Predicted atomic magic numbers

As with electrons in atoms, it is necessary to use the quantum theory to account for the details of nuclear structure and stability. It is favorable to pair nucleons so that nuclei with even numbers of either protons or neutrons (or both) are generally more stable than ones with odd numbers. The shell model of nuclei, analogous to the orbital picture of atoms (see Topics A2 and A3) also predicts certain magic numbers of protons or neutrons, which give extra stability. These are... 

Because it was assumed that the next protonic magic number was 126 (by analogy with the neutrons), early studies of possible superheavy elements did not receive much attention [12—15), since the predicted region was too far away to be reached with the nuclear reactions available at that time. Moreover, the existence of such nuclei in nature was not then considered possible. The situation changed in 1966 when Meldner and Roper [16, 17) predicted that the next proton shell closure would occur at atomic number 114, and when Myers and Swiatecki [18) estimated that the stability fission of a superheavy nucleus with closed proton and neutron shells might be comparable to or even higher than that of many heavy nuclei. 

Element 114. The chemistry of element 114 received particular attention, since this element was expected to be extra-stable due to the magic number of protons (Z=114) and neutrons (N=184). Because of the closed shell 7s 7pi/2 ground state it was expected to be rather inert. Its chemistry was predicted in [174-176] on the basis of atomic DF calculations and extrapolations of properties in the Periodic Table. 

Structural and magnetic studies on [Co3(CO)(7t-Cp)3S], [Co3(7t-Cp)3S2] and [Co3(7t-Cp)3S2] have been reported by Frisch and DahF and the results have been used as a test case for the apparent correlation between metal-metal bond lengths in cluster compounds and the number of extra d-electrons over the magic number for each metal atom, which has recently been extensively studied by Dahl and co-workers (see Vol. 2 p. 207). The first two of the cobalt-sulphur clusters have been reported previously and the cation was prepared by addition of iodine to the neutral analogue and was isolated as the iodide. The structures of the three compounds substantiate the predictions concerning the dominant influence of anti-bonding valence electrons on the metal-metal bond lengths of the cluster system and also provide evidence that the presence of these electrons can induce a dramatic Jahn-Teller distortion of the cluster. The results are evidenced by the data presented in Table 1. ... 

The fact that the magic numbers are the same as for pure Li or Na clusters is easily understood. If we think again in terms of the jellium-on-jellium model of Sect. 6, w + (Li) — n+(Na) = 0.0029 a.u., which is a very small number. This indicates that a jellium model, in which the jellium density is an average of the Li and Na densities, will predict well the magic numbers in the mixed clusters. However this avera I jellium model would be unable to say anything about the distribution of atoms in the cluster, or about mixing properties. 

Quantum calculations suggested that the nuclei of elements with even numbers of protons and neutrons are stable and particularly so when certain magic numbers are met (see chapter 9). An island of stability was predicted in the vicinity of the element having Z = 114 and N = 184. Such elements are of interest both Ifom the standpoint of nuclear physics and chemistry. The chemistries of individual atoms with nuclear half-lives under 10 seconds, sometimes as brief as 1 second, can be studied immediately following their creation, atom-by-atom, in accelerators using online chemical techniques. 

Abstract It is the hypothesis of this chapter that diatomic molecular Franck-Condon factors echo the periodicities of atonos. This means that in isoelectronic series, entire Deslandres tables for molecules that are one proton shift away from rare-gas molecules have distinctive behavior relative to other Deslandres tables in the series. An example is in the 21-electron sequence where BeCl, whose chlorine atom is next to the closed-shell magic-number atom argon. The periodicity is found quantitatively and indeed allows for prediction of the vibration frequency for a hypothetical 11 upper state for CCl. 

The behavior of a large number of aigon atoms represents a difficult task for theoretical description, but is still quite predictable. When the number of atoms increases, they pack together in compact clusters similar to those that we would have with the densest packing of tennis balls (the maximum number of contacts). We may be dealing with complicated phenomena (similar to chemical reactions) that is connected to the different stability of the clusters (e.g., magic numbers related to particularly robust closed shells ). Yet the interaction of the aigon atoms, however difficult for quantum mechanical description, comes from the quite primitive two-body, three-body etc. interactions (as discussed in Chapter 13). 

Chart of the nuclides. Black squares show stable nuclides as a function of atomic number Z and neutron number N. Sp zero and Sn zero curves indicate proton and neutron drip lines, respectively, which can be predicted, e.g., from different mass formulae. The 6/rcurves show limits, where the potential barrier disappears for fission. Grey regions indicate the domain of known nuclides. Magic numbers are shown by horizontal and vertical lines... 

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