Magic number (physics)

As Magic numbers are called in nuclear physics certain neutron and proton numbers in atomic nuclei, in which the ground state of the core higher stability is observed than in neighboring nuclides. Such cores themselves are also called magic nuclei. The magic numbers can be explained by the shell model of nuclear physics. On this basis, islands of stability can be predicted with atomic numbers above the naturally occurring elements.

Stability properties

Higher stability among others, the following observed properties are meant:

• Elements with magic proton numbers are quantitatively particularly strong presence in the universe.
• The binding energy per nucleon is particularly high. This is evident for example in the high energies of alpha and beta decays, which lead to magic nuclei.
• The excitation energy of the first excited state of a magical core is particularly high.
• In magic number of protons exist particularly many stable isotopes in magic neutron number especially many stable isotones.
• The cross section of the nucleus for neutron capture and released in the neutron energy are particularly small.
• The quadrupole moment of the nucleus in the initial state has a minimum, indicating a relatively symmetrical distribution of the spherical electrical charge on the magic numbers.

The observable in this way magic numbers are 2, 8, 20, 28, 50, 82 and 126, the 126 has so far been observed only for neutrons because nuclides with such a high atomic number ( number of protons ) do not occur naturally and artificially not yet be made could.

As an example, shows the accompanying picture a nuclear chart with color coding of the cross section for neutron capture. The magic proton and neutron numbers are highlighted by double lines. It is evident that this cross section in magic nuclei usually small, far away from magic numbers, however, is large.

Physicists at RIKEN in Japan have discovered in experiments also another magic number for neutron. Thus, the isotope calcium -54, composed of 20 protons and 34 neutrons, protons and neutron magic number.

Doubly magic nuclei

Doubly magic called a nuclide when its protons and its neutrons are magical. The stability properties mentioned above are particularly pronounced. Four doubly magic nuclides are also stable in an absolute sense, that is, non-radioactive helium -4, oxygen -16, calcium -40 and lead - 208. More doubly magic nuclides are calcium -48 ( with the half-life of about 6 × 1018 years "almost" absolutely stable ), nickel -56, nickel -78, tin -110 and tin - 132; although they are radioactive because of their too large or too small neutron excess, but show relatively increased stability compared with their Nachbarnukliden, recognizable, for example, on their half-lives.

Statement by the shell model

Natural elements

The shell model of the atomic nucleus explains the magic numbers so that, ( to put it simply ) that there in each case the outermost "shell" fully staffed, so complete, similar to the chemically stable noble gases have completed outer shells characterized by its electron shell. Such degrees - ie a finite maximum number of identical particles that can occupy a particular energy level in a potential field - occurred in the quantum mechanics of fermions due to the Pauli principle generally on.

Artificially generated elements

Above the naturally occurring proton and neutron numbers, the theory predicts more shell closures, ie magic numbers. For protons resulting from sub- shell closures, the numbers 114 and 120 In fact, the half-life of first observed in an experiment in 1999 nuclide Flerovium -289, containing 114 protons with 2.7 seconds conspicuously long. The doubly magic Fl 298 184 neutrons could not be observed, even though an even longer half-life is to be expected for this. A whole island of stability ( a term coined by Glenn Seaborg term ) with this doubly magic nuclide as the center is suspected ( see figure). The term stability can only be understood relative to the surrounding nuclides; absolutely stable nuclides without any spontaneous decay, that is, with the half-life are infinite, to be expected beyond lead hardly. Similar "islands" are also expected in the vicinity of magic atomic numbers 120 and 126. They would cluster around the undiscovered doubly magic nuclides Unbinilium - 304, or Unbihexium - 310.

Are produced experimental investigation of these nuclides by fusion of heavy nuclei by means of heavy ion accelerators. The main difficulty to achieve nuclides such as the Unbinilium, lies in the fact that must be used as a target and as a projectile nuclides with sufficiently high neutron excess; these are generally unstable itself, and not available in large quantity.

Statement by group theory

In a work published in 2010, it is reported that the magic proton and neutron numbers also arise from group-theoretical considerations, without assuming a certain potential form.