Valley of stability

Assuming that all combinations of neutrons and protons can exist, which atomic nuclei are stable enough to survive for as long as the Universe itself, that is, for around 10 billion years Estimates of nuclear stability are available to answer this query. The 270 or so nuclei found in nature in some lasting form all lie along what is known as the valley of stability in the (A, Z) plane (Eig. 4.2). 

In the slow process, neutron captures are separated by n p conversions, so that the result never lies far from the valley of stability. The s process takes place in much less extreme conditions. There are two forms. 

Hence, when neutron irradiation ceases, the exotic and extravagant nuclei undergo a chain of P decays to re-enter the valley of stability, that is, the region of stable nuclei which traces out a parabola in the N, Z) plane, by successive transformation of neutrons into protons. 

One may dissect the origins of the heavy nuclides in the valley of stability - see Fig. 4. Some may be synthesized only by the s-process such a nucleus (Z, N) is shielded... 

One of the most basic questions in nuclear astrophysics is How do the nuclei heavier than iron get produced This question was first answered by Burbidge, Burbidge, Fowler and Hoyle in 1957 [35]. They proposed that these elements are produced through the slow (s) and rapid (r) neutron-capture processes. The words rapid/slow refer to the rate of neutron capture compared to the rate of /3-decay in the astrophysical conditions. Figure 13 shows the nuclei involved in the r- and s-processes. The s-process path stays close to the valley of stability whereas the r-process path moves staying close to the drip line. The figure also shows the nuclei involved in the rp-process these are proton rich nuclei where capture of protons are involved and that the rate is compared to the / + rates. 

If the nuclear flow towards increasing Z values reaches the actinide or transactinide region, it is stopped by neutron-induced or /3-delayed fissions which lead to a recycling of a portion of the material to lower Z values. At freezing of the neutron captures or inverse photodisintegrations, mainly /3-decays, but also spontaneous or /3-delayed fissions and single or multiple /3-delayed neutron emissions, drive the neutron-rich matter towards the valley of stability. These post-freezing transformations are shown schematically in Fig. 22. 

If we restrict ourselves to the most abundant or longest-living nuclides of the elements, i.e., to the line of stability or valley of stability , then the following empirical formula [40], can be used. 

FIG. 3.S. Isobar cut across the valley of stability showing schetnalically the position of difTerent kinds of nuclei. 

In Chapter 3 we observed that the binding energy per nucleon is almost constant for the stable nuclei (Fig. 3.3) and that the radius is proportional to the cube root of the mass number. We have interpreted this as reflecting fairly uniform distribution of charge and mass throughout the volume of the nucleus. Other experimental evidence supports this interpretation (Fig. 3.4). This information was used to develop the liquid drop model, which successfully explains the valley of stability (Fig. 3.1). This overall view also supports the assumption of a strong, short range nuclear force. 

Fig. 32. A schematic representation of the relative yield of various nuclides from photonuclear reactions with 320 Mev X-rays. The yield is indicated by the height above the proton-neutron plane. The dark line in the proton-neutron plane indicates the center of the valley of stability. [Figure from Halpern etal.i Phys. Rev. 97, 1327 (1955).]...

The formation of fission products, which are neutron rich and which stabilize by a sequence of several P-decay processes and/or by the emission of prompt neutrons. This is due to the fact that the valley of stability is bent toward the neutron-rich region from the initial N = Z direction due to the Coulomb term. 

All of the members of the natural decay chains are unstable with respect to spontaneous fission, but the probabilities are small. The decay chains follow the side of the valley of stability where the fissionability parameter Z A is relatively small. However, fission is such an extraordinary event that even a few events can be detected, as long as they can be distinguished from events such as muon-induced fission. For the natural chains has the highest fraction of decays by spontaneous fission, 5.4 x 10. Although this leads to a multitude of natural decay chains consisting of fission followed by decays through fission product chains, the process will not be considered in this chapter. 

Chowdbury, P.R., Samanta, C., Basu, D.N. Search for long lived heaviest nuclei beyond the valley of stability. Phys. Rev. C77 044603(10) (2008)... 

N/Z too high Nnclides that lie above the valley of stability have too many nentrons and tend to convert neutrons to protons via beta decay. The process of undergoing beta decay moves the nnclide down in the plot in Figure 19.5 and closer to (or into) the valley of stability. 

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