Parameterization of deformed nuclei for Glauber modeling in relativistic heavy ion collisions

The density distributions of large nuclei are typically modeled with a Woods–Saxon distribution characterized by a radius R0R0 and skin depth a. Deformation parameters β   are then introduced to describe non-spherical nuclei using an expansion in spherical harmonics R0(1+β2Y20+β4Y40). But when a nucleus is non-spherical, the R0R0 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 β2β2 values typically derived from the reduced electric quadrupole transition probability B(E2)↑ are not directly related to the β2β2 values used in the spherical harmonic expansion. B(E2)↑ is more accurately related to the intrinsic quadrupole moment Q0Q0 than to β2β2. One can however calculate Q0Q0 for a given β2β2 and then derive B(E2)↑ from Q0Q0. In this paper we calculate and tabulate the R0R0, a  , and β2β2 values that when used in a Woods–Saxon distribution, will give results consistent with electron scattering data. We then present calculations of the second and third harmonic participant eccentricity (ε2ε2 and ε3ε3) with the new and old parameters. We demonstrate that ε3ε3 is particularly sensitive to a and argue that using the incorrect value of a   has important implications for the extraction of viscosity to entropy ratio (η/sη/s) from the QGP created in Heavy Ion collisions.