Nucleon shells

Comphcated theoretical calculations, based on filled shell (magic number) and other nuclear stabiUty considerations, have led to extrapolations to the far transuranium region (2,26,27). These suggest the existence of closed nucleon shells at Z = 114 (proton number) and N = 184 (neutron number) that exhibit great resistance to decay by spontaneous fission, the main cause of instabiUty for the heaviest elements. Eadier considerations had suggested a closed shell at Z = 126, by analogy to the known shell at = 126, but this is not now considered to be important. 

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. 

Besides the crust and the hadron shell, the hybrid star contains also a quark core. Both the nucleon shell and the quark core can be in superconducting phases, in dependence on the value of the temperature. Fluctuations affect transport coefficients, specific heat, emissivity, masses of low-lying excitations and respectively electromagnetic properties of the star, like electroconductivity and magnetic field structure, e.g., renormalizing critical values of the magnetic field (/ ,, Hc, Hc2). 

On the other hand, closed nucleon shells stabilize the spherical form of nuclei, and according to the shell model appreciable fission barriers are expected in the region of closed nucleon shells (magic numbers). This led to the question of the next closed proton shell. First, Z = 126 was assumed to be the next magic number of protons, in analogy ioN = 126 (section 2.3). However, theoretical calculations revealed that the next closed proton shell is to be expected for Z = 114, whereas the next magic number of neutrons should be A — 184. Accordingly, an island of relative stability is expected at Z = 114 and N = 184. Other calculations lead to the predietion of an... 

Theoretical calculations of the stability of superheavy elements have to take into account all possible modes of decay - spontaneous fission, a decay and p decay. The energy barriers for spontaneous fission are assessed for nuclei with closed nucleon shells to be about 10 to 13 MeV with an error of 2 to 3 MeV which causes an uncertainty in the half-life of about 10 orders of magnitude. Calculations of the half-lives of a and P decay are less problematic, but they have also an uncertainty of about 3 orders of magnitude. Predictions of half-lives of >10 y for even-even nuclei in the region of 114 and of w lO y for " 110 led to an intense search for superheavy elements in nature, in particular by the group in Dubna (Flerov et al.). However, this search was not successful. 

Cold fusion by use of target nuclei with closed nucleon shells is most promising, because of the low excitation energies (emission of only 1 or 2 neutrons). However, the stabilizing effect of closed shells fades at excitation energies of the order ofSOMeV. 

Between the two extremes of the spheroidal liquid drop (and its rotational spectra) and of the nucleonic shell model, one might still imagine a niche for the presence of a-particles. Much like the helium atom has its first excited level (S = J = 1, L = 0) at higher energy than any other neutral atom, the first excited I-level reported32 of helium 4 occurs at 20.1 MeV (it may be noted from Eq.(6) that the energy needed to knock off a neutron is 19.80 MeV) and is totally symmetric. For the discussion below of the possible structure of baryons, it is very important to analyze the... 

Just as noble gases—with 2, 10, 18, 36, 54, and 86 electrons—are exceptionally stable because of their filled electron shells, nuclides with N or Z values of 2, 8, 20, 28, 50, 82 (and N = 126) are exceptionally stable. These so-called magic numbers are thought to correspond to the numbers of protons or neutrons in filled nucleon shells. A few examples are i N = 28), f Sr (A = 50), and the ten stable nuclides of tin (Z = 50). Some extremely stable nuclides have double magic numbers 2He, 0, 2oCa, and Pb (A = 126). 

It has long been recognized that the liquid-drop model semi-empirical mass equation cannot calculate the correct masses in the vicinity of neutron and proton magic numbers. More recently it was realized that it is less successful also for very deformed nuclei midway between closed nucleon shells. Introduction of magic numbers and deformations in the liquid drop model improved its predictions for deformed nuclei and of fission barrier heights. However, an additional complication with the liquid-drop model arose when isomers were discovered which decayed by spontaneous fission. Between uranium and... 

Some more recent calculations [28], based on careful consideration of the effect of mass asymmetry on the fission barrier and a reduced spin-orbit coupling strength, have indicated that the Z = 114 shell effect is not very large. These calculations do confirm the existence of a shell atN = 184, but also suggest less stability for species with N < 184 that is, the island of stability has a cliff with a sharp drop-off for N < 184. If these considerations are correct, it would become considerably more difficult to synthesize and detect the superheavy elements (defined as those elements stabilized by spherical closed-nucleon shells). A premium would be placed on produdng a nucleus with N = 184 or, very close to this, N = 183, in order that it might have a half-life sufficiently long to make it detectable. 

---