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Physics Letters B 749 (2015) 215–220

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Parameterization of deformed nuclei for Glauber modeling

in relativistic heavy ion collisions

Q.Y. Shou

a,b,∗

, Y.G. Ma

, P. Sorensen

, A.H. Tang

, F. Videbæk

, H. Wang

Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China

Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China

Brookhaven National Laboratory, Upton, NY 11973, USA

a r t i c l e i n f o a b s t r a c t

Article history:

Received

26 March 2015

Received

in revised form 30 July 2015

Accepted

30 July 2015

Available

online 4 August 2015

Editor:

V. Metag

The density distributions of large nuclei are typically modeled with a Woods–Saxon distribution

characterized by a radius R

and skin depth a. Deformation parameters β are then introduced to

describe non-spherical nuclei using an expansion in spherical harmonics R

(1 +β

+β

). But when

a nucleus is non-spherical, the R

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 β

values typically derived from the reduced electric quadrupole transition probability

B(E2)↑ are not directly related to the β

values used in the spherical harmonic expansion. B(E2)↑ is

more accurately related to the intrinsic quadrupole moment Q

than to β

. One can however calculate

for a given β

and then derive B(E2)↑ from Q

. In this paper we calculate and tabulate the R

, a,

and β

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

(ε

and ε

) with the new and old parameters. We demonstrate that ε

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/s ) from the QGP created in Heavy Ion collisions.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

In relativistic nucleus–nucleus collisions, the geometry of the

initial overlap region is reﬂected in the ﬁnal momentum space

distributions of produced particles [1–3]. How much that geom-

etry

is translated into the ﬁnal state distributions is used to infer

information about the properties of the matter created in the col-

lision

ﬁreball like its viscosity [4]. The initial geometry plays a

particularly important role in interpreting the data and in extract-

ing

the viscosity to entropy ratio η/s. It is important therefore to

understand the initial conditions including the exact shape of the

colliding nuclei. The inference of the properties of the ﬁreball from

data is hindered by uncertainties in the characteristics of the ini-

tial

state [5]. Recently collisions between Uranium nuclei (

238

which have an intrinsic prolate shape [6], have been used as a

way to manipulate this initial geometry in order better test our

understanding of the initial state of heavy ion collisions and the

subsequent ﬁreball [7,8].

Corresponding author.

E-mail

address: qiye.shou@cern.ch (Q.Y. Shou).

An important part of describing the initial conditions is to cor-

rectly

model the geometry of the incoming nuclei. For many years

in simulations for heavy ion collisions, nuclei were approximated

as smooth density distributions and the only anisotropies consid-

ered

in the initial state were the intrinsic almond shape caused by

the overlap of two spherical nuclei. As the accumulation of RHIC

data gradually demonstrated that ﬁnal state anisotropies were sen-

sitive

to the initial geometry and its ﬂuctuations, it became nec-

essary

to take into account the lumpiness of the colliding nuclei

[9–14]. This is done through Monte-Carlo simulations (M-C) where

each nucleus is generated with a ﬁnite number of nucleons dis-

tributed

with a density ρ described by a Woods–Saxon distribu-

tion [15]:

ρ(r) =

1 +e

(r−R

)/a

, (1)

where ρ

is the density at the center of the nucleus. The nuclear

radius R

and skin depth a are commonly taken from high-energy

electron scattering measurements [16]. For non-spherical nuclei,

this description was extended by introducing spherical harmon-

ics

in the Woods–Saxon distribution to describe the modulation of

http://dx.doi.org/10.1016/j.physletb.2015.07.078

0370-2693/

SCOAP

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