Reduced transition probability

Comparison with Eq. (E.35) shows a close similarity but with the relevant difference that the matrix 0 is multiplied on the left with the reduced transition-probability matrix P while in Eq. (E.35) 0 it is multiplied with P on the right223 . 

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

E2 transition probabilities from Coulomb excitation. Some reduced transition probabilities obtained by Coulomb excitation are listed in Table 6. These quantities are expressed in units of i0 cm. The reduced transition probability corresponding to Weisskopf s estimate of the transition probability of 2 radiation, in the same units, is given by 3 x where is the nuclear... 

It is interesting to compare the reduced transition probabilities obtained by Coulomb excitation with those obtained by the delayed coincidence methods. 

Table 7. Comparison of reduced transition probabilities in even-even nuclei obtained by Coulomb excitation (Huus, Bjerregaard and Elbek) and by the delayed coincidence method (Sunyar).

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. ... 

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. 

Table 8. Ratios of reduced transition probabilities of the y-rays emitted by 1 levels in even-even nuclei.

The ratio of the reduced transition probabilities of the higher energy y-ray to that of the lower energy y-ray are shown in Table 8. The average is about 0.5. Theoretically a state with spin 1 could have if = 1 or A = 0, and the ratio of the reduced transition probabilities should be given by the ratio of the... 

Nucleus y-ray energies in kev Ratio of reduced transition probability... 

Last levels of three intruder bands discussed in [01Ga52] lifetimes and reduced transition, probabilities (B(M1) etc.) of levels in many bands are given in [01Ga52]. a (p,d) is a linear sum of da/dfl from 10° to 50°. 

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. 

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 ... 

Reduced transition probabilities. The systematics ofB(E2 B(E2 0j data in even-even... 

O Equation (2.50) means that from the measured reduced transition probabilities 5(E2 0] 2 ) one can determine the internal quadrupole moment (Qo) and also the deformation parameter 6, taking into account that... 

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. 

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