Multipole decomposition of potentials in relativistic heavy ion collisions

TL;DR

This paper presents an exact multipole decomposition of Lorentz-transformed Coulomb potentials in relativistic heavy ion collisions, addressing different impact parameters and gauge transformations to simplify the interaction at high energies.

Contribution

It introduces a precise multipole decomposition method for relativistic Coulomb potentials, including gauge transformations to eliminate certain dependencies, advancing theoretical understanding.

Findings

Derived exact multipole decomposition formulas.

Analyzed gauge transformations to remove $\

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Abstract

In relativistic heavy ion collisions an exact multipole decomposition of the Lorentz transformed time dependent Coulomb potentials in a coordinate system with equal constant, but opposite velocities of the ions, is obtained for both zero and different from zero impact parameter. The case of large values of $\gamma$ and the gauge transformation of the interaction removing both the $\gamma$ dependence and the $\ln b$ dependence are also considered.