Transition dipole matrix elements

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

Emission and absorption of electromagnetic radiation by molecular systems takes place in transitions from an initial quantum state i) to a final state /). The dipole transition matrix element associated with such a transition is obtained from the wavefunctions of these states, ipfr) and... 

A(y) = A(v)/v. Whereas A describes the absorption of spectral intensity or energy, A is proportional to the probability of absorbing a photon per unit path length. We will not make great use of the quantity A, because the spectral density G defined above is more closely related to the squared dipole transition matrix elements, even at low frequency G is the preferred quantity. 

Fig. 20. A schematic representation of the emission of an isolated large molecule following internal conversion from the second to the first singlet, a" and 6J1 denote the amplitudes of the second singlet and quasi-degenerate vibrational levels of the first singlet, respectively, in the excited molecular state >/in. /v, and m are the corresponding electronic dipole transition matrix elements coupling < >n and as indicated.

We shall later assume, in Section XI-B, that the zero-order states are BO states, that the ground state is adequately represented as a BO state, and that the ground state is connected, via a dipole transition matrix element, only to the state or fB. Absorption of a photon by a molecule will then lead to the creation of the nonstationary state [Pg.257]

We now suppose that the molecular ground state is accurately described as a BO state, and that the ground state and the BO state dipole transitions between the ground state and the BO states > or are forbidden (see Fig. 26). Thus the dipole matrix element < o e-p., F(0)> is proportional to the coefficient, a(E), of the BO state in the state [Pg.261]

To appreciate the essence of this control scenario, recall the results of applying a laser pulse a(t) to induce a transition between two bound states Ef) and , ). We denote the dipole transition matrix element between these two states by d,- - and define k,j = 2dpopulation transfer between these levels can be accomplished by using a n pulse, that is, a pulse of duration t satisfying... 

Here, nx is the number of molecules per cm3 in the lower level, ju the electric dipole transition matrix element, Tex the excitation temperature of the molecule and f(y) the line shape function normalized to... 

As in configuration A, an examination of the angular momentum attributes of these differential equations provides insight into the effects of averaging over Afi, In this case, however, we can show that in the ten-level case B the M and — A terms contribute equally, so that control is maintained after M averaging. To sefl this, consider how each M dependent 3-j symbol changes when M — — M Given Eqs. (51) and (53), we have for the dipole transition matrix element associated with ] that... 

When discussing the electronic spectra and optical properties of Ceo, it is important to include the effect of screening of the external field. Using the ground state single-particle wavefunctions and energy levels, the dipole transition matrix elements and transition frequencies have been evaluated in order... 

Additional evidence comes from the consideration of the dipole transition matrix elements. As mentioned above, the transition from the a-type state of the benzene cation to the ground state is dipole forbidden [30,75]. For the difluoro derivatives the molecular symmetry is reduced and the selection rules are relaxed [69]. Given that the components of the electric dipole operator transform (in the C2v point group) as ... 

To see the effect of averaging over the M quantum number we examine the relationship between enantiomeric control with a given value of M and with the corresponding value of -M. Consider then the M dependence of the dipole transition matrix elements. The projection of the dl (/ = 0, 1, 2) dipole operators on the polarization directions / can be related (see Ref. 87) to the (x,y,z) body-fixed components of the dipole operators as... 

CH3—CsC—H for molecules having different translational velocities perpendicular to the magnetic field. In this calculation the M-submatrices of the lower and upper rotational state were diagonalized numerically and the electric dipole transition matrix elements were subjected to the corresponding unitary transformation,... 

Here, 1/ T2 is the rate of dipolar dephasing and /iba is the electric dipole transition matrix element for the atom. In ordinary vacuum (as opposed to our 3D PBG material), the textbook formula (Boyd, 1992) for the nonlinear susceptibility is... 

In the calculations of the Rb2 PA, we estimate the -X E+ — electronic-dipole moment to be p, = 3 au. This value corresponds to die 55 i/2(m = 1/2) — 5P3/2(m = 3/2) transition in Rb in a circularly polarized field, and is consistent with all the other 5S - 5P matrix elements for the Rb atom in a polarized laser field. The exact values of the atomic reduced dipole matrix elements can be found in Ref. [92]. The electronic-dipole transition matrix elements in KRb are taken as 3.5 eao fortheXiE+ o- transition, and 0.5 eao for the -o- l n transition, the order-of-magnitude estimate based on the data from Refs. [93,94],... 

Here, Jac is the exchange coupling between states of the rare-earth ion and those of the Cu02 planes with local susceptibility x((u), M is the dipole transition-matrix element of the corresponding CEF transition, and = k T. The local magnetic susceptibility (Becker et al. 1977) is defined as... 

Here, A corresponds to the energy separation of the two lowest CEF states Fa and F4, and Ma = (F4 / [Fa) a=x,y,z) are the components of the dipole transition matrix element between these two states. Ma and A are the characteristic parameters derived fi-om the single-ion susceptibility which is deduced from the INS experiments on the CEF on polycrystalline samples (tables 6 and 8). For a determination of the exchange integrals J" Q), exchange parameters and 7 were introduced that couple the... 

Bu symmetry, the products f0203 r0204, and 0jV 4 transform as Ag, Bu, Bu and Ag, respectively. The electric dipole transition matrix elements are, therefore, nonzero for the first and fourth excitations (the two excitations with Bu symmetry), and zero for the second and third (the two with Ag... 

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