Half-life partial

Example Problem Consider the nucleus 64Cu (ti/2 = 12.700 h). MCu is known to decay by electron capture (61%) and (3 decay (39%). What are the partial half-lives for EC and (3 decay What is the partial width for EC decay ... 

What are the partial half-lives of 22Na for decay by (a) EC and (b) (3+ emission ... 

Solution Assuming that the branches to other states are small and do not contribute to the sum of partial half-lives, we can write... 

The work of this CRP has recently concluded and a report summarizing the results of this task has been prepared. New, highly precise decay data on total and/or partial half-lives for 7 nuclides, a-particle emission probabilities (Pa) for 7 nuclides, and y-ray emission probabilities (Py) for 21 nuclides have been produced. The final list of recommended decay data includes these results, as well as those from other recent measurements, together with carefully evaluated information on a number of other nuclides. In all, this list includes half-life values for 125 nuclides and, for the more prominent transitions only, Pa values for 30 nuclides and Py values for 47 nuclides. [Some of these data represent simply the results of previously published evaluations.] These data will be included in the final report of the CRP, to be published as one of the IAEA Technical Reports Series. 

Fig. 5. Shell-correction energy (a) and partial half-lives for spontaneous fission (b) and a decay (c). See text for a detailed descriptions and for references.

In the case of secular equilibrium, two partial half-lives may be distinguished formally ... 

Introduction of these partial half-lives leads to the relations... 

Table 5.4. Partial half-lives of spontaneous fission (values from R. Vandenbosch, J. R. Huizenga, Nuclear Fission, Academic Press, New York, 1973).

Partial half-lives of spontaneous fission and the number of neutrons set free are listed in Table 5.4. The partial half-lives are calculated by use of eq. (4.41) in section 4.8 (branching decay). They vary between the order of nanoseconds and about lO y. Although the fission barrier for nuclides such as (s 6MeV) is small compared with the total binding energy of the nucleons ( 1800 MeV), spontaneous fission of has a low probability compared with ot decay. 

These partial decay constants correspond to partial half-lives of 29.7 h for electron capture decay, 33.6 h for decay, and 67.5 h for positron decay. 

The existence of cluster substructure in nuclei is supported also by the observation of cluster decay. Besides a particles, the heavy nuclei can emit Ne, Mg, Si clusters, too. The partial half-lives for these decays depend on the penetrability of the Coulomb barrier in a way very similar to a decay (Mikheev and Tretyakova 1990 see Geiger-NuttaU-type relations in O Sect. 2.4.1.1). The heavy cluster decay is a very rare phenomenon. For example, in the decay of Ra there were 65 x 10 a particles observed, while only 14 cluster emissions during the same time (Rose and Jones 1984). For the detection of rare clusters solid state track detectors are very suitable. 

Logarithm of ol partial half-lives as a function of X=Zd where is the a-particle... 

The formula is very useful, e.g., for the prediction of alpha partial half-lives of superheavy nuclei. 

The energy of P decay varies from near zero up to 25-30 MeV, while the P partial half-lives vary in a very wide range from lO s up to >10 s. The P and P energy spectra show continuous distributions (O Fig. 2.39a). As both the initial and final states have well-defined quantum energies, Pauli postulated (in 1931) the existence of a neutral particle (called neutrino), which takes away the missing energy difference. An indirect proof of the existence of the antineutrino was given by Csikai and Szalay (1957) in a cloud chamber photo of the He Li P decay (O Fig. 2.39b). 

As shown in Chap. 2, there is a negative correlation between half-life and alpha energy. The strong energy dependence of partial half-lives explains why the complexity of alpha spectra remained undetected for such a long time the branch producing the most energetic alpha particles often dominates the whole decay process. 

In spite of the lower excitation energies obtained in cold-fusion reactions, hot-fusion reactions produce evaporation residues that are more neutron rich, a consequence of the bend of the line of fi stability toward neutron excess. For the purposes of studying nuclei whose stability is more strongly influenced by the spherical 184-neutron shell clostrre, hot fusion is the more viable path. If nuclei were constrained to be spherical, or deformed into simple quadrupole shapes like those that influence the properties of the actinide isotopes with N — 152, one would expect cold-fusion reactions to quickly veer into ZJ space where nuclides would be characterized by very short partial half-lives for decay by spontaneous fission. In fact, there is a region of nuclear stability centered at Z = 108 and N — 162 [12, 19-21], removed from the line of fi stability toward proton excess, where the nuclei derive a resistance to spontaneous fission from a minor shell closure associated with complicated nuclear shapes, making a emission their most probable decay mode [133, 240]. 

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