Spin-orbit decomposition of ab initio wavefunctions

TL;DR

This paper demonstrates that decomposing ab initio wavefunctions into spin and orbital angular momentum components reveals a simple coupling scheme in light nuclei, aligning with phenomenological models despite modern computational complexity.

Contribution

It introduces a method to analyze ab initio wavefunctions through L-S decomposition, bridging modern calculations with traditional phenomenological models.

Findings

Broad agreement with Cohen-Kurath force calculations

L-S coupling scheme is useful for analyzing light nuclei

Decomposition aligns with older phenomenological models

Abstract

Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum $j$, leading to $j$-$j$ coupling, phenomenological models suggested decades ago that for $0p$-shell nuclides a simpler picture can be realized via coupling of total spin $S$ and total orbital angular momentum $L$. I revisit this idea with large-basis, no-core shell model (NCSM) calculations using modern \textit{ab initio} two-body interactions, and dissect the resulting wavefunctions into their component $L$- and $S$-components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly fifty years and six orders of magnitude in basis dimensions. I suggest $L$-$S$ may be a useful tool for analyzing \textit{ab initio} wavefunctions of light nuclei, for example in the case of rotational bands.