Germany's

United States 2Germany 0

FIFA Women’s World Cup Semifinal

Isospin Equilibration in Heavy-Ion Collisions

S. YennelloTexas A&M University

N/Z equilibration is one way to get a handle on the symmetry energy of the nuclear EOS

Z

N

40Ca, 40Ar + 58Fe, 58Ni

64Ni,64Zn + 64Ni,64Zn; 64,70Zn + 64,70Zn

Z

N

58Ni,58Fe + 58Ni,58Fe

40Ar, 40Ca, 48Ca+112,124Sn

Z

N

Z

N

Also 86Kr + 112,124Sn Heavy residuesSouliotis, PLB 2004

N/Z Equilibration

Yennello, PLB 1994

He

Li

Be

B

Z

N

53 MeV/nuc

E/A= 53 MeV 40Ca, 40Ar + 58Fe, 58Ni

projectile neutronsprojectile protons

target neutronstarget protons

B.A. Li, PRC52(1995)BACKWARD OF COM FORWARD OF COM

time

E/A=33,45 MeV 40Ca, 40Ar + 58Fe, 58Ni Qlab = 40o

Johnston, PLB 371 (1996)

experiment shows equilibration at 33 MeV/nuc but not at 45 Mev/nuc

iBUU shows clear translucency at 45 Mev/nucleon and above

B.A. Li, PRC52(1995)

isospin diffusion using isotope tracer methodMeasured isospin diffusion in112,124 Sn, 50 MeV/nucleonTsang PLB 2004

Isotope tracer method developed to study nuclear stopping FOPI: Rami, PRL2000

symmetry energy will act as driving force to transport n or p between target and projectile

difference between QP and QT N/Z can be used to measure diffusion and extract information about symmetry energy

Diffusion coefficient connected to symmetry potentialL Shi & P Danielewicz, PRC68 (2003)

• Central collisions measure nuclear translucency

• Peripheral collisions inform transport

• Both should depend on EOS

isobaric and isotopic projectile fragmentation with FAUST

• Determine the N/Z of the Quasiprojectile Source– Isobaric yield ratios– Reconstruction of QP

Quasiprojectile ZKnow fragment Z

Apparent Quasiprojectile AKnow fragment A

Apparent Quasiprojectile Excitation EnergyUsing the balance of energy

Keksis, PhD 2007; PRC 2010

40Ar, 40Ca, 48Ca+112,124Sn

Z

N

qpffqp mEmEcms

)(*

PLF reconstruction first done w/ FAUST: Rowland, PhD 2000; PRC 2003Used by Veselsky: PRC 2000; PLB 2001

N/Z Equilibration

32MeV/u

45MeV/u

If no N/Z equilibration occurred the N/Z of the quasiprojectile willequal the N/Z of the projectile

If full N/Z equilibration occurred the N/Z of the quasiprojectile willequal the N/Z of the composite system

If partial N/Z equilibration occurredthe N/Z of the quasiprojectile will be between the N/Z of the composite system and the N/Z of the projectile

Reconstruction Results

32MeV/u

45MeV/u

Undetected neutro

ns cause

reco

nstructi

on to under p

redict th

e N/Z

Isobaric Yield Ratio Method

32MeV/u

45MeV/u

P

P

T

T

S Z

NY

Z

NX

Z

N

Simple equation stating that the N/Z of the quasiprojectile source is some part target and some part projectile

Fit all the isobaric yield ratios simultaneously and maximizing the sum of R2

40Ar, 40Ca, 48Ca+112,124Sn

• A simple way of finding the average amount of N/Z equilibration

N/ZCS

Observing 54%

DIT/SMM Simulation• DIT – Deep Inelastic Transfer model by Tassan-Got– NPA 524, 121 (1991)

• SMM – Statistical Multifragmentation Model by Botvina– NPA 475, 663 (1987)

• FAUST Filter – Software version of the FAUST Array• Analyze fragments exactly like experimental data• Compare results with the N/Z of the quasiprojectile

from the simulation• Back trace to determine the number of neutrons that

were not detected

Simulation Results

Simulation Results

Lessons learned

• Globally, detected fragments reflect the N/Z at the time of fragment formation

• Fragment ratios or fractional yields can be used to determine the N/Z of the source from which they originate – even if it is not totally reconstructed.

•Deep inelastic collisions of 40,48Ca, 40Ar with 112,124Sn at 35 Mev/nucleon show partial but not complete equilibration during the interaction

40Ar, 40Ca, 48Ca+112,124Sn

NIMROD-ISiS Array• Full Silicon Coverage (4π)• Isotopic Resolution to Z=17• Elemental Resolution to Zprojectile

• Neutron Ball (4π)

S. Wuenschel et al., Nucl. Inst. Meth. A 604 578 (2009)

Let’s detect some neutrons

Isospin TransportiBUU 70Zn + 64Zn b = 7 fm collision: density contour plots in XZ plane

Drift (total nucleon density dependent)

Diffusion (isospin concentration dependent)

Z

N

64Ni,64Zn + 64Ni,64Zn; 64,70Zn + 64,70Zn

L. May , PhD Thesis TAMU (2015) Z. Kohley, Ph.D. Thesis, TAMU (2010)

Isospin Transport Ratio• Isospin Transport Ratio (ITR) originally derived for use in

transparency studies• Ratio shows isospin transport between neutron rich

(Ri=1) and neutron poor (Ri=-1) sources• Many observables can be used as surrogates to δ

– Isoscaling parameter α– Triton/3He ratio– Pre-equilibrium neutron/proton ratios– Asymmetry of reconstructed QPs

NPNR

NPNRiiR

2

ii

iiii ZN

ZNI

whereRami, F. et. al. PRL 84, 1920 (2000).Baran, V. et. al. PRC 72 064620, (2005).

iBUU simulation results• The “asy-soft” symmetry

energy reaches N/Z equilibrium at a much larger impact parameter than in the “asy-stiff” case– This is similar to the effect seen

by Tsang et. al. and Baran et. al. when looking at equilibration versus time

• The form of the symmetry energy has a large impact on the QP and its composition

• The “asy-soft” case shows equilibration nearing composite system N/Z– The “asy-stiff” case shows a

neutron enhancement in all cases

• It is clear that impact parameter determination will enhance experimental data

“asy-soft” x=1“asy-stiff” x=-2

Lines are values for the composite system N/Z

L. May , PhD 2015

iBUU comparison to Tsang et al.

» QP N/Z from iBUU at b=8fm» Similar impact parameter to the Tsang et al.

experimental data

» Slightly increased equilibration (~60%)

Tsang, M. B. et. al. PRL 92, 062701 (2004)Tsang, M. B. et. al. PRL 86, 5023 (2001)

Tsang, M. B. et. al. PRL 92, 062701 (2004) Johnston, H. et al. PLB 371, 186 (1996)Tsang, M. B. et. al. PRL 86 5023 (2001) Johnston, H. et al. PRC 56, 1972 (1997)

Experimental comparison to Tsang et al.

» Isoscaling α» Fragments from reconstructed QPs

» Increased equilibration. » Consistent with the work of Johnston et al. in

examining the effect of beam energy on equilibration

Tsang, M. B. et. al. PRL 92, 062701 (2004) Johnston, H. et al. PLB 371, 186 (1996)Tsang, M. B. et. al. PRL 86 5023 (2001) Johnston, H. et al. PRC 56, 1972 (1997)

Experimental comparisonIsobaric yield ratio (A=3, t/3He)

Fragments from reconstructed QPs

Similar closeness of cross systems to isoscaling case

Zn reaction set not centered relative to symmetric systems

Reconstructed QP msCross systems are much closer to each other than in either yield scaling case

Neither reaction set are centered relative to symmetric systems

Equilibration ?

Measures separation between cross systems relative to separation between symmetric systems

Similar to convergence as seen in the iBUU

* Data from Tsang, 2004

64Ni,64Zn + 64Ni,64Zn; 64,70Zn + 64,70Zn

Isoscaling as a function of impact parameter surrogate

A=64 systems clearly exhibit convergence with increasing centrality

» Convergence is neutron-rich compared to symmetric systems

central peripheral

isoscaling

Isobaric yield ratioQPms

More lessons learned» iBUU04 shows clear equilibration dependence on the asymmetry energy» convergence, rather than approaching a specific asymmetry value is a better

signature of equilibration» Impact parameter integrated experimental data agrees well with previous work

(Tsang et al.)» Isobaric Yield ratio (A=3)» QP ms » Isoscaling

» impact parameter dependence» Convergence seen in all three observables

» Isoscaling α» Isobar A=3 (t/3He)

» QP ms

» While slight differences were seen between the Zn (charge symmetric) and A=64 (charge asymmetric) sets of reaction systems, no definitive conclusion can be drawn about the influence of a charge gradient between projectile and target

A. Jedele

70Zn-70Zn at 35MeV/nucleon.Nimrod-ISIS has 4π coverage.

Isotopic identification of charged particles for Z≤17.

ZH=12 ZL=10

ZH=12 ZL=6

ZH=12 ZL=4

ZH=8 ZL=7

ZH=8 ZL=6

ZH=8 ZL=4

ZH=12 ZL=10

ZH=12 ZL=6

ZH=12 ZL=4

ZH=8 ZL=7

ZH=8 ZL=6

ZH=8 ZL=4

N/Z transport within a deformed nuclear system

• Z and A of fragments measured over a large range (Z ≤ 17)• The rotation angle at which the QP decays is used as a clock• At t=0 (180°), there is the largest difference in composition• As time increases (decreasing α) the compositions converge• Observed for a large range of fragment types (6 of 59 shown)

Vheaviest

VlighterVCM

α

Vrel

Stay Tuned

Isospin Equilibration can be studied in multiple ways

Translucency in central collisions

Diffusion between target and projectile in peripheral collisions

Transport in deformed nuclear systems

Many ThanksLarry May, Zach Kohley, August Keksis, Elizabeth Bell, Heather Johnston, Sara Wuenschel, Doug Rowand, Alan McIntosh, Andrea Jaedel, Lauren Heilborn, Paul Cammarata, Andrew Zarella, Paula Marini, Francisco Gimeno-Nogues, Easwar Ramakrishnan, Richard Laforest, Dinesh Shetty, Rahul Tripathi, George Souliotis, Martin Veselsky, Andrew Raphelt, Sarah Soisson, Brian Stein, Jeff Winger, Rich Ibbotson,

B.A. Li

Texas A&M Cyclotron Institute staff

Department of EnergyNational Science FoundationRobert A Welch Foundation