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• W2037945717 abstract "A derivation is given for the integrated absorption coefficient of pressure-induced pure rotational and vibrational transitions in binary collisions of homonuclear diatomic molecules of the same chemical species. The previously neglected effects of excited vibrational states, mechanical anharmonicity, and vibration-rotation interaction are taken into account to obtain more accurate absorption coefficients at high temperatures. In the region of the fundamental wave number the excited vibrational states make more of a contribution to the absorption than their relative population would lead one to expect. LIST OF SYMBOLS Aij(k)function for molecule k involving integral of normalized associated Legendre functionsaṽlinear absorption coefficient for wave number ṽ excluding stimulated emission, m−1Bintegrated Einstein coefficient of absorption, m2 J−1 sec−1Bṽspectral Einstein coefficient of absorption, m3 J−1 sec−1Cℓ1ζ1ℓ2ζ2expansion coefficient for μ0z, C mcspeed of light, m sec−1Dℓ1ζ1ℓ2ζ2expansion coefficient for μ1, CEi(i=1, 9)product of two expansion coefficients, units varyecharge of electron, CGi(i=1, 2, 3, 45)functions of Q, Δ and I, C2 m5hPlanck's constant, J sech̷h2π, J secIi(i=1, 2, …, 9)dipole moment integral, units varyJi(i=1, 2)total angular momentum quantum number for initial state of molecule iJ′i(i=1, 2)total angular momentum quantum number for final state of molecule iKℓ1ζ1ℓ2ζ2expansion coefficient for μz, C mkBoltzmann constant, J K−1Li(i=0, 2)functions of J′ and JMi(i=1, 2, …, 5)functions of Q, Δ, C and D, C mmi(i=1, 2)quantum number for component of total angular momentum along z axis for initial state of molecule im′i(i=1, 2)quantum number for component of total angular momentum along z axis for final state of molecule imHmass of hydrogen atom, kgmrreduced mass of oscillator, kgN, N1, N2number of moleculesn, n1, n2number density of molecules, m−3Oi(Ji)(i=1, 2)O branch for molecule i (J′i−Ji=−2)P(vi, Ji, mi) (i=1, 2)probability of molecule i being in state with quantum numbers having values vi, Ji, mipnumber of pairs of moleculesQk(k=1, 2)vibrational overlap integral for molecule kQi(Ji)(i=1, 2)Q branch for molecule i(J′i−Ji=0)qi(i=1, 2)scalar quadrupole moment of molecule i, C m2qXX, qYY, qZZelements of quadrupole moment tensor, C m2Rintermolecular distance, mrk(k=1, 2)internuclear distance of molecule k, mSi(Ji)(i=1, 2)S branch for molecule i(J′i−Ji=2)sintegrated absorption coefficient of transition with wave number removed, m−1Ttemperature, °Kttime, secVvolume, m3vi(i=1, 2)vibrational quantum number for initial state of molecule iv′i(i=1, 2)vibrational quantum number for final state of molecule iWtransition-dependent factor in s, C2 m5X, Y, ZCartesian coordinates with origin at the midpoint of the line connecting two nuclei of molecule, with Z axis running along the internuclear axis, mx, y, zCartesian coordinates fixed in space (Fig. 1), mXiposition coordinates of electrons, mYJmspherical harmonicZjnumber of elemental charges on the jth nucleusziz coordinate of ith electron, mzjz coordinate of jth nucleus, mαi(i=1, 2)average polarizability of molecule i, C2 m2 J−1Δk(k=1, 2)vibrational matrix element for molecule k, mδi(i=1, 2)anisotropy of polarizability of molecule i, C2 m2 J-1δ(J′, J)Kronecker delta functionεforce constant for Lennard-Jones potential, Jε0electric permittivity of free space, C2 N−1 m−2ΘJmnormalized associated Legendre functionθi(i=1, 2)polar angle of molecule i radμx, μy, μzcomponents of electric dipole moment, C mμi(i=1, 2)∂μz/∂ri evaluated at r1=r01 and r2=r02, Cμz4μz for configuration 4, C m(μx)ϱ′ϱ, (μz)ϱ′ϱcomponents of lectric dipole moment matrix elements, C mṽphoton wave number, m−1ṽ0fundamental wave number of vibration, m−1ϱṽradiation energy density per unit wave number, J m−2dτelements of volume in configuration space, m3Φintermolecular potential averaged over orientations, Jφi(i=1, 2)azimuthal angle of molecule i, radψwave function, units varyψvkJk(k=1, 2)vibrational wave function of molecule k, m−12Superscripts0equilibrium internuclear distance of diatomic molecule′′∂/∂r1 evaluated at r1=r01‡reducedSubscriptseelectronicnnuclearζv1, v2, J1, J2 collectivelyζ′v′1, v′2, J′1, J′2 collectivelyϱv1, v2, J1, J2, m1, m2 collectivelyϱ′v′1, v′2, J′1, J′2, m′1, m′2 collectively" @default.
• W2037945717 created "2016-06-24" @default.
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• W2037945717 date "1971-09-01" @default.
• W2037945717 modified "2023-10-16" @default.
• W2037945717 title "Theory of pressure-induced vibrational and rotational absorption of diatomic molecules at high temperatures" @default.
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• W2037945717 doi "https://doi.org/10.1016/0022-4073(71)90002-1" @default.
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