Transition dipole moment function

Equations (4.30) and (4.31) have been developed and dehned within a time-dependent framework. These equations are identical to Eqs. (35) and (32), respectively, of Ref. 80. They differ only in that a different, more appropriate, normalization has been used here for the continuum wavefunction and that the transition dipole moment function has not been expanded in terms of a spherical harmonic basis of angular functions. All the analysis given in Ref. 80 continues to be valid. In particular, the details of the angular distributions of the various differential cross sections and the relationships between the various possible integral and differential cross sections have been described in that paper. 

The transition dipole moment function of the parent molecule, pi. 

The transition dipole moment functions are — like the potentials — functions of Q. Their magnitudes determine the overall strength of the electronic transition ki —> kf. If the symmetry of the electronic wavefunc-tions demands likfki to be exactly zero, the transition is called electric-dipole forbidden. The calculation of transition dipole functions belongs, like the calculation of the potential energy surfaces, to the field of quantum chemistry. However, in most cases the fikfkt are unknown, especially their coordinate dependence, which almost always forces us to replace them by arbitrary constants. 

The intermolecular term has the same general form as the absorption cross section in the case of direct photodissociation, namely the overlap of a set of continuum wavefunctions with outgoing free waves in channel j, a bound-state wavefunction, and a coupling term. For absorption cross sections, the coupling between the two electronic states is given by the transition dipole moment function fi (R,r, 7) whereas in the present case the coupling between the different vibrational states n and n is provided by V (R, 7) = dVi(R, r, 7)/dr evaluated at the equilibrium separation r = re. 

In the following paragraphs we give selected examples of the use of our wavefunctions and potential curves to predict or confirm various spectroscopic features of the alkalis. We know of plans to observe Li2 spectra in at least two laboratories (23, 24) so some predictions regarding the spectra appear to be in order. Julienne (25) has used our wavefunctions for LI2 to calculate the electronic transition dipole moment function corres-... 

Julienne has used the calculated transition dipole moment function to obtain the radiative lifetimes for the j +... 

Fig. 3.5 Potential curves for the X and (2) states of Na2 and the X state of NaJ. The transition dipole moment function fj,ge and photoionization matrix elements Qm for the molecule parallel to the pump and probe polarization are also shown for a kinetic energy of 0.60 eV. The partial waves I = 0, 2, and 4 with m = 0 are denoted by long, medium, and short dashed lines, respectively. (Reprinted with permission from Y. Arasaki et al, J. Chem. Phys. 112, 8871 (2000)).

Potential energy curves and transition dipole moment functions for the NH molecule have been computed by Goldfield and Kirby (1987). The photodissociation cross sections into the excited and H states give rise to an unshielded rate of about 5 x 10 s (Kirby and Goldfield 1988), which is comparable to that of OH, and about a factor of two smaller than that of CH (van Dishoeck 19876). The photodissociation rate of NH is based on cross sections calculated by van Dishoeck (1986). Although many of the exdted electronic potentials are repulsive, most of them have vertical excitation energies larger than 13.6 eV, so that the destruction by interstellar radiation is not very rapid. 

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