Reduced transition probability, for

The quantities gQ and g in (77-5) are the gyromagnetic ratios corresponding to the intrinsic angular momentum of the odd particle and to the rotational motion respectively. The former is a characteristic of the state of the odd particle and the latter is theoretically equal to Z/A. Thus the reduced transition probabilities for magnetic transitions are of the order of the square of the nuclear magneton number, while those oi E 2 transitions are of the order of or cm. ... 

O Figure 2.14 presents the reduced transition probabilities for transitions (E2 Oj" 2j") in even-even nuclei. The B(E2) values have the following characteristics ... 

We start with the system without B-desorption (/cb = 0). This case is realistic for the oxidation of CO because the O atoms (B particles) are strongly bound to the metal surface and desorption does not occur at the temperatures used for this reaction. In this case the parameter Ebb does not play a role because the transition probabilities for the A and B particles depend on fcg/pg and on k°A/pQA, respectively. Therefore we have reduced the number of energetic parameter to two (EAA and Ebb)- In the following we present all values of E fl in knT units. 

The strategy we have been following is to pump the v" = 0 - V = 0 vibrational band in the UV and observe the resulting fluorescence. This method reduces complexity caused by eliminating the need to consider vibrational relaxation and results in most of the fluorescence signal appearing in the 0-0 vibrational band. Moreover, the energy levels, transition frequencies and transition probabilities for this band have been studied extensively and can be found in the literature. 

In general, in the above considerations the coordinate x is presumed to describe nuclear motion normal to the intersection line L of the diabatic.potential energy surfaces of reactants and products. In particular cases, however, the coordinate x can coincide with a dynamically separable reaction coordinate. Then, the whole manydimensional problem of calculating the transition probability for any energy value is simply reduced to a one-dimensional one. Such is, for instance, the situation in a system of oscillators making harmonic vibrations with the same frequency in both the initial and final state /67/ which we considered in Sec.3.1.1. The diabatic surfaces (50.1) then represent two similar (N+1>dimensional rotational paraboloids which intersect in a N-dimensional plane S, and the intersection... 

To obtain the reduced transition probability B(E2) for decay from (73.2) it must be remembered that the transition probabihty for absorption differs... 

The significance of these results lies not only in the few instances where the ratios of the reduced E2 transition probabilities can be measured and found to be in agreement with theory, but also the fact that the absolute values are in accord with other data on the electric quadrupole moments. There is now an increasing volume of experimental data relating to the relative values of reduced E2 transition probabilities for competitive y-rays emitted by rotational states. We shall not now go into the details of this subject although we shall discuss some instances in Sect. 82. 

P) M transitions. The reduced transition probability of the M component, as we have shown above, can be obtained from that of the E 2 component in Coulomb excitation, when the ratio of the components is found from angular distributions, angular correlations of successive y-rays, or from internal conversion measurements. Since this extra information is required there is at present less data available on Ml than on 2 transitions. For Ta the reduced Ml transition probabilities obtained by Stelson and McGowan for the 137kev transition and for the l66kev cascade transition were 0.105 and 0.226 in units of (efll2Mc). From these quantities the square of the difference between the gyromagnetic ratios gQ — gr [see Eq. (77-5)] was found to be 0.20 and 0.28, respectively the difference between the two results, these authors state, is probably not outside experimental errors, and illustrates the experimental difficulties involved in this kind of work. 

Reduced y-ray transition probabilities. According to O Fig. 2.14, the reduced transition probabilities B(E2 Oj —> 2f) in even-even nuclei have especially low values at magic numbers. See, for example, data for soSn and s2Pb. 

The electric reduced transition probability B(EL) J, of de-excitation from an initial (upper) state (7i) to the final state (7f) is related to the reduced transition probability B(EL) for the excitation of the state 7i by... 

It is assumed that the radial wave functions in the initial and final states are constant within a sphere of radius R, that is R ij r) = const. 0 if r < 1 and zero if 1 < r. This is a rather crude approximation, not taking into account the real shapes of the radial wave functions, but it simplifies the calculations considerably and it is very useful in practice. The reduced transition probability is evaluated for / = L 1/2 initial and J = 1/2 final states. 

IBM-1 theoretical results (dots), (b) Reduced B(E2) transition probabilities for Sm isotopes. 

Thus, formally, the change of the proton state is reduced to the change of the electron resonance integral, Vjf by V f S, All the temperature dependence of the transition probability for a fixed value of the coordinate of the reactant center of mass is related to the classical overcoming of the Franck-Condon barrier created by the solvent polarization. 

This is in perfect agreement with deformation values from reduced transition probabilities B E2) and from the spectroscopic quadrupole moment using Eqs. (29) and (30). The detailed calculations include small corrections and higher-order terms in Eqs. (29) and (32), which have been omitted for the sake of clarity. 

This is most easily shown in the following way. In the integration over the angle from the transitions m m -h 1 and n n - 1 of the magnetic quantum numbers only the first term, 1/2810191 sin i 2e " yields a contribution, for m -> m — 1, n n + 1 only the second term and for m -> m, n — n only the third term. The remaining six transition probabilities, for which Am -h An 0 (which violate the conservation of angular momentum), yield no contributions. So the sum in (6) reduces from the square of three terms to the sum of three squares, which correspond... 

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