Application of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>jj</mml:mi></mml:math>-Coupling Model to Moderately Light Nuclei

Abstract

An investigation based on the strong spin-orbit coupling model is made for nuclei in the $1{d}_{\frac{3}{2}}$ and $1{f}_{\frac{7}{2}}$ shells. Hartree-Fock wave functions and central forces are used in calculating ground state spins and binding energy differences. Coupling rules are found for configurations of identical nucleons and for the simplest odd-odd nuclei. Approximate wave functions are constructed for odd-$A$ and even-even nuclei having both neutrons and protons in the $1{f}_{\frac{7}{2}}$ shell. Binding energy differences, magnetic moments, and beta decay matrix elements are calculated with these functions. The result of comparing binding energy differences with experiment is interpreted as favoring strong spin-orbit coupling over weak spin-orbit coupling.