Parameterization of Deformed Nuclei for Glauber Modeling in Relativistic 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 $R_0(1+{\beta }_2{Y}_2^0+{\beta }_4{Y}_4^0)$. 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 ${\epsilon }_2$ and ${\epsilon }_3$ with the new and old parameters. We demonstrate that ${\epsilon }_3$ 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.

6 pages, 6 figures

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