Argument
Nuclear shell model
Overview
In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model utilizes the Pauli exclusion principle to model the structure of atomic nuclei in terms of energy levels. The first shell model was proposed by Dmitri Ivanenko (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by several physicists, most notably Maria Goeppert Mayer and J. Hans D. Jensen, who received the 1963 Nobel Prize in Physics for their contributions to this model, and Eugene Wigner, who received the Nobel Prize alongside them for his earlier foundational work on atomic nuclei.
The nuclear 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 better stability. When adding nucleons (protons and 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 specific magic quantum numbers of nucleons (2, 8, 20, 28, 50, 82, and 126) that are more tightly bound than the following higher number is the origin of the shell model.
The shells for protons and neutrons are independent of each other. Therefore, there can exist both "magic nuclei", in which one nucleon type or the other is at a magic number, and "doubly magic quantum nuclei", where both are. Due to 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 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.
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 term is added. Even so, the total perturbation does not coincide with the experiment, and an empirical spin-orbit coupling must be added with at least two or three different values of its coupling constant, depending on the nuclei being studied.
The magic numbers of nuclei, 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 complicated potential is known as the Woods–Saxon potential.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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We have seen that the world of the atom is a world of revolution rather than evolution: the electron which has been moving in one orbit hops quite suddenly into another, so that the motion is what is called “discontinuous”, that is to say, the electron is first in one place and then in another, without having passed over any intermediate places. This sounds like magic, and there may be some way of avoiding such a…
Bertrand Russell, Philosophy
States what Nuclear shell model is.
But, after all, the nexus binding the many with one another is by no means a mere accident: as we have already remarked, the nexus is founded on their very nature. To Kant we owe the completed theory of matter as the unity of repulsion and attraction. The theory is correct, so far as it recognises attraction to be the other of the two elements involved in the notion of Being-for-self: and to be an element no less…
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Nuclear shell model is.
There is still a resource; the ultimate elements of bodies are electrons, some charged negatively, the others charged positively. The negative electrons have no mass, this is understood; but the positive electrons, from the little we know of them, seem much greater. Perhaps they have, besides their electrodynamic mass, a true mechanical mass. The real mass of a body would, then, be the sum of the mechanical masses…
Henri Poincaré, The Foundations of Science
States what Nuclear shell model is.
Related ideas
Place in the tradition
Part of Scientific realism.