Abstract
A crystalline solid model for nuclei: equivalent to the shell model, independent particle model, spheron model, and collective model: arises from Langmuir's Volume Exclusion Principle. Protons (or neutrons) are considered to be located in concentric spherical shells numbered n = 1, 2, 3, — of radii r = nr°, thickness d = r° and volume V = 4π(nr°)2 d. With volume 2 π r°2 d for each particle, the number of protons (or neutrons) in filled shells equals numbers by Pauli Exclusion Principle. Shells are sub-divided into zones specified by orbital (l), spin (s), resultant (j), and component (mj) angular momentum quantum numbers. The order of filling zones with protons (or neutrons) follows successive series of even numbers 2; 4, 2; 6, 4, 2; 8, 6, 4, 2; — corresponding to the maximum number of particles with j = 1/2; 3/2, 1/2; 5/2, 3/2, 1/2; 7/2, 5/2, 3/2; —. Shell number, orbital quantum number, and j; in order of filling are specified as 1s1/2; 2p3/2, 2p1/2; 3d5/2, 3d3/2, 2s1/2; 4f7/2, 4f5/2, 3p3/2, 3p1/2, 5g9/2, —–. Magic numbers are the total protons, or neutrons, when the first j zone in a shell is filled. There is one magic number for each shell. The magic number Mn for shell n is related to the next smaller magic number M(n−1) by▪.
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