Stability nucleons

Since the radioactive half-lives of the known transuranium elements and their resistance to spontaneous fission decrease with increase in atomic number, the outlook for the synthesis of further elements might appear increasingly bleak. However, theoretical calculations of nuclear stabilities, based on the concept of closed nucleon shells (p. 13) suggest the existence of an island of stability around Z= 114 and N= 184. Attention has therefore been directed towards the synthesis of element 114 (a congenor of Pb in Group 14 and adjacent superheavy elements, by bombardment of heavy nuclides with a wide range of heavy ions, but so far without success. 

The nature of spheron-spheron interactions is such that maximum stability is achieved when each spheron ligates about itself the maximum number of neighbors, to produce a nucleus with a closest-packed structure. A simple argument (12) leads to the conclusion that the spherons in a nucleus are arranged in concentric layers. The packing radius of a spheron varies from 1.28 f for the dineutron to 1.62 f for the helion. The radius (to nucleon density half that of the inner region) of the largest nucleus is 6.8 f... 

The conclusion that each inner-core spheron in a stable core should ligate its neighbors about itself in a way corresponding to local stability is a reasonable consequence of the self-generating character of the potential energy function for nucleons in nuclei (mutual interdependence of structure and potential energy function) and the short range of internucleonic forces. 

The alpha particle is a helium nucleus produced from the radioactive decay of heavy metals and some nuclear reactions. Alpha decay often occurs among nuclei that have a favorable neutron/proton ratio, but contain too many nucleons for stability. The alpha particle is a massive particle consisting of an assembly of two protons and two neutrons and a resultant charge of +2. 

Another difference between nucleons and electrons is that nucleons pair whenever possible. Thus, even if a particular energy level can hold more than two particles, two particles will pair when they are present. Thus, for two particles in degenerate levels, we show two particles as II rather than II. As a result of this preference for pairing, nuclei with even numbers of protons and neutrons have all paired particles. This results in nuclei that are more stable than those which have unpaired particles. The least stable nuclei are those in which both the number of neutrons and the number of protons is odd. This difference in stability manifests itself in the number of stable nuclei of each type. Table 1.3 shows the numbers of stable nuclei that occur. The data show that there does not seem to be any appreciable difference in stability when the number of protons or neutrons is even while the other is odd (the even-odd and odd-even cases). The number of nuclides that have odd Z and odd N (so-called odd-odd nuclides) is very small, which indicates that there is an inherent instability in such an arrangement. The most common stable nucleus which is of the odd-odd type is 147N. 

In this case, the 38i7Cl is an odd-odd nucleus, whereas 3917C1 is an odd-even nucleus. Thus, even though 3917C1 is farther away from the band of stability, it has a slightly longer half-life. Finally, let us consider two cases where both of the nuclei are similar in terms of numbers of nucleons. Such cases are the following ... 

Models of hot isentropic neutron stars have been calculated by Bisnovatyi-Kogan (1968), where equilibrium between iron, protons and neutrons was calculated, and the ratio of protons and neutrons was taken in the approximation of zero chemical potential of neutrino. The stability was checked using a variational principle in full GR (Chandrasekhar, 1964) with a linear trial function. The results of calculations, showing the stability region of hot neutron stars are given in Fig. 7. Such stars may be called neutron only by convention, because they consist mainly of nucleons with almost equal number of neutrons and protons. The maximum of the mass is about 70M , but from comparison of the total energies of hot neutron stars with presupemova cores we may conclude, that only collapsing cores with masses less that 15 M have... 

There are four naturally occurring isotopes of iron ( Fe 5.82%, Fe 91.66%, Fe 2.19%, Fe 0.33%), and nine others are known. The most abundant isotope ( Fe) is the most stable nuclear configuration of all the elements in terms of nuclear binding energy per nucleon. This stability, in terms of nuclear equilibrium established in the last moments of supernova events, explains the widespread occurrence of iron in the cosmos. The isotope Fe has practical applications, most notably in Mossbauer spectroscopy, which has been widely exploited to characterize iron coordination complexes. 

The fundamental reason why an even number of protons and an even number of neutrons is favoured is that a solitary nucleon, frustrated by a lack of relationship with one of its own kind, can only be harmful to nuclear stability. 

Fig. 4.2. Valley of nuclear stability and nuclear binding energy. Top Beyond Z = 20, the distribution of stable isotopes curves downwards in the (N, Z) plane, showing that stable nuclei grow richer in neutrons as their atomic numberincreases. Bottom The binding energy per nucleon, A / A, is a measure of how robust a nuclear species is in the face of attempts to break it up. This curve reaches a peak around iron.

Any of the foregoing conditions may be achieved when the nucleus contains an even number of both protons and neutrons, or an even number of one and ail odd number of the oilier. Since Ihere is an excess of neutrons over protons for all but the lowest atomic number elements, in the odd-odd situation there is a deficiency of protons necessary to complete the two-proton-two-neutron quartets. It might be expected that these could be provided by the production of protons via beta decay. However, there exist only four stable nuclei of odd-odd composition, whereas there are 108 such nuclei in the even-odd form and 162 in the even-even series. It will be seen that the order of stability, and presumably the binding energy per nucleon, from greatest to smallest, seems to be even-even, even-odd, odd-odd. 

The (3 decay of nuclei far from the bottom of the valley of (3 stability can feed unbound states and lead to direct nucleon emission. This process was first recognized during the discovery of fission by the fact that virtually all the neutrons are... 

The correlation of nuclear stability with special numbers of nucleons is reminiscent of the correlation of chemical stability with special numbers of electrons— the octet rule discussed in Section 6.12. In fact, a shell model of nuclear structure has been proposed, analogous to the shell model of electronic structure. The magic numbers of nucleons correspond to filled nuclear-shell configurations, although the details are relatively complex. 

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