u+u collisions at rhic

David L. Winter

U+U Collisions at RHIC

Columbia Experimental Heavy-Ion Research Group Journal Club

27 Feb 2007

27 Feb 2007 D.Winter: U+U Collisions at RHIC

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Outline• Introduction to the 238U nucleus

– Fun facts– Definition of quadrupole moment

• How do we accelerate ions at RHIC?– Overview– Tandem source/acceleration– Onward to RHIC

• U+U Collisions– Anisotropic Flow and Jet Quenching – Multiplicity distribution and source

deformation


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238U


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Fun facts about Uranium

• Z = 92, A=233, 235, 238 (three natural isotopes)• Not rare – more common than beryllium or tungsten • Solid at 298 K • Metallic grey in color

Isotope Atomic Mass

(ma/u)

Natural Abundance

(atom %)

Nuclear Spin

(I)

Magnetic Moment

(/N)

Q

(barn)

233U 234.04 0.0055 0 0

235U 235.04 0.7200 7/2 -0.35 4.936

238U 238.05 99.2745 0 0

197Au 196.96 100 3/2 0.14 0.547

63Cu 62.92 69.17 3/2 2.22 -0.22


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Electric Quadrupole Moments

• Non-zero quadrupole moment indicates that the charge distribution is not spherically symmetric

• Q0 is the classical form of the calculation– Represents the departure from spherical symmetry in

the rest frame of the nucleus• Q is the quantum mechanical form

– Takes into account the nuclear spin I and projection K in the z-direction

Q(U)>0


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Accelerating Ions at RHIC


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Overview of the Transport to RHIC• LINAC for source of

protons• Two Tandem Van-der-

Graff accelerators available– Allows asymmetric

collisions, for example

• Heavy-ion Transfer Line

• AGS Booster• AGS• AGS-to-RHIC Transfer

Line


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Originating Source of Heavy Ions

• Positive Cs ions strike sputter target• Ions emerging from target have picked up one

electron• Ions accelerated thru extraction potential of

approximately 25 kV


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Accelerating Ions at the Tandem

• Beam passing thru carbon foils strips off electrons• Multiple stages of acceleration/stripping used (2 or 3 depending on

A of species)• Au Ions exit the tandem in +32 state


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Tandem to RHIC

• Heavy Ion Transfer Line transports ions (with no additional stripping or acceleration) to the Booster

• Foil at the Booster exit strips all but two tightly bound K-shell electrons– Au ions exit the booster at 95 MeV/A with +77 charge

• AGS accelerates (Au) bunches to ~9 GeV/A• At the AGS exit, ions are fully stripped• Transported to RHIC via the AGS-to-RHIC (AtR) line• In ~ 2 min, RHIC can acclerate ions to top energy


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Current Capabilities of RHIC• RHIC can accelerate range of species from p to

Au– Which ions specifically? Those which can be easily

produced from a sputter source• Major issue: U does not form an abundant

negative ion, making acceleration from sputter target a challenge– Using a sputter target drilled out in the middle to allow

O2 into bleed in – result: UO- ions accelerated (Benjamin et al. 1999)

• “Uranium is a viable species but must be considered as a future upgrade, since at present, an adequate source for Uranium does not exist at Brookhaven and further R & D will be needed to achieve this goal”– H. Hahn et al., NIM A488 (2003) 245-263


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Future Capabilities of RHIC

EBIS: Electron Beam Ion Source • Replace 35-year-old tandem by

2009• Advantages:

– Simpler operation at lower cost– Simpler booster injection– New species available: U, 3He

Scaled results from½ length prototype exceed RHIC needs


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Location of EBISW

. Fisch

er,

PA

NIC

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U+U: Anisotropy and Jet Quenching


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1a. U+U: Anisotropic Flow

• The final momentum anisotropy v2 is driven by the initial spatial eccentricity x

• Systematic studies of v2 at midrapidity in Au+Au and Pb+Pb of different centralities show:– v2/ x scales with

• Predictions from ideal hydro agree with data only in the highest RHIC energy at almost central Au+Au collisions– Need to increase beyond the ~ 25 fm-2

available in central Au+Au

• U+U to the rescue: full-overlap collisions could achieve ~ 40 fm-2

0

1s

dy

dN

Sch (initial entropy density of overlap region)

dy

dN

Sch1


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1b. U+U: Jet Quenching

• Experiments show that in semi-peripheral Au+Au collisions fast partons suffer more energy loss in the direction perpendicular to the RP compared to the in-plane direction

• Small size of fireball in semi-periph Au+Au lacks resolving power of the path length difference between in- and out-of-plane directions

• Again, full-overlap U+U to the rescue


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Full-overlap (b=0 and coplanar) U+U Collisions

“Side-on-side”“Tip-on-tip”

Or “Edge-on-edge”

Initial entropy density in transverse

plane @ z=0

Wounded nucleon density

Binary collision density

= 0.75, from fit to Au+Aus tuned to central Au+Au also

Very important assumption: we can select these collisions with tight spectator cuts


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Initial Energy and Entropy Density vs. Npart

Conversion of entropy density to energy density assumes ideal quark-gluon gass EOS

Larger energy density in central U+U yields larger lever arm to probe approach to ideal hydro


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Multiplicity and Eccentricity Probabilities

Integrate over

Model fluctuations with probability density for n = dNch/dy

Initial eccentricity in overlap region

Eccentricity probability distribution for cuts shown to the left• Full-overlap collisions vary from 0-0.25

<n>() computed from transverse integral over s(rT;)


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Aside: Multiplicity Fluctuations

nucl-ex/0409015

Total multiplicityMultiplicity of 4 highest centrality bins

Analogous centrality-selected (b=0)multiplicity distribution


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Estimating Radiative Energy Loss

• Compare energy loss of inward-moving partons

• t0: parton density constant• t: includes dilution due to

longitudinal expansion• Difference in e-loss

between in- and out- emission is 2x Au+Au– Better discriminating power

Look familiar?


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U+U: Multiplicity and Source Deformation


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2. Multiplicity Distribution for Full-overlap U+U

• Assuming we can select full-overlap (b=0, coplanar nuclei) collisions with ZDC signal, cutting on multiplicity we can select different spatial deformations of overlap zone

0

1s

dy

dN

Sch (initial entropy density of overlap

region)

Centrality dependence of dNch/dy

Integrate over to obtain multiplicityprobability distribution.

Tuning and s


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Allowing for misalignment• Slightly misaligned tip-on-tip and fully aligned side-on-side collisions

can have the same Npart (and ZDC signal)• Assessing the effect of imperfect overlap requires the inclusion of

noncentral U+U collisions• In general, need to characterize collision with 5 variables

– Impact parameter b– Euler angles of orientation of U: = (, )

Initial entropy density becomes:Region of full-overlap events


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Cutting on number of spectators

• Number of spectator nucleons: Nspec = 2 x 238 - Npart

• Selecting low-spectator events biases sample towards– b ~ 0 and 1,2 ~ 0– Symmetry axes of nuclei approximately parallel

• Result: single-peaked mult dist whose center shifts left as spectator cut loosens

~0-5%

tight

loose


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Effect on eccentricity distribution• For sufficiently tight spectator

cuts, expect events corresponding to left edge of mult dists to have larger contribution from side-on-side collisions

• Therefore, cutting on low spectators and low multiplicity should select strongly deformed overlap regions

• Loosening the spectator cut broadens the eccentricity distributions– Allows contributions from non-

zero impact parameter– Thus x can exceed 0.25

Impact: have ability to select spatial deformation of collision zone


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Summary• The authors show that full-overlap U+U collisions at

RHIC can be used to:– Test the hydro behavior of elliptic flow to energy densities much

higher than available to non-central Au+Au– Produce highly-deformed reaction zones to explore more

detailed study of path-length dependence of energy loss by a fast parton as it passes thru the plasma

• Full-overlap collisions can be selected by tight cuts on the number of spectators (i.e. ZDC signal)

• Further cuts on the multiplicity of low-spectator events can discriminate between degrees of spatial deformation of the fireball– Via correlation with “side-on-side-ness” of collision

• This approach is reasonably robust against trigger inefficiencies– Extracting physics from U+U collision program at RHIC is

feasible


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References• “Tandem Injected Relativistic Heavy Ion Facility

at Brookhaven, Present and Future” P. Thieberger et al., NIM A268 (1988) 513-521

• “The RHIC Design Review” H. Hahn et al., NIM A499 (2003) 245-263

• “Anisotropic Flow and Jet Quenching in Ultrarelativistic U+U Collisions” U. Heinz and A. Kuhlman, PRL 94, 132301 (2005)

• “Multiplicity distribution and source deformation in full-overlap U+U collisions” A. Kuhlman and U. Heinz, PRC 72, 037901 (2005)

u+u collisions at rhic

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