Rigid-rotator transition

Table 1. Rigid-rotator transition probabilities for four...

Under some circumstances the rotationally anisotropy may be even further simplified for T-R energy transfer of polar molecules like HF (41). To explore this quantitatively we performed additional rigid-rotator calculations in which we retained only the spherically symmetric and dipole-dipole terms of the AD potential, which yields M = 3 (see Figures 1, 3, and 4). These calculations converge more rapidly with increasing N and usually yield even less rotationally inelastic scattering. For example Table 2 compares the converged inelastic transition probabilities... 

Molecules in the gas phase have rotational freedom, and the vibrational transitions are accompanied by rotational transitions. For a rigid rotor that vibrates as a harmonic oscillator the expression for the available energy levels is ... 

Figure 3.25 Outline of the absorption spectrum of a rigid polyatomic molecule. The bands corresponding to electronic transitions are broad as they include vibrational and rotational transitions and they coalesce to form an absorption continuum...

Figure 8.15. Correlation diagram between levels of a rigid rotor K = 0 (water dimer with Cs symmetry in the nontunneling limit), a rotor with internal rotation of the acceptor molecule around the C2 axis (permutation-inversion group G ), and group G16. The arrangement of levels is given in accordance with the hypothesis by Coudert et al. [1987], The arrows show the allowed dipole transitions observed in the (H20)2 spectrum. The pure rotational transitions E + (7 = 0) - E (J = 1) and E (7 = 1) <- E + (/ = 2) have frequencies 12 321 and 24 641 MHz, respectively. The frequencies of rotationtunneling transitions in the lower triplets AI (7 = 1) <- A,+ (7 = 2) and A," (7 = 3) <- A,+ (7 = 4) are equal to 4863 and 29 416 MHz. The transitions B2(7 = 0)<- B2(7 = l) and BJ(7 = 2) <- B2 (7 = 3) with frequencies 7355 and 17123 MHz occur in the higher multiplets.

In addition to vibrational motions, the molecule can undergo rotational motion perpendicular to the bond axis. For linear molecules, the energy associated with rotational transitions is approximated by the rigid-rotor model. 

It would be desirable to identify the residual donors in GaAs from the transition involving an exclton bound to the first non-rigid-rotational state. The terminal state consists of the excited state (n = 2) of the electron on the donor. The observation of different residual donor species from this transition is made possible by performing the experiment in a magnetic field. The magnetic field produces two effects (a) It separates out states with different orbital angular momentum and (b) it compresses the wave function which sharpens the lines and separates the donors. 

Figure 2.1.b. Schematic diagram of the energy levels and vibration-rotation transitions (after Herzberg, 1950). The lower lines (v/ = 0) correspond to the fundamental vibrational state with different rotational states (J// = 0,1, 2,3,4). The first vibrationally excited state (v/ = 1) with related rotational states (J/ = 0 to 4) are shown by the upper lines. The transitions corresponding to the P and R branches are indicated. Transition AJ = 0 is not allowed in the case of the idealized rigid rotor, harmonic oscillator for a linear molecule, but can be observed (Q-branch) in other cases. The notations are from Herzberg (1950). 

As can be seen in equation (6.16), this rotational transition part of the cross-section has to be convoluted with the scattering function for the molecule centre of mass. If the molecule is rigidly bound, 6 moi Q, (o) = 8(co). If it is free to recoil, its cross-section will be as for scattering from a perfect gas. The assumption here is that the initial state of the molecule has a defined momentum taken from a Maxwell-Boltzmaim distribution and that all final states are available for the recoiling molecule. In this case, the molecular scattering function can be written ... 

---