Parameterization of Deformed Nuclei for Glauber Modeling in Relativistic Heavy Ion Collisions

TL;DR

This paper refines the parameters for modeling deformed nuclei in Glauber models, ensuring consistency with electron scattering data, and explores how these parameters affect eccentricity calculations relevant to heavy ion collision analysis.

Contribution

It provides a new set of parameters for Woods-Saxon distributions that align with experimental data and discusses their impact on eccentricity and quark-gluon plasma properties.

Findings

New parameters for R0, a, and β2 consistent with electron scattering data.

Eccentricity ε3 is highly sensitive to the skin depth a.

Incorrect a values can significantly affect η/s extraction in heavy ion collisions.

Abstract

The density distributions of large nuclei are typically modeled with a Woods-Saxon distribution characterized by a radius $R_{0}$ and skin depth $a$. Deformation parameters $\beta$ are then introduced to describe non-spherical nuclei using an expansion in spherical harmonics $R_{0}(1+\beta_2Y^0_2+\beta_4Y^0_4)$. But when a nucleus is non-spherical, the $R_{0}$ and $a$ inferred from electron scattering experiments that integrate over all nuclear orientations cannot be used directly as the parameters in the Woods-Saxon distribution. In addition, the $\beta_2$ values typically derived from the reduced electric quadrupole transition probability B(E2)$\uparrow$ are not directly related to the $\beta_2$ values used in the spherical harmonic expansion. B(E2)$\uparrow$ is more accurately related to the intrinsic quadrupole moment $Q_{0}$ than to $\beta_2$. One can however calculate $Q_0$ for a given $\beta_2$ and then derive B(E2)$\uparrow$ from $Q_0$. In this paper we calculate and tabulate the $R_0$, $a$, and $\beta_2$ values that when used in a Woods-Saxon distribution, will give results consistent with electron scattering data. We then present calculations of the eccentricity $\varepsilon_2$ and $\varepsilon_3$ with the new and old parameters. We demonstrate that $\varepsilon_3$ is particularly sensitive to $a$ and argue that using the incorrect value of $a$ has important implications for the extraction of $\eta/s$ from the QGP created in Heavy Ion collisions.