Coupling between a deuteron and a lattice

TL;DR

This paper explores a novel lattice Hamiltonian linking electron and deuteron nuclear states, calculating the coupling matrix element for deuteron internal transitions to understand energy transfer mechanisms.

Contribution

It introduces a new fundamental lattice Hamiltonian incorporating nuclear-electronic coupling, with calculations based on the Hamada-Johnston model for deuteron states.

Findings

Coupling matrix element for deuteron states calculated as 2.98 x 10^{-3} M_J c \, \hat{P}_z.

Deuteron triplet states couple to a virtual singlet P state at 125 MeV.

Potential connection between nuclear transitions and lattice vibrations suggested.

Abstract

We recently put forth a new fundamental lattice Hamiltonian based on an underlying picture of electrons and deuterons as elementary Dirac particles. Within this model there appears a term in which lattice vibrations are coupled to internal nuclear transitions. This is interesting as it has the potential to provide a connection between experiment and models that describe coherent energy transfer between two-level systems and an oscillator. In this work we describe a calculation of the coupling matrix element in the case of the deuteron based on the old empirical Hamada-Johnston model for the nucleon-nucleon interaction. The triplet S and D states of the the deuteron in the rest frame couples to a singlet P state through this new interaction. The singlet P state in this calculation is a virtual state with an energy of 125 MeV, and a coupling matrix element for $z$-directed motion given by $2.98 \times 10^{-3} ~M_J c \hat{P}_z$.