Predicted nuclear 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... 

This model tends to predict more magic numbers than are actually seen in the mass spectrum. The reason for this may have geometric origins since only certain nuclearities can adopt highly spherical structures which coincide with a closed shell of electrons. When the cluster cannot adopt a highly spherical structure, a splitting of the jellium shells occurs, leading to some instability. A further and more crucial limitation is that the spherical jellium model provides no direct information on the structure, even for clusters with closed shells. 

The isotope of element 114 with 184 neutrons is predicted to be especially stable, since it has magic numbers of both protons and neutrons in its nuclei. This element may sit atop an island of stability in the sea of possible combinations of subatomic nuclear particles. Other islands, here picked out in contours whose height denotes the degree of stability, occur for lighter elements such as some isotopes of lead and tin... 

The magic numbers were successfully explained by the nuclear shell model [5,6], and an extrapolation into unknown regions was reasonable. The numbers 126 for the protons and 184 for the neutrons were predicted to be the next shell closures. Instead of 126 for the protons also 114 or 120 were calculated as closed shells. The term superheavy elements, SHEs, was coined for these elements, see also Chapter 8. 

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. 

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. 

SECTION 21.2 The neutron-to-proton ratio is an important factor determining nuclear stability. By comparing a nuclide s neutron-to-proton ratio with those in the band of stability, we can predict the mode of radioactive decay. In general, neutron-rich nuclei tend to emit beta particles proton-rich nuclei tend to either emit positrons or im-dergo electron capture and heavy nuclei tend to emit alpha particles. The presence of magic numbers of nucleons and an even number of protons and neutrons also help determine the stability of a nucleus. A nuclide may undergo a series of decay steps before a stable nuclide forms. This series of steps is called a radioactive series or a nuciear disintegration series. 

Fig. 36. Snapshots in the nuclidic chart of flow patterns in a ID model of a detonating He layer accreted onto a 0.8M WD. The selected times and corresponding temperatures or densities are given in different panels. The stable nuclides are indicated with open squares. The magic neutron and proton numbers are identified by vertical and horizontal double lines. The drip lines predicted by a microscopic mass model are also shown. The abundances are coded following the grey scales shown in each panel. At early times (bottom left panel), an r-process type of flow appears on the neutron-rich side of the valley of nuclear stability. At somewhat later times (top left panel), the material is pushed back to the neutron-deficient side rather close to the valley of /3-stability. As time passes (two right panels), a pn-process [87] develops...

In the late sixties the dream of the superheavy elements arose. Theoretical nuclear physicists around S.G. Nilsson (Lund) [1] and from the Frankfurt school [2-4] predicted that so-called closed proton and neutron shells should counteract the repelling Coulomb forces. Atomic nuclei with these special "magic" proton and neutron numbers and their neighbors could again be rather stable. These magic proton (Z) and neutron (N) numbers were thought to be Z = 114 and N = 184 or 196. Typical predictions of their life times varied between seconds and many thousand years. Figure 8.1 summarizes the expectations at the time. One can see the islands... 

These elements near the predicted islands of nuclear stability around the spherical closed shells at proton numbers 110-114 (or even 126) and 184 neutrons are typically referred to as SHEs. Although arguments have been made (Armbruster and Miinzenberg 1989) that the heavy elements that would not exist except for stabilization by nuclear shells, whether or not they are spherical, should be designated as SHEs, the term has usually been reserved for those elements in the region of the predicted spherical doubly magic nuclei. 

The nuclear models that resulted in the prediction of an island of superheavy nuclei have evolved in response to experimental measurements of the decay properties of the heaviest elements. While the prediction of a spherical magic N = 184 is robust and persists across the models [8], the shell closure associated with Z — 114 is weaker, and different models place it at higher atomic numbers, from Z = 120 to 126 [60-69] or even higher [70] (see Nuclear Structure of Superheavy Elements ). Interpretation of the decay properties of the heaviest elements may support this [71, 72], but the most part decay and reaction data do not conclusively establish the location of the closed proton shell. Because of this, the domain of the superheavy elements can be considered to start at approximately Z = 106 (seaborgium), the point at which the liquid-drop fission barrier has vanished [9]. For our purposes, the transactinide elements (Z > 103) will be considered to be superheavy (see Nuclear Structure of Superheavy Elements ). 

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