Nucleus magic number

Acts only over a very short distance, approximately the diameter of the nucleus Magic numbers... 

The Structural Basis of the Magic Numbers.—Elsasser10 in 1933 pointed out that certain numbers of neutrons or protons in an atomic nucleus confer increased stability on it. These numbers, called magic numbers, played an important part in the development of the shell model 4 s it was found possible to associate them with configurations involving a spin-orbit subsubshell, but not with any reasonable combination of shells and subshells alone. The shell-model level sequence in its usual form,11 however, leads to many numbers at which subsubshells are completed, and provides no explanation of the selection of a few of them (6 of 25 in the range 0-170) as magic numbers. 

Summary.—The assumption that atomic nuclei consist of closely packed spherons (aggregates of neutrons and protons in localized Is orbitals—mainly helions and tritions) in concentric layers leads to a simple derivation of a subsubshell occupancy diagram for nucleons and a simple explanation of magic numbers. Application of the close-packed-spheron model of the nucleus to other problems, including that of asymmetric fission, will be published later.13... 

The close-packed-spheron theory leads to a simple structural interpretation of the magic numbers (16) they are the numbers at which each layer of the nucleus achieves completion of... 

The arrangement of 22 spherons around an inner tetrahedron of four spherons shown in Fig. 7 involves icosahedral packing each of the four inner spherons is surrounded by an icosahedron of 12, three of which are the three other inner spherons. This structure (26 spherons, 52 neutrons) with one spheron missing may be assigned to magic number 50. The complete structure, with 26 spherons, corresponds to the stable nucleus as discussed in the following section. 

Alpha (a.) decay. As we shall see later, the alpha particle, which is a helium nucleus, is a stable particle. For some unstable heavy nuclei, the emission of this particle occurs. Because the a particle contains a magic number of both protons and neutrons (2), there is a tendency for this particular combination of particles to be the one emitted rather than some other combination such as s3Li. In alpha decay, the mass number decreases by 4 units, the number of protons decreases by 2, and the number of neutrons decreases by 2. An example of alpha decay is the following ... 

The magic numbers which impart stability to a nucleus are 2, 8, 20, 28, 50, 82 or 122. The isotope, 39K, has a magic number equal to its number of neutrons, so it is probably stable. The others have a larger neutron-to-proton ratio, making them neutron-rich nuclei, so 40K and 41K might be expected to decay by beta emission. In fact, both 39K and 41K are stable, and 40K does decay by beta emission. 

Scientists have known that nuclides which have certain "magic numbers" of protons and neutrons are especially stable. Nuclides with a number of protons or a number of neutrons or a sum of the two equal to 2, 8, 20, 28, 50, 82 or 126 have unusual stability. Examples of this are He, gO, 2oCa, Sr, and 2gfPb. This suggests a shell (energy level) model for the nucleus similar to the shell model of electron configurations. 

Aggregation of the atoms or microclusters may give metal nuclei. The micro-cluster itself may work as the nucleus. Although the size of microcluster or nucleus is not clear, the nucleus may consist of 13 atoms, which is the smallest magic number, This idea may be supported by the structural analysis of PVP-stabilized Pt nanoparticles (64) and other systems. In fact, a particle of 13 atoms is considered an elemental duster. In the case of preparation of PVP-stabilized Rh nanoparticle dispersions by alcohol reduction, formation of very tiny particles, the average diameter of which is estimated to be 0.8 nm, was observed (66). These tiny particles in the metastable state may consist of 13 atoms each and easily increase in size to the rather nanoparticles with average diameter of 1.4 nm, i.e., the particles composed of 55 atoms. This observation again supports the idea that the elemental cluster of 13 atoms is the nucleus. 

Fmmi Magic numbers for nuclei are /1 / analogous to noble-gas electron configurations for atoms. A nucleus with 2,8,20, 28, 50, 82, or 126 protons or neutrons is particularly stable, just as an atom having a noble-gas electron configuration with 2,10,18,36,54, or 86 electrons tends to be stable. 

IV has a larger neutron binding energy than any heather odd-A nucleus, a consequence of its magic number N = 28 neutrons. It is one of jive elements (Ca, Ti, V, Cr, and Fe) having a stable isotope with 28 neutrons, a record exceeded only by N = 82 neutrons. 

Theoreticians thought that stable heavier elements might be in prospect. The stability of a nucleus (based on a model of nuclear stability analogous to that of the Rutherford-Bohr model of electronic structure) is determined by the inter-nucleon forces (nucleons are protons and neutrons), an attractive force between all nucleons and a Coulombic repulsion force between protons, the latter becoming proportionately more important as the number of protons increases. Extra stability is associated with filled shells of nucleons, magic numbers for neutrons they are 2,8,20,28,50,82,126,184, and 196 and for protons they are 2, 8, 20, 28, 50, 82, 114, and 164. 

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. 

In addition to the proton magic number 114, a second superheavy magic proton number was investigated M. Z —164 [23, 28). Although the realization of such a nucleus seems to be far from any practical possibility at the moment, one should bear this region in mind because many most interesting questions could be answered if it were possible to produce these elements. One way to actually proceed... 

---