Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei

TL;DR

This paper uses a covariant model to analyze electromagnetic form factors and charge densities in hadrons and nuclei, highlighting relativistic effects and their impact on observable charge distributions.

Contribution

It provides an exact covariant calculation of form factors, clarifies the meaning of transverse density, and explores relativistic effects on charge distributions in hadrons and nuclei.

Findings

Rest-frame charge distribution is not observable due to current conservation failure.

Heavier constituents are closer to the transverse origin in neutral two-charged systems.

Relativistic effects significantly alter form factors, especially in nucleons and heavy nuclei.

Abstract

A simple exact covariant model in which a scalar particle is modeled as a bound state of two different particles is used to elucidate relativistic aspects of electromagnetic form factors. The model form factor is computed using an exact covariant calculation of the lowest-order triangle diagram and shown to be the same as that obtained using light-front techniques. The meaning of transverse density is explained using coordinate space variables, allowing us to identify a true mean-square transverse size directly related to the form factor. We show that the rest-frame charge distribution is generally not observable because of the failure to uphold current conservation. Neutral systems of two charged constituents are shown to obey the lore that the heavier one is generally closer to the transverse origin than the lighter one. It is argued that the negative central charge density of the neutron arises, in pion-cloud models, from pions of high longitudinal momentum. The non-relativistic limit is defined precisely and the ratio of the binding energy to that of the mass of the lightest constituent is shown to govern the influence of relativistic effects. The exact relativistic formula for the form factor reduces to the familiar one of the three-dimensional Fourier transform of a square of a wave function for a very limited range of parameters. For masses that mimic the quark-di-quark model of the nucleon we find substantial relativistic corrections for any value of $Q^2$. A schematic model of the lowest s-states of nuclei is used to find that relativistic effects decrease the form factor for light nuclei but increase the form factor for heavy nuclei. Furthermore, these states are strongly influenced by relativity.