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In nuclear physics and nuclear chemistry, the nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels.〔(【引用サイトリンク】url=http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html )〕 The first shell model was proposed by Dmitry Ivanenko (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by several physicists, most notably Eugene Paul Wigner, Maria Goeppert Mayer and J. Hans D. Jensen, who shared the 1963 Nobel Prize in Physics for their contributions. The shell model is partly analogous to the atomic shell model which describes the arrangement of electrons in an atom, in that a filled shell results in greater stability. When adding nucleons (protons or neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. This observation, that there are certain magic numbers of nucleons: 2, 8, 20, 28, 50, 82, 126 which are more tightly bound than the next higher number, is the origin of the shell model. The shells for protons and for neutrons are independent of each other. Therefore, one can have "magic nuclei" where one nucleon type or the other is at a magic number, and "doubly magic nuclei", where both are. Due to some variations in orbital filling, the upper magic numbers are 126 and, speculatively, 184 for neutrons but only 114 for protons, playing a role in the search for the so-called island of stability. Some semimagic numbers have been found, notably Z=40 giving nuclear shell filling for the various elements; 16 may also be a magic number.〔 (this refers to the nuclear drip line)〕 In order to get these numbers, the nuclear shell model starts from an average potential with a shape something between the square well and the harmonic oscillator. To this potential a spin orbit term is added. Even so, the total perturbation does not coincide with experiment, and an empirical spin orbit coupling, named the Nilsson Term, must be added with at least two or three different values of its coupling constant, depending on the nuclei being studied. Nevertheless, the magic numbers of nucleons, as well as other properties, can be arrived at by approximating the model with a three-dimensional harmonic oscillator plus a spin-orbit interaction. A more realistic but also complicated potential is known as Woods Saxon potential. Igal Talmi developed a method to obtain the information from experimental data and use it to calculate and predict energies which have not been measured. This method has been successfully used by many nuclear physicists and has led to deeper understanding of nuclear structure. The theory which gives a good description of these properties was developed. This description turned out to furnish the shell model basis of the elegant and successful Interacting boson model. ==Deformed harmonic oscillator approximated model== Consider a three-dimensional harmonic oscillator. This would give, for example, in the first two levels (''"l"'' is angular momentum) We can imagine ourselves building a nucleus by adding protons and neutrons. These will always fill the lowest available level. Thus the first two protons fill level zero, the next six protons fill level one, and so on. As with electrons in the periodic table, protons in the outermost shell will be relatively loosely bound to the nucleus if there are only few protons in that shell, because they are farthest from the center of the nucleus. Therefore nuclei which have a full outer proton shell will have a higher binding energy than other nuclei with a similar total number of protons. All this is true for neutrons as well. This means that the magic numbers are expected to be those in which all occupied shells are full. We see that for the first two numbers we get 2 (level 0 full) and 8 (levels 0 and 1 full), in accord with experiment. However the full set of magic numbers does not turn out correctly. These can be computed as follows: :In a three-dimensional harmonic oscillator the total degeneracy at level n is . Due to the spin, the degeneracy is doubled and is . :Thus the magic numbers would be : :for all integer k. This gives the following magic numbers: 2,8,20,40,70,112..., which agree with experiment only in the first three entries. These numbers are twice the tetrahedral numbers (1,4,10,20,35,56...) from the Pascal Triangle. In particular, the first six shells are: * level 0: 2 states (''l'' = 0) = 2. * level 1: 6 states (''l'' = 1) = 6. * level 2: 2 states (''l'' = 0) + 10 states (''l'' = 2) = 12. * level 3: 6 states (''l'' = 1) + 14 states (''l'' = 3) = 20. * level 4: 2 states (''l'' = 0) + 10 states (''l'' = 2) + 18 states (''l'' = 4) = 30. * level 5: 6 states (''l'' = 1) + 14 states (''l'' = 3) + 22 states (''l'' = 5) = 42. where for every ''l'' there are 2''l''+1 different values of ''ml'' and 2 values of ''ms'', giving a total of 4''l''+2 states for every specific level. These numbers are twice the values of triangular numbers from the Pascal Triangle: 1,3,6,10,15,21.... 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「nuclear shell model」の詳細全文を読む スポンサード リンク
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