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Isospin Equilibration in Heavy-Ion Collisions S. Yennello Texas A&M University N/Z equilibration is one way to get a handle on the symmetry energy of the nuclear EOS Z N 40 Ca, 40 Ar + 58 Fe, 58 Ni 64 Ni, 64 Zn + 64 Ni, 64 Zn; 64,70 Zn + 64,70 Zn Z N 58 Ni, 58 Fe + 58 Ni, 58 Fe 40 Ar, 40 Ca, 48 Ca+ 112,124 Sn Z N Z N Also 86 Kr + 112,124 Sn Heavy residues Souliotis, PLB 2004

N/Z Equilibration Yennello, PLB 1994 He Li Be B Z N 53 MeV/nuc E/A= 53 MeV 40 Ca, 40 Ar + 58 Fe, 58 Ni

projectile neutrons projectile protons target neutrons target protons B.A. Li, PRC52(1995) BACKWARD OF COMFORWARD OF COM time

E/A=33,45 MeV 40 Ca, 40 Ar + 58 Fe, 58 Ni  lab = 40 o 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 method Measured isospin diffusion in 112,124 Sn, 50 MeV/nucleon Tsang 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 potential L 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 Z Know fragment Z Apparent Quasiprojectile A Know fragment A Apparent Quasiprojectile Excitation Energy Using the balance of energy Keksis, PhD 2007; PRC Ar, 40 Ca, 48 Ca+ 112,124 Sn Z N PLF reconstruction first done w/ FAUST: Rowland, PhD 2000; PRC 2003 Used by Veselsky: PRC 2000; PLB 2001

N/Z Equilibration 32 MeV/u 45 MeV/u If no N/Z equilibration occurred the N/Z of the quasiprojectile will equal the N/Z of the projectile If full N/Z equilibration occurred the N/Z of the quasiprojectile will equal the N/Z of the composite system If partial N/Z equilibration occurred the N/Z of the quasiprojectile will be between the N/Z of the composite system and the N/Z of the projectile

Reconstruction Results 32 MeV/u 45 MeV/u Undetected neutrons cause reconstruction to under predict the N/Z

Isobaric Yield Ratio Method 32 MeV/u 45 MeV/u 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 R 2 40 Ar, 40 Ca, 48 Ca+ 112,124 Sn

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

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 40,48 Ca, 40 Ar with 112,124 Sn at 35 Mev/nucleon show partial but not complete equilibration during the interaction 40 Ar, 40 Ca, 48 Ca+ 112,124 Sn

NIMROD-ISiS Array Full Silicon Coverage (4π) Isotopic Resolution to Z=17 Elemental Resolution to Z projectile Neutron Ball (4π) S. Wuenschel et al., Nucl. Inst. Meth. A (2009) Let’s detect some neutrons

Isospin Transport iBUU 70 Zn + 64 Zn b = 7 fm collision: density contour plots in XZ plane Drift (total nucleon density dependent) Diffusion (isospin concentration dependent) Z N 64 Ni, 64 Zn + 64 Ni, 64 Zn; 64,70 Zn + 64,70 Zn 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 (R i =1) and neutron poor (R i =-1) sources Many observables can be used as surrogates to δ – Isoscaling parameter α – Triton/ 3 He ratio – Pre-equilibrium neutron/proton ratios – Asymmetry of reconstructed QPs where Rami, F. et. al. PRL 84, 1920 (2000). Baran, V. et. al. PRC , (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, (2004) Tsang, M. B. et. al. PRL 86, 5023 (2001)

Tsang, M. B. et. al. PRL 92, (2004)Johnston, H. et al. PLB 371, 186 (1996) Tsang, M. B. et. al. PRL (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, (2004)Johnston, H. et al. PLB 371, 186 (1996) Tsang, M. B. et. al. PRL (2001)Johnston, H. et al. PRC 56, 1972 (1997) Experimental comparison Isobaric yield ratio (A=3, t/ 3 He) Fragments from reconstructed QPs Similar closeness of cross systems to isoscaling case Zn reaction set not centered relative to symmetric systems Reconstructed QP m s Cross 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, Ni, 64 Zn + 64 Ni, 64 Zn; 64,70 Zn + 64,70 Zn

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 ratio QPms

QP m s vs impact parameter surrogate »All 7 systems show an increase in m s at more central collisions than at peripheral collisions »Similar to what was seen in the “asy-stiff” case in the iBUU »Amount of convergence in Zn systems is stronger than in the “asy-soft” case central peripheral

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 m s »Isoscaling »impact parameter dependence »Convergence seen in all three observables »Isoscaling α »Isobar A=3 (t/ 3 He) »QP m s »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 70 Zn- 70 Zn at 35MeV/nucleon. Nimrod-ISIS has 4π coverage. Isotopic identification of charged particles for Z≤ Zn- 70 Zn 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) V heaviest V lighter V CM α V rel

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 Thanks Larry 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 Energy National Science Foundation Robert A Welch Foundation