The spectroscopy underlying the coupled-channel Schrödinger equation (CSE) model of the N₂ photoabsorption spectrum is discussed in detail in Lewis et al. (2005, 2008), Haverd et al. (2005), and related publications. A reference list of these publications and a bibliography of the experimental and calculational database informing the CSE model are available elsewhere on this website. The computed N₂ photoabsorption spectrum replicates the experimental database, to within the stated experimental uncertainties, for the isotopologues ¹⁴N₂, ¹⁴N¹⁵N, and ¹⁵N₂. Detailed comparisons of the model’s predictions with measured values of line positions, line strengths, and line widths can be found in the above references.

Brief summaries of the relevant spectroscopy and of the CSE model are presented below. A summary of the characteristics of the N₂ photoabsorption spectrum in the 100,000 to 105,000 cm^-1 region follows.

Spectroscopy and CSE Model

The electric-dipole-allowed absorption spectrum of N₂ shortward of 100 nm arises from transitions to the strongly perturbed vibrational progressions of three Rydberg and two valence states. c'₄ ¹Σ_u⁺ and c₃ ¹Π_u are the lowest members (n = 3) of the npσ_u and npπ_u Rydberg series converging to the X ²Σ_g⁺ ground state of N₂⁺; the o₃ ¹Π_u state is the n = 3 lowest member of the nsσ_g series converging to A ²Π_u of N₂⁺; and b ¹Π_u and b ¹Σ_u⁺ are valence states. Stahel et al. (1983) first reproduced the anomalous absorption strength patterns observed within the vibrational progressions by treating the homogeneous Rydberg-Rydberg and Rydberg-valence interactions among the five electronic states. Interactions between the ¹Π and ¹Σ manifolds were not incorporated in the model. Spelsberg & Meyer (2001) refined the analysis of Stahel et al. by combining ab initio potential curves with R-dependent electronic coupling parameters and transition moments optimized to reproduce laboratory measurements.

Lewis et al.(2005) developed a quantitative model for the b, c₃, and o₃ ¹Π_u states that clarifies the predissociation mechanisms affecting the photoabsorption spectrum. Their CSE model of the b, c₃, and o₃ interactions with the C and C' ³Π_u states showed that the spin-orbit interaction between the b ¹Π_u and C ³Π_u levels, along with an electrostatic interaction between the C state and the continuum of C' ³Π_u, accounts for the observed line-broadening patterns. In an extension of the ¹Π_u and ³Π_u CSE model, the measured rotational effects in line strengths and predissociation line widths in the X(0) → ¹Π_u vibrational bands were modeled by Haverd et al. (2005). A further extension of the CSE model by Lewis et al. (2008), which includes the 3sσ_gF₃ ³Π_u and 3pπ_uG₃ ³Π_u Rydberg states, identified a strong Rydberg-Rydberg interaction between the F and G states, and enabled the extension of the ¹Π_u predissociation model to higher transition energies. The computed photoabsorption spectra presented in this website are calculated from a version of the CSE model that incorporates heterogeneous interactions of the ^1,3Π_u manifold with the c'₄ ¹Σ_u⁺ and b' ¹Σ_u⁺ states. The details of this expanded model have not yet been published. The expanded CSE model was recently used to calculate nitrogen isotopic fractionation in the atmosphere of Titan (Liang et al. (2007), as well as to elucidate the radiative properties of the c'₄ ¹Σ_u⁺ ← X ¹Σ_g⁺ band system (Liu et al. (2008), Khakoo et al. (2008), Liu et al. (2009)).

The N₂ Photoabsorption Spectrum: 100,000 – 105,000 cm^-1

The 100,000 to 105,000 cm^-1 region of the photoabsorption spectrum is dominated by the lowest-v members of the X(0) → b(v) ¹Π_u vibrational progression along with the strong X(0) → c₃(0) ¹Π_u and X(0) → c'₄(0) ¹Σ_u⁺ bands. The weak X(0) → b'(0,1) ¹Σ_u⁺ bands complete the dipole-allowed transitions in this region. A number of very weak and broad transitions to the C(v) ³Π_u levels are present, along with the very weak, but sharp, X(0) → F₃(0) ³Π_u and X(0) → G₃(0) ³Π_u bands. Detailed spectroscopic evidence for the transitions to the triplet levels is presented in Lewis et al. (2008b).

Band identifications are indicated in the figure below, which displays the computed ¹⁴N₂ spectrum at T = 0 K.


The strong Rydberg-Rydberg, Rydberg-valence, and valence-valence interactions among the singlet and triplet states of N₂ produce striking rotation-dependent effects on line strengths and widths. Evidence for these effects is presented in Stark et al. (2005, 2008), Heays et al. (2009), and Haverd et al. (2005). Extreme departures from standard line intensity patterns (i.e., those associated with Hönl-London factors) and strong J-dependences in line widths may significantly affect radiative transfer models. The CSE model spectrum reproduces the observed line strength and line width patterns in the all of the isotopologues of N₂. Examples of measured rotation-dependent line-strength and line-width patterns in the 100,000 to 105,000 cm^-1 region are shown below.


Experimentally determined Lorentzian components of line widths (FWHM) in the b(2) – X(0) band.

b(5) – X(0) band f-values determined from rotational line f-values and Hönl-London factors (P branch – open squares; Q branch – solid circles; R branch – open diamonds).

The spectra of the isotopologues of N₂ differ not only in associated line positions, but also in line-strength and line-width patterns. As an example, the figure below shows modeled ¹⁴N₂ and ¹⁵N₂ cross sections of the b(3) – X(0) band at 300 K. The ¹⁴N₂ band is strongly broadened (see Haverd et al. (2005)), with Lorentzian line widths near the band head on the order of 3 cm^-1, while the ¹⁵N₂ band-head line widths are about 0.7 cm^-1 (Sprengers et al. 2005).