Nucleus shell model

The above qualitative conclusions made on the basis of the results of [116, 124-127] correlate with the results of [129,130] in which the calculation is based on composite models with nucleus-shell inclusions. The authors illustrate this with the calculation of a system consisting of a hard nucleus and elastomeric shell in a matrix of intermediate properties, and a system where the nucleus and matrix properties are identical whereas the shell is much more rigid. The method may, however, be also applied to systems with inclusions where the nucleus is enclosed in a multi layer shell. Another, rather unexpected, result follows from [129,130] for a fixed inclusions concentration, the relative modulus of the system decreases with increasing nucleus radius/inclusion radius ratio, that is with decreasing shell thickness. 

To avoid confusion with the shells of the shell model of the nucleus we shall refer to the layers of spherons by special names the mantle for the surface layer, and the outer core and inner core for the two other layers of a three-layer nucleus. 

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. 

Sir Ernest Rutherford (1871-1937 Nobel Prize for chemistry 1908, which as a physicist he puzzled over) was a brilliant experimentalist endowed with an equal genius of being able to interpret the results. He recognized three types of radiation (alpha, beta, and gamma). He used scattering experiments with alpha radiation, which consists of helium nuclei, to prove that the atom is almost empty. The diameter of the atomic nucleus is about 10 000 times smaller than the atom itself. Furthermore, he proved that atoms are not indivisible and that in addition to protons, there must also be neutrons present in their nucleus. With Niels Bohr he developed the core-shell model of the atom. 

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. 

These are derived frum a. lensui force resulting from a coupling between individual pairs of nucleons and from the coupling between spin and orbital angular moments of the individual nucleus, as described by the shell model of the nucleus. 

Exotic atomic nuclei may be described as structures than do not occur in nature, but are produced in collisions. These nuclei have abundances of neurons and protons that are quite different from the natural nuclei. In 1949, M.G, Mayer (Argonne National Laboratory) and J.H.D. Jensen (University of Heidelberg) introduced a sphencal-shell model of die nucleus. The model, however, did not meet the requirements and restrains imposed by quantum mechanics and the Pauli exclusion principle, Hamilton (Vanderbilt University) and Maruhn (University of Frankfurt) reported on additional research of exotic atomic nuclei in a paper published in mid-1986 (see reference listedi. In addition to the aforementioned spherical model, there are several other fundamental shapes, including other geometric shapes with three mutually peipendicular axes—prolate spheroid (football shape), oblate spheroid (discus shape), and triaxial nucleus (all axes unequal). 

Quantum Number (Orbital). A quantum number characterizing the orbital angular momentum of an electron in an atom or of a nucleon in the shell-model description of the atomic nucleus. The symbol for the orbital quantum number is l. 

The simple shell model is very robust and is even successful in describing nuclei at the limits of stability. For example,1 Li is the heaviest bound lithium isotope. The shell model diagram for this nucleus is indicated in Figure 6.5. Notice the prediction... 

Figure 6.5 Energy level pattern and filling for the exotic nucleus nLi in the schematic shell model.

A1 is a nucleus with 13 protons and 13 neutrons. If we fill in the shell model energy level diagram from the bottom, we find the following configurations ... 

Au is a nucleus with 79 protons and 119 neutrons. Filling in the shell model energy level diagram we should find that the highest partially filled orbitals are... 

As we have seen, the nucleons reside in well-defined orbitals in the nucleus that can be understood in a relatively simple quantum mechanical model, the shell model. In this model, the properties of the nucleus are dominated by the wave functions of the one or two unpaired nucleons. Notice that the bulk of the nucleons, which may even number in the hundreds, only contribute to the overall central potential. These core nucleons cannot be ignored in reality and they give rise to large-scale, macroscopic behavior of the nucleus that is very different from the behavior of single particles. There are two important collective motions of the nucleus that we have already mentioned that we should address collective or overall rotation of deformed nuclei and vibrations of the nuclear shape about a spherical ground-state shape. 

To improve on this situation, we have used the Glasgow shell model code, rewritten to treat bosons [MOR80], to perform a least-squares fit to the excitation energies of a single nucleus using the IBM-2 Hamiltonian (1) without the Majorana term. In general, the model is applicable to only 10 to 12 experimentally known energy levels... 

Examples of large-basis shell-model calculations of Gamow-Teller 6-decay properties of specific interest in the astrophysical s-and r- processes are presented. Numerical results are given for i) the GT-matrix elements for the excited state decays of the unstable s-process nucleus "Tc and ii) the GT-strength function for the neutron-rich nucleus 130Cd, which lies on the r-process path. The results are discussed in conjunction with the astrophysics problems. 

The structures of the neutron-rich isotopes 97Y, 98Y and 99Y reflect with special clearness the rapid change of the nuclear shape at neutron number 60. The discovery of a new isomer in 97Y has provided evidence for the shell-model character of this nucleus even at high excitation energies while 99Y shows the properties of a symmetric rotor already in the ground state. The level pattern of the intermediate isotope 98Y indicates shape coexistence. 

Now, new information on 97Y has been obtained at the fission product separator JOSEF [LAW76] which indicates that this nucleus has shell model... 

Element abundance data were useful not only in astrophysics and cosmology but also in the attempts to understand the structure of the atomic nucleus. [74] As mentioned, this line of reasoning was adopted by Harkins as early as 1917, of course based on a highly inadequate picture of the nucleus. It was only after 1932, with the discovery of the neutron as a nuclear component, that it was realized that not only is the atomic mass number related to isotopic abundance, but so are the proton and neutron numbers individually. Cosmochemical data played an important part in the development of the shell model, first proposed by Walter Elsasser and Kurt Guggenheimer in 1933-34 but only turned into a precise quantitative theory in the late 1940s. [75] Guggenheimer, a physical chemist, used isotopic abundance data as evidence of closed nuclear shells with nucleon numbers 50 and 82. 

---