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Using Isoscaling to understand the symmetry energy of the nuclear equation of state.

Using Isoscaling to understand the symmetry energy of the nuclear equation of state. Motivation Current status Outlook. D.V. Shetty, G. A. Souliotis, D. Rowland, A. Keksis, E. Bell, M. Jandel, M. Veselsky, R. Laforest, E. Ramakrishnan, H. Johnston,

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Using Isoscaling to understand the symmetry energy of the nuclear equation of state.

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  1. Using Isoscaling to understand the symmetry energy of the nuclear equation of state. • Motivation • Current status • Outlook D.V. Shetty, G. A. Souliotis, D. Rowland, A. Keksis, E. Bell, M. Jandel, M. Veselsky, R. Laforest, E. Ramakrishnan, H. Johnston, L. Trache, F. Gimeno-Nogues, A. Ruangma Cyclotron Institute, Texas A&M University, College Station, Texas 77843 This work was supported in part by:The Robert A. Welch Foundation: Grant Number A-1266 and,The Department of Energy: Grant Number DE-FG03-93ER40773 S.J. Yennello

  2. Atomic nuclei & Neutron star ( two vastly different systems ) A heavy nucleus (like 208Pb) is 18 orders of magnitude smaller and 55 orders of magnitude lighter than a neutron star ! Yet bounded by a common entity, the nuclear Equation Of State (EOS) !

  3. EOS in Astrophysics and Stellar Properties Size & Structure of Neutron Star depends on EOS EOS influence R,M relationship maximum mass. cooling rate. core structure Softer EOS leads to a smaller star mass and radius for a given central density H. Huber et al, Phys. Rev. C 50 (1994) 1287(R)

  4. Host of nuclear EOS employed in astrophysical modeling of neutron star & supernova explosion Still leaves a wide range of possibilities ! Some are excluded by causality & some by known masses of existing neutron stars F. Weber, IoP publishing, Bristol (1999)

  5. What is known about the EOS of symmetric matter? Danielewicz, Lacy, Lynch, Science 298,1592 (2002) Not well constrained Pressure (MeV/fm3) E(, d) = E(, d=0) + Esym(,d) d2 d = (n - p)/(n + p)

  6. Multifragmentation reaction (Probing the low density dependence)

  7. Observables sensitive to the asymmetry term in the EOS ? Moderate density (r < 1.5 ro) : Fragment isotope distribution, isotopic & isobaric yield ratios Isospin distillation/fractionation, relative n & p densities Isospin diffusion Nuclear stopping & N/Z equilibration Pre-equilibrium emission Particle - particle correlation Light cluster production High density (r > 1.5 ro) : Collective flow Subthreshold particle production

  8. Isospin distillation in asymmetric (N/Z > 1) nuclear matter ( H. Muller & B. Serot. Phys. Rev. C 52, 2072 (1995) ) An inhomogeneous distribution of the neutrons and protons within the system is predicted, resulting in a dilute neutron rich (N/Z > 1) gas (light clusters) and a dense and symmetric (N/Z ~ 1) liquid (heavy fragments)

  9. Studying isospin distillation Measure the yields of the light clusters (gas phase) Determine the n & p densities Compare them from one reactions to another with different isospin (N/Z)

  10. Relative n & p density from isotope & isotone yields free neutron & proton densities Relative n density Relative p density

  11. Relative n & p densities : 58Ni + 58Fe (reaction 2, N/Z = 1.15 ) & 58Ni + 58Ni (reaction 1, N/Z = 1.07)) Relative n & p density 58Fe + 58Fe (reaction 2, N/Z = 1.23) & 58Ni + 58Ni (reaction 1, N/Z = 1.07) @ 30, 40, 47 MeV/nucl.

  12. If the clusters in reaction 2 are more neutron-rich than in reaction 1 Relative n density , > 1 Relative p density , < 1

  13. Ratio of isotopic yields58Ni, 58Fe + 58Ni, 58Fe 30 MeV/nuc R21(N,Z) = C eaN+ bZ

  14. D D D D D D Relative neutron and proton densities at 30 MeV/nuc Isotope ratios Isotone ratios

  15. D D D D D D neutron and proton densities at 30, 40, 47 MeV/nuc Isotope ratios Isotone ratios

  16. D D D D D D SMM model comparison Experimental Isotope ratios Isotone ratios Excitation energy (MeV/A)

  17. Temperature dependence of the scaling parameter a 58Fe + 58Fe / 58Ni + 58Ni Tsang PRC64, 054615 (2002)

  18. Symmetry energy and the fragment yield distribution in Multifragmentation reaction Secondary fragments Primary fragments Symmetry energy of the primary fragments are significantly lower D. V. Shetty et al, (2004)

  19. EOS and dynamical simulation of fragment production (AMD model calculations) A. Ono et al, Phys. Rev. C 68 (2003) 051601(R)

  20. Symmetry energy and the scaling parameter a Csym ~ 18 – 20 MeV ; r ~ 0.08 fm-3 D. V. Shetty et al, Phys. Rev. C 70 (2004) 011601(R)

  21. Formation of hot neutron rich nuclei in supernova explosion During supernova II type explosion the thermodynamical conditions of stellar matter between the protoneutron star & the shock front correspond to nuclear liquid-gas coexistence region. Neutron rich hot nuclei can be produced in this region which can influence the dynamics of the explosion contribute to the synthesis of heavy elements A slight decrease in the symmetry energy co-efficient can shift the mass distribution to higher masses A. Botvina et al, Phys. Lett. B 584 (2004) 233

  22. Neutron richness Deep InelasticTransfer mechanism can produce neutron-rich heavy residues DA

  23. 0.833 mg/cm2 2.535 mg/cm2 4.778 mg/cm2 Mylar FAUST FAUST has solid angle coverage of 90% from 2.31º to 33.63º, 71% from 1.6º to 2.3º, and 25% from 33.6º to 44.9º. F. Gimeno-Nogues, et al. NIM A 399 (1997) 94 http://cyclotron.tamu.edu/sjygroup/external/Detectors/FAUSTWeb/faust.html

  24. Neutron richness Production of quasi projectiles over a wide range in N/Z from 33Mev/nuc 20Na, 20Ne, 20F + Au reactions Rowland, Phys. Rev. C 67, 064602 (2003).

  25. Botvina IsoscalingR21 = C exp(a’A + b’(N-Z) a ’ = D(mn + mp)/2T b ’ = D(mn - mp)/2T 28Si + 112,124Sn 50 MeV/nuc 30 MeV/nuc b’ = 0.186±0.017 b’ = 0.237±0.038

  26. Botvina IsoscalingR21 = C exp(a’A + b’(N-Z) 28Si + 112,124Sn ; 50 MeV/nuc

  27. Al quasiprojectiles

  28. b’T b ’ = D(mn - mp)/2T

  29. MARS Recoil Separator and Setup Dispersive Image D2 D1 Production Target Wien Filter Q3 Q2 Q1 Final Achromatic Image D3 PPAC1 Start T X,Y Q4 Q5 Rotatable Arm Reaction Angle: 0-12o (selectable) PPAC2 Stop T Beam angle set to: 0o (1.0-3.0o) for Kr+Ni (gr = 3.5o) 4o (2.5-5.5o) for Kr+Sn (gr = 6.5o) Silicon Telescope: ΔE1, X,Y (Strips) ΔE2, Eresidual MARS Acceptances: Anglular: 9 msr Momentum: 4 %

  30. The Superconducting Solenoid Rare Isotope Line at TAMU: Schematic diagram of the setup for heavy-residue studies from DIC:

  31. DIT mechanism can produce neutron-rich heavy residues Mass Distribution of Germanium from 86Kr(25MeV/u) + 124Sn,112Sn, 64Ni Data using targets: 124Sn 112Sn  64Ni ------ EPAX2 Ge Target N/Z Valley of stability 124Sn 1.48 n-rich 118Sn 112Sn 1.24 n-poor 64Ni 1.29 n-rich 60Ni Souliotis, Phys. Rev. Lett. 91, 022701 (2003)

  32. Comparison: Data/EPAX : 86Kr (25 MeV/u) + 64Ni, 124Sn For near-projectile fragments and above the projectile N/Z, the cross sections are larger. DIC between massive n-rich nuclei appear to be advantageous for very high N/Z RIB production

  33. Scaling of Yield Ratios : R21 (N,Z)= Y2/Y1 •86Kr+124Sn,112Sn (data inside gr=6.2ο) R21 = C exp ( α N ) •86Kr+64Ni,58Ni (data outside gr=3.5o)

  34. Isoscaling Parameter α : * • 86Kr+124Sn,112Sn • 86Kr+64Ni,58Ni α =0.43 α =0.27 R21 = C exp ( α N ) α = 4 Csym/T ( (Z/A)12– (Z/A)22) Quasi-projectiles 1: n-poor 2:nrich * G.A. Souliotis et al., Phys. Rev. C 68, 024605

  35. Isoscaling data from residues of 64Ni (25MeV/nucleon) BigSol data R21 (N,Z)= Y2/Y1 R21 = C exp ( α N )

  36. 86Kr, 64Ni, 136Xe data: Isocaling parameter a vs Δ(Z/A)2: N/Z equilibrated, no effect of pre-eq. 86Kr+124,112Sn *  2.0 MeV/u 86Kr+64,58Ni *  2.4 MeV/u 64Ni+124,112Sn 64Ni+64,58Ni 64Ni+232Th,208Pb *  2.9 MeV/u Quasi-projectiles : E/A ~20-25 MeV α = 4Csym/T ( (Z/A)12– (Z/A)22) c 136Xe+124,112Sn 136Xe+64,58Ni 136Xe+232Th,Au *  2.5 MeV/u

  37. Variation w.r.t excitation energy: Data : 86Kr+124,112Sn 86Kr+64,58Ni 64Ni+ Ni,Sn,Th-Pb 136Xe+Ni,Sn,Th-Au Calculation: Fermi Gas (K=13) Mononucleus expansion model (L. Sobotka, J. Toke) Csym = cT / 4

  38. Summary and Outlook • Projectile residue distributions from peripheral to mid-peripheral • collisions show enhanced production of neutron –rich nuclei • Heavy-Residue Isoscaling can be used as probe of N/Z Equilibration, Esym() • Multifragmentation reactions may be able to distinguish between various functional form of the density dependence of the symmetry energy • Symmetry energy can be significantly below saturation density and could be interesting in the studies relating to the elemental abundances in core collapse supernova explosion • Effect of Secondary Decay on isoscaling parameters needs to be understood • Comparisons with Reaction Models: • Extension of studies using higher DN/Z beams and heavy targets

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