On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei

TLDR

The investigation examines nuclear multiplet structure using a spin‑independent, equal‑force Hamiltonian as a first approximation. The methodology employs a three‑step Hamiltonian: a first spin‑independent, equal‑force model; a second step that either adds spin forces (method 2) or distinguishes protons from neutrons (method 3); and a third step that combines both distinctions, with method 2 schematically developed to qualitatively reproduce the stable‑nucleus chart up to molybdenum. The results show that nuclear multiplets are characterized by three quantum numbers (S, T, Y) instead of a single spin, and that the spin‑dependent method 2 qualitatively explains the pattern of stable nuclei up to molybdenum.

Abstract

The structure of the multiplets of nuclear terms is investigated, using as first approximation a Hamiltonian which does not involve the ordinary spin and corresponds to equal forces between all nuclear constituents, protons and neutrons. The multiplets turn out to have a rather complicated structure, instead of the $S$ of atomic spectroscopy, one has three quantum numbers $S$, $T$, $Y$. The second approximation can either introduce spin forces (method 2), or else can discriminate between protons and neutrons (method 3). The last approximation discriminates between protons and neutrons in method 2 and takes the spin forces into account in method 3. The method 2 is worked out schematically and is shown to explain qualitatively the table of stable nuclei to about Mo.