Nucleus, atomic shell model

Atom-kem, m. atomic nucleus, -kette,/. chain of atoms, atomic chain, -lage, /. atomic layer atomic position, -lehre, /, doctrine of atoms, atomic theory, -mechanik, /. mechanics of the atom, -modell, n, atomic model, -nummer, /, atomic number, -ord-nung, /. atomic arrangement, -refraktion, /. atomic refraction, -rest, m. atomic residue (= Atomrumpf). -ring, m. ring of atoms, -rumpf, m. atomic residue or core (remainder of an atom, as after removal of some electrons), -schale, /, atomic shell, -strabl, m. atomic ray, -tafel, /, atomic table, atomtbeoretisch, a. of or according to the atomic theory,... 

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. 

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. 

In order to improve the theoretical description of a many-body system one has to take into consideration the so-called correlation effects, i.e. to deal with the problem of accounting for the departures from the simple independent particle model, in which the electrons are assumed to move independently of each other in an average field due to the atomic nucleus and the other electrons. Making an additional assumption that this average potential is spherically symmetric we arrive at the central field concept (Hartree-Fock model), which forms the basis of the atomic shell structure and the chemical regularity of the elements. Of course, relativistic effects must also be accounted for as corrections, if they are small, or already at the very beginning starting with the relativistic Hamiltonian and relativistic wave functions. 

Calculations by Gryzinski and Kowalski (1993) for inner shell ionization by positrons also confirmed the general trend. Theirs was essentially a classical formulation based upon the binary-encounter approximation and a so-called atomic free-fall model, the latter representing the internal structure of the atom. The model allowed for the change in kinetic energy experienced by the positrons and electrons during their interactions with the screened field of the nucleus. 

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. 

The principal quantum number n may have positive integer values (1, 2, 3,. ..). n is a measure of the distance of an orbital from the nucleus, and orbitals with the same value of n are said to be in the same shell. This is analogous to the Bohr model of the atom. Each shell may contain up to 2n2 electrons. 

To further illustrate the importance of coupling the electrostatic and short-ranged repulsion interactions, we consider the example of a dimer of polarizable rare gas atoms, as presented by Jordan et al. In the absence of an external electric field, a PPD model predicts that no induced dipoles exist (see Eq. [12]). But the shell model correctly predicts that the rare gas atoms polarize each other when displaced away from the minimum-energy (force-free) configuration. The dimer will have a positive quadrupole moment at large separations, due to the attraction of each electron cloud for the opposite nucleus, and a negative quadrupole at small separations, due to the exchange-correlation repulsion of the electron clouds. This result is in accord with ab initio quantum calculations on the system, and these calculations can even be used to help parameterize the model. ... 

Electron distribution is affected by the presence of external electric fields and the polarisation interaction that arises in the presence of other atoms. One of the most common models to take into accoimt polarisation is the shell model. In the shell model the total charge of the atom is distributed between the nucleus and a mass-less spherical shell. This shell is connected to the nucleus by a spring of a given force constant. 

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