# The many-nucleon theory of nuclear collective structure and its macroscopic limits: an algebraic perspective

## TL;DR

This paper reviews the evolution of nuclear collective models, demonstrating how macroscopic Bohr-Mottelson models emerge as limits of microscopic many-nucleon quantum mechanics, enabling reassessment of nuclear properties.

## Contribution

It provides an algebraic framework showing the microscopic foundations of collective models as their macroscopic limits, bridging the gap between quantum mechanics and nuclear phenomenology.

## Key findings

- Macroscopic models are derived as limits of microscopic quantum models
- Reassessment of nuclear properties based on microscopic foundations
- Algebraic perspective clarifies the connection between models

## Abstract

The nuclear collective models introduced by Bohr, Mottelson and Rainwater, together with the Mayer-Jensen shell model, have provided the central framework for the development of nuclear physics. This paper reviews the microscopic evolution of the collective models and their underlying foundations. In particular, it is shown that the Bohr-Mottelson models have expressions as macroscopic limits of microscopic models that have precisely-defined expressions in many-nucleon quantum mechanics. Understanding collective models in this way is especially useful because it enables the analysis of nuclear properties in terms of them to be revisited and reassessed in the light of their microscopic foundations.