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George A. Souliotis Laboratory of Physical Chemistry, Department of Chemistry,

Studies of N/Z equilibration via Heavy-Residue Isoscaling. George A. Souliotis Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Athens, Greece and Cyclotron Institute, Texas A&M University, College Station, Texas, USA

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George A. Souliotis Laboratory of Physical Chemistry, Department of Chemistry,

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  1. Studies of N/Z equilibration via Heavy-Residue Isoscaling George A. Souliotis Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Athens, Greece and Cyclotron Institute, Texas A&M University, College Station, Texas, USA International Workshop on Nuclear Dynamics and Thermodynamics, in honor of Prof. Joe Natowitz TAMU, College Station, 19-22 Aug. 2013

  2. BigSol Setup at TAMU: Sept. 2002

  3. BigSol Line results: Rare Isotope Production ( Sept.-Oct. 2003) Example of Z-A distribution of fragments from 64Ni(25MeV/u)+64Ni B=1.473, IBigSol=79.3 A Angular acceptance: 1.5-3.0 deg. Z A Co -1p+1n Neutron-Rich fragments from 64Ni (25MeV/u) + 64Ni (4.0mg/cm2) B=1.900 Tm, IBigSol=102.5 A ibeam = 1 pnA, 4 hour run Angular acceptance: 1.5-3.0 deg. Fe -2p+2n Mn Cr Z -4p A

  4. Overview of Heavy-Residue work : Experimental work at Texas A&M: deepinelastic collisions below the Fermi energy: 86Kr(25MeV/nucleon) + 64Ni,124Sn PRL 91, 022701 (2003) 86Kr(15MeV/nucleon) + 64Ni,124Sn PRC 84, 064607 (2011) Findings:Peripheral collisions: enhanced production of n-rich nuclei Heavy Residues as probes of nuclear dynamics and EOS: Heavy-residue isoscaling: PRC 68, 024605 (2003) PRC 73, 024606 (2006) N/Z equilibration: PLB 588, 35 (2004) Present work: Heavy residue Isoscaling in 15 MeV/nucleon reactions Evolution of the N/Z w.r.t. to TKEL (~ degree of dissipation) Comparisons with the DIT and CoMD models.

  5. Approaching phase: Projectile (Zp,Ap) • Neutrons • Protons θ b: impact parameter θ: scattering angle b Target (Zt,At) Collisions between Heavy Ions at Fermi Energies (10<E/A < 40MeV) Grazing angle, θgr: nuclei in touching configuration Overlap (interaction) phase: exchange of nucleons: Deep Inelastic Transfer (DIT) Model L. Tassan-Got and C. Stephan, Nucl. Phys. A 524, 121 (1991) excited projectile-like fragment (PLF) or quasi-projectile excited target-like fragment (TLF) or quasi-target

  6. 86Kr 86Kr 36 36 50 50 124 Sn Excited Projectile-like Fragment (PLF) or Quasi-projectile 50 74 Projectile 112 Sn 50 62 Target The Process of N/Z Transport * and Equilibration N/Z = 1.40 N/Z = 1.48 (N/Z)eq = 1.44 N/Z = 1.40 Nucleon exchange: Deep Inelastic Transfer (DIT) Model L. Tassan-Got and C. Stephan, Nucl. Phys. A 524, 121 (1991) N/Z = 1.24 (N/Z)eq = 1.30 *or isospin diffusion

  7. CoMD Evolution of 86Kr Nucleus: t = 0-500 fm/c Δt = 10 fm/c • Neutrons • Protons 86Kr 36 50 z Microscopic Calculations: Constrained Molecular Dynamics (CoMD)* CoMD : Quantum Molecular Dynamics model (Semiclassical) • Nucleons are considered as Gaussian wavepackets • N-N effective interaction ( Skyrme-type with K = 200 ) • Several forms for N-N symmetry potential Vsym(ρ) • Pauli principle imposed (via a phase-space ‘constraint’ algorithm ) • Fragment recognition algorithm (Rmin = 3.0 fm) *M. Papa, A. Bonasera et al., Phys. Rev. C 64, 024612 (2001)

  8. b = 10 fm t = 0-300 fm/c Δt = 10 fm/c b = 8 fm t = 0-300 fm/c Δt = 10 fm/c Peripheral Collision Semi-Peripheral Collision • Neutrons • Protons 124Sn 124Sn 50 50 74 74 z z z z 86Kr 86Kr 36 36 50 50 CoMD Calculations: 86Kr (15 MeV/nucleon) + 124Sn CoMD: Constraint Molecular Dynamics;M. Papa, A. Bonasera, Phys. Rev. C 64, 024612 (2001)

  9. Separation Stage I Dispersive Image SeparationStage II Production Target D2 D1 Q3 Wien Filter Q2 Final Achromatic Image Q1 PPAC1 Start T,X,Y Rotatable Arm Reaction Angle: 0-12o (selectable) Q4 Q5 MARS Acceptances: Angular: 9 msr Momentum: 4 % Βρ = mυ/Q Si Telescope ErΔE PPAC2 Stop T, X,Y MARS Recoil Separator and Setup for Heavy-Residue / RIB Studies* K500 Beam D3 *G. A. Souliotis et al., Nucl. Instr. Methods B, 266, 4692 (2008) and references therein

  10. Experimental Details Reactions studied with MARS: Δθ = 2.2-5.8o86Kr22+ (15 MeV/u, 5 pnA) + 64Ni, 58Ni (gr~ 6o) Δθ =5.6-9.2o86Kr + 124Sn, 112Sn (gr~ 9o) Extracted physical quantities: Velocity, Energy loss, Total Energy Mass-to-charge ratio: A/Q B ~ A/Q  Atomic Number ZZ ~  ΔE1/2 Ionic charge Q Q ~ f(E, , B) Mass number A A = Qint  A/Q Reconstructed: Fragment Yield Distribution Y(Z, A, υ)

  11. Experimental Mass Distributions: 86Kr (15 MeV/u) + 64,58Ni* • 86Kr + 64Ni (15 MeV/u) • 86Kr + 58Ni (15 MeV/u) • 1p • 2p 35Br 34Se Large cross sections of n- pickup products • 3p • 4p 33As 32Ge • 5p • 6p 30Zn 31Ga 23 *G. A. Souliotis et al., Phys. Rev. C 84, 064607 (2011)

  12. Comparison of calculations with data: 86Kr (15 MeV/nucleon) + 64Ni 86Kr + 64Ni (15 MeV/u)* DIT/SMM ------ DITm/SMM 35Br 34Se 33As 32Ge *data: G.A. Souliotis et al., PRC 84, 064607 (2011) DIT : L. Tassan-Got, C. Stephan, Nucl. Phys. A 524, 121 (1991) DITm: M. Veselsky, G.A. Souliotis, Nucl. Phys. A 765, 252 (2006) SMM: Statistical Multifragmentation Model: A. Botvina et al., Phys. Rev. C 65, 044610 (2002); Nucl. Phys. A 507, 649 (1990) 30Zn 31Ga * P.N. Fountas, G.A. Souliotis et al., in preparation

  13. Comparison: Data, Calculations: 86Kr (15 MeV/nucleon) + 64Ni 86Kr + 64Ni (15 MeV/u)* CoMD/SMM -----CoMD/GEMINI 35Br 34Se 33As 32Ge *data: G.A. Souliotis et al., Phys. Rev. C 84, 064607 (2011) CoMD: Constrained Molecular Dynamics: M.Papa et. al., Phys. Rev. C 64, 024612 (2001) GEMINI: Binary Decay Code: R. Charity, Nucl. Phys. A 483, 391 (1988) SMM: Statistical Multifragmentation Model: A. Botvina et al., Phys. Rev. C 65, 044610 (2002); Nucl. Phys. A 507, 649 (1990) 31Ga 30Zn * P.N. Fountas, G.A. Souliotis et al., in preparation

  14. Scaling of Yield Ratios: 15MeV/nucleon data* R21 (N,Z)= Y2/Y1 •86Kr+64Ni,58Ni data at 4o (gr=6.0o) R21 = C exp ( α N ) •86Kr+124Sn,112Sn data at 7o (gr=9.0ο) *G. A. Souliotis et al., in preparation

  15. Isoscaling Parameter α : 15MeV/u data** ○86Kr+64Ni,58Ni ( 4o data) ●86Kr+124Sn,112Sn (7o data) R21 = C exp ( α N ) α = 4 Csym/T ( (Z/A)12– (Z/A)22) * Quasi-projectiles 1: n-poor 2:nrich M. B. Tsang et al. Phys. Rev. C 64, 054615 (2001) A.S. Botvina et al. Phys. Rev. C 65, 044610 (2002) P. Marini et al, Phys. Rev. C 85, 034617 (2012) * **G. A. Souliotis et al., (in preparation)

  16. Peripheral collision: tinteraction short Velocity, TKEL, E* vs Z 15MeV/udata** Semi-peripheral collisions: tinteraction longer ○86Kr+64Ni,58Ni ( 4o data) ●86Kr+124Sn,112Sn (7o data) **G. A. Souliotis et al., (in preparation)

  17. Residues: 86Kr (15 MeV/u) + 64,58Ni 86Kr+58Ni -------- DIT -------- CoMD (asy-stiff) -------- CoMD (asy-soft) 86Kr+ 64Ni DIT: Deep Inelastic Transfer: L. Tassan-Got, Nucl. Phys. A 524, 121 (1991) CoMD: Constraint Molecular Dynamics •MARS Isoscaling data* Δ(Z/A)2 = (Z/A)21- (Z/A)2 2 = α T / (4 Csym ) Fermi gas: T2 = K0 (/o)2/3 * K0 : inv. lev. dens. param. at o (K0 = 12 ) Assume QP at normal density=o Csym =23 MeV * G.A. Souliotis et al. (in preparation)

  18. Residues: 86Kr (15 MeV/u) + 124,112Sn 86Kr+112Sn -------- DIT -------- CoMD (asy-stiff) -------- CoMD (asy-soft) 86Kr+ 124Sn •MARS Isoscaling data* Δ(Z/A)2 = (Z/A)21- (Z/A)2 2 = α T / (4 Csym )

  19. α,V,TKEL, E* vs Z 25MeV/udata** ●86Kr+124Sn,112Sn (4o data) Peripheral collision: tinteraction short Semi-peripheral collisions: tinteraction long **G. A. Souliotis et al., PLB 588, 35 (2004)

  20. Residues: 86Kr (25 MeV/u) + 124,112Sn 86Kr+112Sn -------- DIT -------- CoMD (asy-stiff) -------- CoMD (asy-soft) 86Kr+ 124Sn •MARS Isoscaling data: G.A.Souliotis et al. PRC 68, 024605 (2003) Δ(Z/A)2 = (Z/A)21- (Z/A)2 2 = α T / (4 Csym )

  21. Interaction time vs TKEL : CoMD calculation ●86Kr+124Sn,112Sn (25 MeV/u) ●86Kr+124Sn,112Sn (15 MeV/u) ●86Kr+64Ni,58Ni (15MeV/u) ●40Ar+64Ni,58Ni (15MeV/u) TKEL/TKELmax = 1- exp(-t/τ) τ ~ 150 fm/c

  22. FAUST/Q-Triplet Setup at TAMU* * Paul Cammarata et al, ( SJYgroup )

  23. Summary and Conclusions ● Study of heavy-residue isoscaling from peripheral collisions. Information on N/Z transport and equilibration via the correlation: Δ vs TKEL ● Microscopic calculations of peripheral collisions with CoMD. No sensitivity to Vsym(ρ) found in the Δ vs TKEL correlation Plans for future work: ● Detailed comparisons with the theoretical codes ( DIT, CoMD,…. ) ● Experimental measurements of 15 MeV/nucleon reactions with the TAMU FAUST/Q-Triplet system (reconstruct QP). Extension of experimental studies using neutron-rich RIBs from TAMU RIB Upgrade*, SPES at Legnaro, SPIRAL-II at GANIL and other facilities *TAMU Cyclotron Upgrade, see :http://cyclotron.tamu.edu

  24. Acknowledgements: CollaboratorsM. Veselsky, S. Galanopoulos, Z. Kohley, A. McIntosh, L.W. May, B.C. Stein, S.J. YennelloSpecial thanks to: A. Bonasera, TAMU and INFN, Catania, Italy,A. Botvina, FIAS, Frankfurt, GermanyThis 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

  25. END of Talk : Additional material here:

  26. ρoverlap = ρprojectile + ρtarget R =12 fm 124Sn 124Sn 86Kr 86Kr ρoverlap ~ 1/4 ρo 74 74 50 50 50 50 36 36 Peripheral collision: tinteraction short n p ρoverlap ~ 1.0-1.5 ρo R =10 fm Semi-peripheral collision: tinteraction longer n p Peripheral Collisions: 86Kr + 124Sn Peripheral Collisions: can provide information on the evolution of the N/Z degree of freedom and ( via microscopic calculations) the effective nucleon-nucleon interaction Calculations with a Thomas-Fermi code: V. Kolomietz, Phys. Rev. C 64, 024315 (2001)

  27. Isoscaling: 40Ar (15MeV/nucleon) + 64Ni,58Ni •40Ar + 64Ni,58Ni (data inside gr=6.2ο) R21 = C exp ( α N ) α = 4 Csym/T ( (Z/A)12– (Z/A)22) Quasi-projectiles 1: n-poor 2:nrich GS files in “ar07” : anal_mars_ar_jun07 z1_iso_arni_tex.fit z1_iso_arni_figure.tex => *.ps a_iso_arni_tex.fit a_iso_arni_figure.tex => *.ps

  28. Velocity, E*, TKEL vs Z correlations:15MeV/u data ●40Ar+64Ni,58Ni (4o data) υmin => E*/A ~2.0 MeV GS files in “ar07” : anal_mars_ar_jun07 vz_iso_arni_tex.fit vz_iso_arni_figure.tex => *.ps

  29. Residues: 40Ar (15 MeV/u) + 64,58Ni 40Ar+58Ni Csym(ρ) 40Ar+ 64Ni -------- DIT -------- CoMD (linear) -------- CoMD (a-soft) -------- CoMD (a-stiff) -------- CoMD (Vsym = 0) •MARS Isoscaling data* Δ(Z/A)2 = (Z/A)21- (Z/A)2 2 = a T / (4 Csym ) GS files in “ar07” : anal_mars_ar_jun07 azel1_arni_tex.fit azel1_arni_figure.tex => *.ps

  30. TKEL correlations (I): All available MARS data О86Kr(15MeV/u)+64,58Ni(4o data) ●86Kr(15MeV/u)+124,112Sn(7o data) ■86Kr(25MeV/u)+124,112Sn(4o data) ▲40Ar(15MeV/u)+64,58Ni (4o data) GS files in “kr07” : anal_mars_kr_jun07 azel_xxxx_tex.fit azel_xxxx_figure.tex => *.ps

  31. TKEL correlations (II): All available MARS data О86Kr(15MeV/u)+64,58Ni(4o data) ●86Kr(15MeV/u)+124,112Sn(7o data) ■86Kr(25MeV/u)+124,112Sn(4odata) ▲40Ar(15MeV/u)+64,58Ni (4o data) υrel / υrel,max GS files in “kr07” : anal_mars_kr_jun07 azelv_xxxx_tex.fit azelv_xxxx_figure.tex => *.ps

  32. Nuclide cross sections from: 40Ar (15MeV/nucleon) + 64Ni,58Ni, 27Al 40Ar +64Ni K Ar (+1p) 40Ar +58Ni 40Ar +27Al Cl S 38S σ = 20 mb (-1p) (-2p) largest cross sections with the n-rich 64Ni target Si P (-3p) (-4p)

  33. Mass Distributions: 86Kr (15 MeV/u) + 64Ni* • 86Kr + 64Ni (15 MeV/u) • 86Kr + 64Ni (25 MeV/u)* • ----- DIT/GEMINI ----- EPAX • 1p • 2p 35Br 34Se Large cross sections of n- pickup products • 3p • 4p 33As 32Ge • 5p • 4p 30Zn 31Ga 23 *G. A. Souliotis et al., Phys. Lett. B 543, 163 (2002)

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

  35. Results of BigSol Line tests: Charge State Distributions Charge state distribution at PPAC1 (thru 2-inch hole) of 64Ni (35MeV/u) after a mylar stripper. B=2.020 Tm, IBigSol=109.0 A Angular acceptance: 2.0-6.0 deg. Y 28+ 27+ Angular acceptance: 3.0-6.0 deg. X

  36. BigSol Line: 136Xe DIC data Example of Z-E/A distribution of fragments from 136Xe (20 MeV/u) data: ( ΔΕ-Ε-TOF techniques, use of large area Si and PPACs) : 136Xe+124Sn 136Xe+232Th up to + 6 p 136Xe “elastic” 136Xe “elastic” Z Z E/A (MeV/u) E/A (MeV/u) B=1.325 Tm, Angular acceptance: 1.5-3.0 deg.

  37. END of Talk ( ΙI ) Quad Triplet :

  38. Quadrupole Triplet: 1st order optics PPAC1 t,X,Y x-z plane PPAC2, ΔE,E Q1 Q2 Q3 Target Beam θ0= 30 mr φ0 =30mr y-z plane Rays through QTS: 46Ar18+(14.7 MeV/u) Bρ=1.400Tm Ion Optics calculations with COSY-Infinity (M. Berz et al.)

  39. Quadrupole Triplet: 3d order optics x-z plane Q1 Q2 Q3 PPAC1 t,X,Y PPAC2, ΔE,E Target Beam θ0= 30 mr φ0 =30mr y-z plane Rays through QTS: 46Ar18+(14.7 MeV/u) Bρ=1.400Tm Ion Optics calculations with COSY-Infinity (M. Berz et al.)

  40. Quadrupole Triplet: 3d order optics PPAC1 t,X,Y x-z plane Q1 Q2 Q3 PPAC2, ΔE,E Target Beam 0.0% Δp/p 2.5% Δp/p 5.0% Δp/p θ0= 30 mr φ0 =30mr y-z plane Rays through QTS: 46Ar18+(14.7 MeV/u) Bρ=1.400Tm Ion Optics calculations with COSY-Infinity (M. Berz et al.)

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