallel manifold of optically-forbidden states of triplet character.
The present study is an extension of this, whereby triplet states are observed directly by using an increased gas column density and by recording absorption at lower temperatures.
The motivation of the present work is to test the ability of a CSE model, developed by Lewis et al.<cit.> with reference to the ^14N_2 and ^15N_2 isotopologues, to predict the triplet spectrum of ^14N^15N.
In the longer term, the new experimental data on the ^3 Π_u states of ^14N^15N presented here,<cit.> together with similar
planned measurements on ^15N_2, will enable the improvement and extension of the CSE model of N_2 predissociation, with 
particular application to studies of isotopic fractionation.



§ EXPERIMENTAL DETAILS



High-resolution absorption spectra of ^14N^15N were recorded with the VUV-FT instrument installed at the DESIRS beam line of the SOLEIL synchrotron.<cit.> This instrument is based upon a wave-front interferometer that allows the extension of the FT technique into the deep VUV. Spectral coverage is determined by the undulator synchrotron radiation source, delivering a bandwidth of about 5 nm illuminating the FT instrument. The ^14N^15N gas flows continuously through a 100 mm-long windowless absorption cell with capillaries at both ends, thus providing a condition of quasi-static gas pressure inside the cell.
The absolute frequency calibration is based on the intrinsically-linear frequency scale generated by the FT spectrometer, and from comparison of selected H2 and Ar I lines appearing in the spectrum with high-precision reference data.
The specific absorption lines used are Ar I at 95399.833;<cit.> H2 at 99755.399, 101668.268, 101746.449, and 101825.295;<cit.> and H2 at 107114.785 and 105549.599.<cit.>
The estimated absolute calibration uncertainty is 0.004, but individual ^14N^15N line wavenumbers have greater uncertainties due to fitting errors of ∼ 0.02 cm^-1, or more for lines that are blended or saturated.



Our experimental and analysis procedures are similar to those previously adopted by Heays et al.<cit.> except that measurements were performed with the cell externally cooled by a flowing liquid-nitrogen jacket, and employing ∼ 300× greater column density.
The optically-allowed transitions to  ^1Π_u and ^1Σ^+_u states previously studied<cit.> are then completely saturated in our spectra near their bandheads, but the targeted forbidden transitions exciting ^3Π_u levels are now measurable; e.g., in Fig. <ref> showing b ^1Π_u(v=0)← X ^1Σ^+_g(v=0) and C ^3Π_u(v=7)← X ^1Σ^+_g(v=0).
The main advantage of using cooled gas is the reduced spectral congestion from singlet-state absorption, due to fewer thermally-populated ground state rotational levels.
Additionally, the profiles of predissociation-broadened ^3Π_u← X ^1Σ^+_g bands are more revealing, with their oscillator strengths concentrated into J”≲ 10 transitions.



The population distribution of  ^14N^15N ground-state rotational levels was assumed to correspond to a mixture of room-temperature (295 K) and cold gases, with the column density, N_i, of each, and the cold-gas rotational temperature determined by a fit to the unsaturated rotational transitions of the b(0)← X(0) (Fig. <ref>) and b(1)← X(0) bands.<cit.>
The resulting best-fit values are N_room=(2.2± 0.3)× 10^15 cm^-2, N_cold=(3.9± 0.6)× 10^17 cm^-2, and T_cold=98± 5 K.
The absolute N_i calibration was made with reference to b(0)← X(0) and b(1)← X(0) f-values determined by Heays et al.<cit.> and has an estimated 15% uncertainty arising from a combination of the estimated uncertainty of Heays et al.<cit.> and our own fitting errors.
The cooled-gas temperature uncertainty was estimated subjectively based on its range giving a good quality-of-fit to the b(v)← X(0) spectrum.
The assumed two-temperature model fits the spectrum quite well and we found no benefit from adopting more complicated temperature profiles.
Contributions to the experimental spectra from species other than the desired ^14N^15N were found, inevitably from
cold ^14N2 and ^15N2, yielding, e.g., weak lines overlapping b(0)← X(0) in Fig. <ref>, and from room-temperature H2 contaminant, e.g., at 100870 in Fig. <ref>.

The 98 K Doppler width of ^14N^15N resonances amounts to 0.14 (full-width half-maximum) at 105000. Spectra were recorded at a setting of the VUV-FT instrument giving rise to an unapodised sinc-shaped instrumental lineshape with width 0.215.
Several non-ideal instrumental effects were included in the modelling of the total instrumental broadening function.
Asymmetric lineshapes are evident in spectral regions near highly-saturated bandheads of ^1Π_u← X(0) and ^1Σ^+_u← X(0) transitions where the near-zero recorded intensity appears to locally interfere with the frequency-dependent FT phase correction.<cit.>
This effect was modelled phenomenologically by convolution of the ideal instrumental function with the following:

    F_asym(ν) =
      
        1    if ν=0
    
        a/ν   otherwise ,

where ν is the wavenumber gap from line centre and the parameter a was fitted to each spectral region studied.
An example of the degradation of the model fit to the measured spectra from neglecting this asymmetry is shown in Fig. <ref>, but this effect is significant only for those ^3Π_u← X(0) bands overlapped by strong singlet-state excitation.

A second non-ideal instrumental effect appears as a weak aliasing of the experimental spectrum shifted by ±1000, where the aliasing is additive for one sign and subtractive for the other.
This is due to a periodic error in the stepping system of the FT translation<cit.> and was handled by counteracting the aliasing through the addition and subtraction of ±1000-shifted copies of the experimental spectrum, with best-fit correction magnitude determined separately for each spectral-region studied.
Neglecting this aliasing introduces a significant model error near 101000 in Fig. <ref>, e.g., which is due to negative aliasing of the strong b(2)← X(0) absorption at +1000.
The magnitude of this correction is 1–3% of the measured intensity and second-order corrections were deemed unnecessary.

Finally, an additional phenomenological Gaussian-shaped broadening was included in the instrumental broadening, with width  0.1, as found necessary for this instrument by Heays et al.<cit.>
Full information could not be retrieved from the experimental spectrum in heavily saturated regions, even with these corrections, as is evident in the residual error of the best-fit model shown in Fig. <ref> where the worst affected portions were neglected from model fitting (zero residual).



§ SPECTRAL ANALYSIS METHODS




Molecular parameters summarizing the observed ^3Π_u states were extracted by fitting model spectra to the experimental absorption measurements.
Each observed ^14N^15N line was assigned a transition wavenumber,
 ν_i, line f-value according to the definition of Morton and Noreau, <cit.> f_i, and predissociation linewidth, Γ_i.<cit.>
Resulting temperature-dependent line cross sections were computed according to

    σ_i(ν;T) = (e^2· 10^2/4ϵ_0m_ec^2) f_i α_J_i”(T) V(ν-ν_i,Γ_i,Γ_D(T))

where σ_i is in cm^2, T is the temperature in Kelvin, and e, ϵ_0, m_e, and c are the usual physical constants.
The parenthesised prefactor has the numerical value [cm]8.853e-13.
In Eq. (<ref>), V is a unit-area Voigt function centred on ν_i with Lorentzian width Γ_i and Gaussian (Doppler) width Γ_D(T); and α_J_i”(T) is the Boltzmann population of ground-state rotational level J_i”.


A total absorption opacity was constructed, allowing for absorption by ^14N^15N lines at 98 K and 295 K, together with contaminants:

    τ(ν) = ∑_i N_98Kσ_i(ν;98K) + N_295Kσ_i(ν;295K) 
    
      + ∑_jτ^int_jV(ν-ν_j,Γ_j,Γ_Dj),

using the ^14N^15N column densities discussed in Sec. <ref>.
The second summation in Eq. (<ref>) accounts for any ^14N_2, ^15N_2 or H_2 contaminant lines using their fitted frequencies, integrated optical depths, τ^int_j, and line shapes.

This opacity was converted into an absorption spectrum:<cit.>

    I(ν) = [ I_0(ν)e^-τ(ν)] ∗ F(ν),

for a direct pointwise comparison with the experimental spectrum.
Here, the incoming intensity of synchrotron radiation, I_0(ν), was fitted to a slowly-varying function of ν; and the ideal absorption spectrum broadened by convolution with the instrumental function, F(ν), described in Sec. <ref>.

The Q-branch rotational transitions of strong and unblended ^3Π_u← X ^1Σ^+_g bands were modelled individually and their P(J'+1) and R(J'-1) transition in pairs, with a common upper-state term value and linewidth, different ground-state X(v=0,J”) term values, and different oscillator strengths.
Ground-state energy levels were computed from the Dunham coefficients of Le Roy et al.<cit.>

It was not possible to fit parameters to the individual rotational lines of the weak or broadened features observed experimentally.
Instead, smaller sets of parameters were optimized, controlling an effective Hamiltonian matrix representing all upper-state levels.
For this purpose, the  Hund's case-(a) Hamiltonian of Brown and Merer<cit.> was adopted, fully specified in their Table 1 for the case of a ^3Π state, and a standard Hamiltonian was used to represent the observed ^1Π and ^1Σ levels:

    T_^1Σ   = T + BJ(J+1) - D[J(J+1)]^2, 
    and   T_^1Π   = T + BJ(J+1) - D[J(J+1)]^2 + qJ(J+1),

where the parameter q is only included for f-parity levels.
The spin-orbit mixing of case-(a) ^3Π_u and ^1Π_u states is restricted to their Ω=1 levels of common e/f parity and is modelled with an interaction matrix element ξ, treated as a free parameter for each pair of interacting electronic-vibrational levels.
The mixed-level energies and mixing-coefficients are then computed by diagonalizing the full Hamiltonian matrix of ^3Π_uΩ and ^1Π_u1 levels.

The absorption strength of ^3Π_u← X ^1Σ^+_g(0) transitions is borrowed from nearby ^1Π_u← X ^1Σ^+_g(0) transitions through their mutual spin-orbit coupling.<cit.>
We model the rotational line strengths of the ^1Π_u← X ^1Σ^+_g(0) transitions using an empirical electronic-vibrational transition moment and Hönl-London rotational-linestrength factors.<cit.>
Mixing coefficients from the Hamiltonian-matrix diagonalization are then used to generate the full rotational structure of the observed mixed ^3Π_u ∼^1Π_u← X ^1Σ^+_g spectrum.

Ω labels are assigned to the observed ^3Π_u levels forming continuous e/f-parity rotational progressions, based on their dominant character at low J.
The relative contribution of nominal Ω-levels to the observed absorption depends on their admixture of pure Ω=1 character and is controlled by J and the diagonal spin-orbit constant A.
Sufficiently large-A and low-J states are of nearly unmixed Ω character and transitions to the central Ω=1 levels appear strongly.
For increasing J, these transitions weaken and the higher- and lower-energy triplet levels are more readily excited.
An example of this phenomenon is given in a detailed study on the E^1Π∼ k^3Π interaction in isotopologues of CO.<cit.>
Other level and intensity patterns may occur where the magnitudes of A and the rotational constant B are comparable,<cit.> e.g., as found for the C ^3Π_u(v=7) level.

  The spin-orbit borrowing of absorption intensity is reciprocated by a sharing of dissociation proclivity. However, while the source of the intensity is always the
dipole-allowed ^1Π_u ← X(0) transition, both the ^3Π_u and ^1Π_u levels have nonzero inherent predissociation widths, prior to mixing,
which are derived from different multichannel dissociation pathways, although ultimately involving the C^' ^3Π_u valence state. This can lead to interference effects and J-dependent linewidths.
Here, we adopt a hybrid procedure to fit the experimental ^3Π_u ← X(0) band cross sections, 
empirically modelling the dissociation linewidth of ^3Π_u effective-Hamiltonian levels by means of an imaginary energy, iΓ,<cit.>
mixing the ^3Π_u and ^1Π_u levels with the ξ parameter, and using the results of previous work to treat the ^1Π_u ← X(0) transition.<cit.> 
This approach is necessary since, as implied above, it is not usual to find simultaneous consistency between the two-state modelled linewidths and the corresponding intensity sharing, due to the inherent multilevel nature of the interaction. 
It should be noted,
however, that the independently-fitted ^3Π_u experimental linewidths determined here are meaningful and very suitable for comparison with the CSE computations.



§ CSE MODELLING


