# The many-nucleon unified model and the dynamics of nuclear rotations

## TL;DR

This paper demonstrates that the symplectic model uniquely extends the Bohr-Mottelson unified model to many nucleons, providing insights into nuclear rotation dynamics and revealing that rotational energies are mixtures of potential and kinetic energies.

## Contribution

It establishes the symplectic model as the unique many-nucleon extension of the unified model, enabling detailed analysis of nuclear rotation dynamics.

## Key findings

- Rotational energies are mixtures of potential and kinetic energies.
- The symplectic model spans the Hilbert space of fully anti-symmetric nuclear states.
- Provides a framework for examining nuclear rotation dynamics.

## Abstract

It is determined that a many-nucleon version of the Bohr-Mottelson unified model that contains the essential observables of that model and has irreducible representations that span the Hilbert space of fully anti-symmetric states of nuclei, is given uniquely by the symplectic model. This model is shown to provide a framework for an examination of the dynamics of nuclear rotations. A first discovery is that rotational energies are mixtures of potential and kinetic energies even in an adiabatic limit.