Probability, transition, Fermi golden

The microscopic rate constant is derived from the quantum mechanical transition probability by considering the system to be initially present in one of the vibronic levels on the initial potential surface. The initial level is coupled by spin-orbit interaction to the manifold of vibronic levels belonging to the final potential surface. The microscopic rate constant is then obtained, following the Fermi-Golden rule, as ... 

The transition probability for multiphonon, nonadiabatic ET can be formulated in terms of first-order perturbation theory, i.e., by means of the Fermi golden rule, as (2)... 

The transition probability of an electron from i p, to Xv in first-order perturbation theory is then given by the Fermi golden rule. 

The physical mechanism of XANES can be understood from the Fermi Golden rule, where the probability of a transition (w) from an initial state I > to a final state [Pg.538]

So transition probabilities based on the Fermi golden rule. Only a combined reaction coordinate of anti pyramidalization and twisting at the double bond provides a low-energy pathway that reproduces the experimentally observed transition probabilities, whereas the traditional model invoking only a pure twist around the double bond fails. 

The whole derivation will be therefore identical, except that the constant cokm will be replaced by o)km i Hence, we have a new form of the Fermi golden rule for the probability per unit time of transition from the mth to the kth state ... 

The transition probability due to an interaction H can be expressed by the Fermi Golden Rule as... 

Various models that take this problem into account exist. Here, we will mention a model by Kestner et al. based on the Fermi golden rule. It is possible to show (see Section 7.3.2) that the probability per unit time that a system in an initial vibronic (electronic and vibrational) state, n, will undergo a transition into a set of vibronic levels mw is given by... 

The probability for a transition to occur between two states per unit time is determined by Fermi s golden rule and depends on the operator of interaction between the subsystem concerned and a thermostat. As orientational states are characterized by a low-energy spectrum, they will be substantially influenced by the... 

Not only is the master equation more convenient for mathematical operations than the original Chapman-Kolmogorov equation, it also has a more direct physical interpretation. The quantities W(y y ) At or Wnn> At are the probabilities for a transition during a short time At. They can therefore be computed, for a given system, by means of any available approximation method that is valid for short times. The best known one is time-dependent perturbation theory, leading to Fermi s Golden Rule f)... 

For a quantitative treatment of establishing connections between vibronic coupling and vibrational progressions in electronic spectra, band profiles from vibronic wavefunctions must be calculated using common procedures of time-dependent perturbation theory and Fermi s golden rule [57], For emission, e.g., the transition rate which is the transition probability per unit time summed over... 

Therefore the transition probability Wi >y becomes independent of time (hallelujah ) this is Fermi s golden rule ... 

The transition probability per unit time given by the time-dependent perturbation theory, that Fermi named Golden Rule in view of its prevalence in radiationless transitions, has the form... 

The quantum mechanical treatment of non-adiabatic electron transfers are normally considered in terms of the formalism developed for multiphonon radiationless transitions. This formalism starts from Fermi s golden rule for the probability of a transition from a vibronic state Ay of the reactant (electronic state A with vibrational level v) to a set of vibronic levels B of the product... 

The absorption of an X-ray photon leads to the excitation of an inner-shell electron. The transition probability per unit time P i from an initial core level i) to a final state near the vacuum level /), is given according to Fermi s Golden Rule ... 

According to Fermi s golden rule [40, 42], the integral intensity A of the absorption band of the normal mode is proportional to the probability per unit time of a transition between an initial state i and a final state j. Within the framework of the first (dipole) approximation of time-dependent perturbation quantum theory [46, 65], this probability is proportional to the square of the matrix element of the Hamiltonian H = —E p, where E is the electric field vector and p is the electric dipole moment, resulting in the absorption... 

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