Transition dipole matrix

The second term in the above expansion of the transition dipole matrix element Za 3 if i/3Ra (Ra - Ra,e) can become important to analyze when the first term ifi(Re) vanishes (e.g., for reasons of symmetry). This dipole derivative term, when substituted into the integral over vibrational coordinates gives... 

The derivation above may be generalized to wave functions other than electronic ones. By evaluation of transition dipole matrix elements for rigid-rotor and harmonic-oscillator rotational and vibrational wave functions, respectively, one arrives at the well-known selection rules in those systems that absorptions and emissions can only occur to adjacent levels, as previously noted in Chapter 9. Of course, simplifications in the derivations lead to many forbidden transitions being observable in the laboratory as weakly allowed, both in the electronic case and in the rotational and vibrational cases. 

The results are shown in Fig. 3 and Table I. Apparently, optimal IR femtosecond/picosecond laser pulses with durations tp = 500 fs may induce nearly perfect transitions (12), (13) in the model OH. Similar examples are documented in Refs. 13, 18, and 23. A detailed discussion of the derivation of the optimal laser parameters, depending on the vibrational level Ev and the transition dipole matrix elements nvw, is also given in Refs. 13, 18, and 23. Suffice it here to say that in many (but not all) cases the optimal frequency is close (but not identical) to the resonance frequency,... 

The other comment I would like to make is that the positive value of the 0 parameter you observe is due to a quantum interference effect. A simple mixing of the ground state with the excited state in the final continuum state hardly affects the directional properties of the dipole matrix elements per se because the transition dipole matrix elements between different states within the ground state are very small. Namely, if... 

Consequently, F(u> t) will contain the transition dipole matrix elements in forming a common scalar product. The full quantum expression for the emission rate (rate of ideal time and frequency resolved emission) takes the form... 

These dynamical parameters are integrals over the internuclear separations R, as well as the electronic coordinates r through the electronic transition dipole matrix elements, R). These electronic transition dipole matrix elements... 

It is frequently the case that the electronic transition dipole matrix element is only weakly dependent on the nuclear coordinates R such that the Franck-Condon approximation [37] may be employed. Within this approximation,... 

Equation (45) explicitly expresses the sensitivity of the LF PAD to the molecular axis distribution. In fact, an equivalent expression is obtained by convolution of the molecular axis distribution with the vibronic transition dipole matrix elements without explicit consideration of molecular rotation [55]. The... 

Traditional molecular excitation and subsequent system evolution, discussed in Chapter 2, affords little opportunity for us to control the outcome of molecular events. According to perturbation theory, as developed in Section 2.3, the branching ratio (i.e the relative probability to populate different product charnels) at the end of the process depends entirely [see Eq. (2.77)] on the ratio between squares ( , n e d ,>[2/ ( , nr e d ) 2 of the purely material transition dipole matrix elements. Thus, the electric field profile does not appear in the branching ratio expression. Since the electric field profile of the pulse is the means by which one could hope to influence and possibly control the outcome of the event, it seems that there is no way that we can change the natural branching ratio [37, 38],... 

Continuum-continuum transitions involving excited electronic states [368 be thought useful insofar as they ought to require less power than those occ1 the ground state because in this case the laser can couple to strong elec transition dipoles. However, in this case the continuum-continuum nuclear lead to smaller transition dipole matrix elements, and moreover, once the i deposited on an unbounded excited electronic surface, it is impossible to reaction on that surface and the resultant retention of the absorbed photon] chain of events resembles that of conventional (weak-field) photochemistry the laser is used to impart energy to the reaction, rather than to catalyze it ./... 

For diatomic molecules some of the transition dipole matrix elements will be parallei% to the molecular axis and some will be perpendicular to it. Hence / ... 

Ordinary STIRAP is only sensitive to the energy levels and the magnitudes of transition-dipole coupling matrix elements between them. These quantities are identical for enantiomers. Its insensitivity to the phase of the transition-dipole matrix elements renders STIRAP incapable of selecting between enantiomers. Recently we have demonstrated [11] that precisely the lack of inversion center, which characterizes chiral molecules, allows us to combine the weak-field one-and two-photon interference control method [29,54,95,96] with, the strong-field STIRAP to render a phase-sensitive AP method. In this method, which we termed cyclic population transfer (CPT), one forms a STIRAP loop by supplementing the usual STIRAP 1) o 2) <=> 3) two-photon process by a one-photon process 1) <=> 3). The lack of inversion center is essentrat, because one-photon and two-photon processes cannot connect the same states in the presence of an inversion center, where all states have a well defined parity, because a one-photon absorption (or emission) between states 1) and 3) requires that these states have opposite parities, whereas a two-photon process requires that these states have the same parity. 

For many molecules of interest there exist radiationless transitions that couple the levels of an electronically excited surface to a dense manifold of quasidegenerate levels on one or more other electronic surfaces, and these latter levels have vanishingly small transition dipole matrix elements with the initial level on the ground state surface. As shown in the preceding section, exponential decay of the amplitude of a wavepacket on an excited state surface via, say, a radiationless process, reduces the amplitude of a coherent emission signal but does not destroy the coherence. 

We assume that an isolated molecule has a nonzero transition dipole matrix... 

In the above expression u)M(0) = E (0)/h, where E (0) is the energy of a mechanical exciton p for k = 0, P0.0 (0) is the transition dipole matrix element of a unit cell, which is obtained by using the crystal ground state wavefunctions and the wavefunctions of a crystal with the mechanical exciton of type p for k = 0 A is the unit cell volume. 

There is a formal similarity in the mathematics used to describe vibrational transitions pumped by a resonant radiation field [148] and vibrational transitions pumped by phonons in a crystal lattice. In the lowest-order approximations, the radiation field and the vibrational transition are coupled by a transition dipole matrix element that is a linear function of a coordinate. The transition dipole describes charge displacement that occurs during the transition. Some of the cubic anharmonic coupling terms described by Eq. (10) result in a similar coupling between vibrational transitions and a phonon coordinate. These generally have the form / vibVph, so that the energy of the vibration with normal coordinate /vib is linearly proportional to the phonon coordinate /ph. Thus either an incoherent photon field or an incoherent phonon field can result in incoherent... 

The residue at the pole = ( — q) contains the transition dipole matrix element between the states 0) and m),... 

Thus, if state IE2) is unstable, giving rise to the /T2 term, there is no real E for which the transition dipole matrix element vanishes. In case of 2 = 0 detuning and cos 16 = 0, we have... 

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