Despite the fact that the main constituents of the Earth's atmosphere are nitrogen (∼ 79%) and oxygen (∼ 20%), other minor (∼ 1%) pollutants and natural gases (CO 2 , CO, H 2 O, Ar, and so on) play a very important role. A particular place is occupied by water vapour which is the principle absorber of solar radiation concentrated mainly in the spectral region 0.3-15 µm. It is in this region that its strongest vibrotational bands are situated. Currently, about 50,000 spectral transitions of water vapour molecule are identified with the vibrational quantum numbers v 1 + v 2 + v 3 ≤ 10 and the rotational quantum numbers J ≤ 42, K a ≤ 32. _________________________________________________________________ Let us specify the meaning of these quantum numbers. In the Н 2 О molecule, there are three normal vibrational modes, two of which refer to the variations in the OH bond length (stretching vibrations) and one describes the variations of ∠ НОН angle (bending vibration). The symmetric and anti-symmetric stretching vibrations are characterised by the vibrational quantum numbers v 1 and v 3 , whereas the bending vibration is associated with the vibrational quantum number v 2 . Any vibrational state in the molecule is therefore defined by three quantum numbers: V ≡ (v 1 v 2 v 3 ).Since the H 2 O molecule is an asymmetric top, its rotational energy levels [J K a K c ] are defined by three rotational quantum numbers J, K a , K c . The (pseudo-)quantum numbers K a and K c represent the projections of the angular momentum operator along the molecular axes a (axis of the smallest moment of inertia) and c (axis of the largest moment of inertia). They are not good quantum numbers but become them in the limit cases of prolate or oblate symmetric tops, respectively, reducing to the rotational quantum number K. It is for this reason that they are often referred to as pseudoquantum numbers. The point group of symmetry is C 2v , so that all vibrotational states and wave functions belong to one of four symmetry types: A 1 , A 2 , B 1 or B 2 . These types of symmetry (usually denoted by Γ) are presented in Table 3.1 [1]. The symmetry type Γ also defines the nuclear spin statistical weight w needed for the line-broadening and intensity calculations (Table 3.2). The allowed transitions between the vibrotational states of H 2 O molecule are: A 1 ↔ A 2 , B 1 ↔ B 2 , i.e. only the transitions between different A-states (A-bands) or B-states (B-bands) are Collisional Line Broadening and Shifting of Atmospheric Gases Downloaded from www.worldscientific.com by KAINAN UNIVERSITY on 12/27/14. For personal use only. * Here µa and µb are the dipole moment components in the molecular frame with a, b, c axes corresponding to the moments of inertia Ia < Ib < Ic. The molecule lies in the XOZ plane and its symmetry axis OX is the permanent dipole moment axis (i.e. for the equilibrium configuration µx ≠ 0 and µz = 0). Other notations for the rotational states can be found in Refs [1-3].
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