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Hamiltonian radiative

Let us emphasize that the Porter-Thomas distribution is here applied to the resonances of the molecular Hamiltonian in the absence of a radiation held. In the case of NO2 mentioned in Section III, the same distribution with v = 1 was applied, by contrast, to the radiative linewidths of the molecular Hamiltonian [5, 6]. [Pg.540]

A time-dependent process, such as radiative absorption, internal conversion, intersystem crossing, unimolecular isomerization, or collision, may be treated in terms of a zero-order Hamiltonian H0 and a perturbation T. An unperturbed eigenstate of H0 evolves in time, since it is not an eigenstate to the perturbed Hamiltonian... [Pg.10]

Prepared State. Here the Hamiltonian H is the time-independent molecular Hamiltonian. Both H0 and T are time independent. The initial prepared state is an eigenket to H0 and thus is nonstationary with respect to H = H0 + T. One example is provided by considering H0 as the spin-free Hamiltonian 77sp and the perturbation T as a spin interaction. A second example is provided by considering H0 as the spin-free Born-Oppenheimer Hamiltonian and T as a spin-free nonadiabatic perturbation. In the first example spin-free symmetry is not conserved but double-point group symmetry may be. In the second example point-group symmetry is not conserved, but spin-free symmetry is. The initial prepared state arises from some other time-dependent process as, for example, radiative absorption which occurs at a rate very much faster than the rate at which our prepared state evolves. Mechanisms for radiationless transitions in excited benzene may involve such prepared states, as is discussed in Section XI. [Pg.12]

It is very important, in the theory of quantum relaxation processes, to understand how an atomic or molecular excited state is prepared, and to know under what circumstances it is meaningful to consider the time development of such a compound state. It is obvious, but nevertheless important to say, that an atomic or molecular system in a stationary state cannot be induced to make transitions to other states by small terms in the molecular Hamiltonian. A stationary state will undergo transition to other stationary states only by coupling with the radiation field, so that all time-dependent transitions between stationary states are radiative in nature. However, if the system is prepared in a nonstationary state of the total Hamiltonian, nonradiative transitions will occur. Thus, for example, in the theory of molecular predissociation4 it is not justified to prepare the physical system in a pure Born-Oppenheimer bound state and to force transitions to the manifold of continuum dissociative states. If, on the other hand, the excitation process produces the system in a mixed state consisting of a superposition of eigenstates of the total Hamiltonian, a relaxation process will take place. Provided that the absorption line shape is Lorentzian, the relaxation process will follow an exponential decay. [Pg.151]

To describe the shifts and intensities of the m-photon assisted collisional resonances with the microwave field Pillet et al. developed a picture based on dressed molecular states,3 and we follow that development here. As in the previous chapter, we break the Hamiltonian into an unperturbed Hamiltonian H(h and a perturbation V. The difference from our previous treatment of resonant collisions is that now H0 describes the isolated, noninteracting, atoms in both static and microwave fields. Each of the two atoms is described by a dressed atomic state, and we construct the dressed molecular state as a direct product of the two atomic states. The dipole-dipole interaction Vis still given by Eq. (14.12), and using it we can calculate the transition probabilities and cross sections for the radiatively assisted collisions. [Pg.321]

Physically, the wavefunction of Eq. (19.6a) corresponds to adding one electron to Ba2+ to make the Ba+ n C states and then adding the second n electron to form the neutral Ba n Cni states. On each state of Ba+ there is built an entire system of Rydberg states and continua, as shown in Fig. 19.1 for the three lowest lying states of Ba+. Note that the Rydberg states converging to the 5d and 6p states of Ba+ are above the Ba+ 6s state. With the independent electron Hamiltonian H0 these states can only decay radiatively. They are not coupled to the degenerate continua above the Ba+ 6s state. [Pg.396]

We consider a non-radiative transition caused by linear diagonal and quadratic non-diagonal vibronic interactions. If the states belong to different representations of the point group of the center, then the Hamiltonian of the system reads ... [Pg.161]

Duan et al. (2007) present an alternative approach to these ab initio calculations. They suggest that, rather than attempting to calculate the multitude of 5d energy levels directly, ab initio approaches could concentrate on producing useful parameter values for only the subset of terms in the parametrized Hamiltonian (see section 2) which cannot be experimentally determined. That is, the ab initio calculations could produce reliable values, for example, for the / (fd) and <7v(fd) parameters that could then be incorporated into parametrized calculations. The parameters may then be fine tuned to give a reliable calculation that might be used to investigate other properties of the ions, such as the non-radiative relaxation discussed in section 3.4. [Pg.92]

As a result, the radiative Hamiltonian UIt [Eq. (12.3)] assumes the quantized formff... [Pg.268]

Since the state E, n", N", t) contains the effect of the full Hamiltonian at time fq then the photodissociation amplitude A(E, n, N, t i, A)) into the final state will energy E, internal quantum numbers n and radiation field described by N, starting in the initial state ] , initial state and the incoming fully interacting state. That is,... [Pg.272]

The Hamiltonian is made up of 2 terms, the molecular (H oi) and the molecule-field interaction (H ). LuP is a damping term in the density matrix due to transitions caused by interaction with the vacuum state [45], but also includes non-radiative processes and vibrational damping. LphP represents damping due to phase... [Pg.75]

Fig. 4. (a) A schematic representation of the small molecule limit. The states are the same as those represented in Fig. 1. The molecular eigenstates approximately diagonalize the effective molecular Hamiltonian (20), and each carries only a portion of the original oscillator strength to s can therefore decay radiatively to Fig. 4. (a) A schematic representation of the small molecule limit. The states are the same as those represented in Fig. 1. The molecular eigenstates approximately diagonalize the effective molecular Hamiltonian (20), and each carries only a portion of the original oscillator strength to <fig. (b) A representation of the statistical limit. The 0j form a dense manifold of states which acts as a dissipative quasicontinuum on the time scales of real experiments. (j>s can therefore decay radiatively to <pQ and nonradiatively to <pt ...
Hu (sb) and T(sb) are the molecular Hamiltonian and the damping matrix, respectively, within the states s, 4>b, while A is the matrix of nonradiative decay rates which has only one nonzero matrix element As = Ass within this BO basis set. The states jx, 1 which diagonalize (25) are then the resonant states, each with some energy Er and some radiative and nonradiative decay rates Tr and Ar, respectively. When these resonances are overlapping, i.e.,... [Pg.121]


See other pages where Hamiltonian radiative is mentioned: [Pg.1143]    [Pg.2475]    [Pg.433]    [Pg.314]    [Pg.44]    [Pg.52]    [Pg.144]    [Pg.1106]    [Pg.69]    [Pg.182]    [Pg.247]    [Pg.271]    [Pg.113]    [Pg.442]    [Pg.126]    [Pg.80]    [Pg.268]    [Pg.270]    [Pg.271]    [Pg.271]    [Pg.763]    [Pg.180]    [Pg.6516]    [Pg.130]    [Pg.21]    [Pg.763]    [Pg.165]    [Pg.190]    [Pg.114]    [Pg.118]    [Pg.119]    [Pg.121]    [Pg.122]    [Pg.447]    [Pg.646]    [Pg.652]   
See also in sourсe #XX -- [ Pg.268 ]




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