Including nuclear degrees of freedom in a lattice Hamiltonian

TL;DR

This paper introduces a novel Hamiltonian model that integrates nuclear degrees of freedom into lattice systems using a relativistic Dirac formalism, revealing new coupling effects and nuclear excitation mechanisms.

Contribution

It develops a new fundamental Hamiltonian incorporating nuclear states into lattice models via a relativistic approach, addressing previous challenges in separating nuclear center of mass and relative motions.

Findings

Derived a Hamiltonian coupling lattice and nuclear states.

Identified new terms enabling nuclear excitation through lattice interactions.

Revealed effects of Lorentz boosts on nuclear state dynamics.

Abstract

Motivated by many observations of anomalies in condensed matter systems, we consider a new fundamental Hamiltonian in which condensed matter and nuclear systems are described initially on the same footing. Since it may be possible that the lattice will respond to the mass change associated with a excited nuclear state, we adopt a relativistic description throughout based on a many-particle Dirac formalism. This approach has not been used in the past, perhaps due to the difficulty in separating the center of mass and relative degrees of freedom of the nuclear system, or perhaps due to an absence of applications for such a model. In response to some recent ideas about how to think about the center of mass and relative separation, we obtained from the Dirac model a new fundamental Hamiltonian in which the lattice couples to different states within the composite nuclei within the lattice. In this description the different nuclear states have different mass energies and kinetic energies, as we had expected. In addition there appear new terms which provide for nuclear excitation as a result of coupling to the composite momentum. This new effect comes about because of changes in the composite nuclear state as a result of the dynamical Lorentz boost in the lattice.