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The atomic analog to nuclear magic numbers are those numbers of electrons leading to discontinuities in the ionization energy. These occur for the noble gases helium, neon, argon, krypton, xenon, radon and oganesson. Hence, the "atomic magic numbers" are 2, 10, 18, 36, 54, 86 and 118.
Some semi-magic numbers have been found, notably Z = 40, which gives the nuclear shell filling for the various elements; 16 may also be a magic number. [3] To get these numbers, the nuclear shell model starts with an average potential with a shape somewhere between the square well and the harmonic oscillator. To this potential, a spin-orbit ...
The numbers of nucleons for which shells are filled are called magic numbers. Magic numbers of 2, 8, 20, 28, 50, 82 and 126 have been observed for neutrons, and the next number is predicted to be 184. [6] [27] Protons share the first six of these magic numbers, [28] and 126 has been predicted as a magic proton number since the 1940s. [29]
The concept of magic numbers in the field of chemistry refers to a specific property (such as stability) for only certain representatives among a distribution of structures. It was first recognized by inspecting the intensity of mass-spectrometric signals of rare gas cluster ions. [ 1 ]
For example, observations of unstable isotopes have shown shifting and even a reordering of the single particle levels of which the shell structure is composed. [8] This is sometimes observed as the creation of an island of inversion or in the reduction of excitation energy gaps above the traditional magic numbers.
2.1 Nuclear structure. 2.2 Nuclear decay. ... Magic; Even/odd; Halo. Borromean; ... Z = Atomic number = Number of protons = Number of electrons
The formula gives a good approximation for atomic masses and thereby other effects. However, it fails to explain the existence of lines of greater binding energy at certain numbers of protons and neutrons. These numbers, known as magic numbers, are the foundation of the nuclear shell model.
For very small atomic mass number (H, He, Li), binding energy per nucleon is small, and this energy increases rapidly with atomic mass number. Nickel-62 (28 protons, 34 neutrons) has the highest mean binding energy of all nuclides, while iron-58 (26 protons, 32 neutrons) and iron-56 (26 protons, 30 neutrons) are a close second and third. [ 13 ]