Absorption coefficients for hydrogen—II. Calculated pressure-induced H 2–H 2 vibrational absorption in the fundamental region

Abstract

The coefficient for pressure-induced vibrational absorption in H 2ndash;H 2 collisions was calculated for temperatures from 298 to 7000°K and wave numbers between 100 and 40,000 cm −1 for local thermodynamic equilibrium. Because only transitions with a net change of +1 vibrational quanta were considered, the absorption was centered near the fundamental at 4161 cm −1 in the infrared. The model included electronic configuration interaction, mechanical anharmonicity, vibration-rotation interaction, excited vibrational states, and more realistic intermolecular potential and line shapes than previously used. The integrated absorption coefficient at 3000°K was 2.1 times the previous theoretical value. An approximate formula for the absorption coefficient is given for rapid calculation. LIST OF SYMBOLS A ṽ spectral absorption coefficient including wave number and stimulated emission à ṽ spectral absorption coefficient with wave number removed and excluding stimulated emission a(1), b(1), c(1) orbital of electron 1 about proton a, b and c, respectively a ṽ linear absorption coefficient excluding stimulated emission B, F constants in Q-branch line shape C 2000 expansion coefficient for z component of dipole moment (see Ref. 11) C a 2000 overlap contribution to C 2000 c speed of light c i(i=1,2,3,4) constants for faired curve D ℓ1ξ1ℓ2ξ2 expansion coefficient for derivative of z component of dipole moment with respect to r ab (see Ref. 11) D aℓ1ξ1ℓ2ξ2 overlap contribution to D ℓ1ξ1ℓ2ξ2 d v 1 element of volume for electron 1 E denominator of μ az f ṽ line shape function G, H, M constants in O- and S-branch line shape g, j, t, γ functions of temperature in modified Q-line shape h Planck constant I i(i=1,2,…9) dipole moment integral (see Ref. 11) I transmitted light intensity I° incident light intensity J, J 1, J 2 total angular momentum quantum number of diatomic molecule (subscript is number of molecule) k Boltzmann constant L(σ, τ) function of σ and τ ℓ path length m r reduced mass of oscillator m ab , S ab , s ac molecular integrals N i(i=1,2,3) contributions to numerator of μ az n H 2 number density of H 2 molecules n 0 Loschmidt number O i(J i)(i=1,2) O branch for molecule i (see Ref. 11) q scalar quadrupole moment of H 2 R intermolecular distance r a 1 distance from proton a to electron 1 r, r ab , r ac internuclear distance (subscripts specify nuclei) S integrated absorption coefficient with wave number and density removed S i(J i)(i=1, 2) S branch for molecule i (see Ref. 11) s integrated absorption coefficient with wave number removed (see Ref. 11) T temperature T(σ), U(σ) functions of σ v i(i=1, 2) vibrational quantum number of molecule i w q , w s , w 1, w 2 line widths x, y, z Cartesian coordinates fixed in space (see Ref. 11) z a 1 z component of vector from proton a to electron 1 z ab 1 z component of vector from center of line ab to electron 1 α average polarizability of H 2 δ anisotropy of polarizability of H 2 ζ, ζ ab , ζ cd orbital exponent (subscripts specify orbitals) θ ab 1 angle between proton b and electron 1 at proton a θ abz angle at proton a between proton b and a line through proton a parallel to the z axis θ abc angle between protons b and c at proton a K, K ab , K cd attractive distortion parameter of H 2 (subscripts specify orbitals) λ, λ ac repulsive distortion parameter (subscripts specify repelling orbitals) μ a overlap contribution to dipole moment vector μ az z component of μ a ṽ wave number of photon ṽ 0, ṽ c wave number of line center ρdot; H 2 dimensionless H 2 density [see equation (22)] σ ac r ac times the average value of ζ for orbitals a(1) and c(1) τ ac function of r ac and the difference of orbital exponents of orbitals a(1) and c(1) Φ average intermolecular potential Φ i(i=1, 2, 3, 5) intermolecular potential for configuration i (see Ref. 11) φ cabz dihedral angle between plane cab and a plane containing a, b and a line parallel to the z axis Superscript ′ ∂/∂ ab