1. 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 Studies of N/Z equilibration via Heavy-Residue Isoscaling

3. BigSol Setup at TAMU: Sept. 2002 BigSol Setup at TAMU: Sept. 2002

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

6. Experimental work at Texas A&M: deep inelastic collisions below the Fermi energy: 86 Kr(25MeV/nucleon) + 64 Ni, 124 Sn PRL 91, 022701 (2003) PRC 84, 064607 (2011) 86 Kr(15MeV/nucleon) + 64 Ni, 124 Sn 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: Heavy-residue isoscaling: PRC 68, 024605 (2003) PRC 73, 024606 (2006) 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. Overview of Heavy-Residue work :

7. Collisions between Heavy Ions at Fermi Energies (10<E/A < 40MeV) b: impact parameter θ: scattering angle Approaching phase: Target (Z t,A t ) θ b Projectile (Z p,A p ) Neutrons Protons 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 Grazing angle, θ gr : nuclei in touching configuration

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

9. *M. Papa, A. Bonasera et al., Phys. Rev. C 64, 024612 (2001) 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 V sym (ρ)  Pauli principle imposed (via a phase-space ‘constraint’ algorithm )  Fragment recognition algorithm (R min = 3.0 fm) Neutrons Protons CoMD Evolution of 86 Kr Nucleus: t = 0-500 fm/c Δt = 10 fm/c z 86 Kr 36 50

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

11. Si Telescope E r ΔE PPAC1 Start T,X,Y Production Target D1D2 Wien Filter Q1 Q2 Q3 Q4 Q5 Dispersive Image Final Achromatic Image Rotatable Arm Reaction Angle: 0-12 o (selectable) PPAC2 Stop T, X,Y MARS Acceptances: Angular: 9 msr Momentum: 4 % Βρ = mυ/Q Separation Stage I Separation Stage II D3 MARS Recoil Separator and Setup for Heavy-Residue / RIB Studies* K500 Beam *G. A. Souliotis et al., Nucl. Instr. Methods B, 266, 4692 (2008) and references therein

12. Extracted physical quantities: Velocity, Energy loss, Total Energy Mass-to-charge ratio: A/Q B  ~ A/Q   Atomic Number Z Z ~  ΔE 1/2 Ionic charge Q Q ~ f(E, , B  ) Mass number A A = Q int  A/Q Reconstructed: Fragment Yield Distribution Y(Z, A, υ) Experimental Details Reactions studied with MARS: Δθ = 2.2-5.8 o 86 Kr 22+ (15 MeV/u, 5 pnA) + 64 Ni, 58 Ni (  gr ~ 6 o ) Δθ = 5.6-9.2 o 86 Kr + 124 Sn, 112 Sn (  gr ~ 9 o )

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

14. Comparison of calculations with data: 86 Kr (15 MeV/nucleon) + 64 Ni * P.N. Fountas, G.A. Souliotis et al., in preparation 86 Kr + 64 Ni (15 MeV/u)* DIT/SMM ------ DITm/SMM 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) 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn *data: G.A. Souliotis et al., PRC 84, 064607 (2011)

15. Comparison: Data, Calculations: 86 Kr (15 MeV/nucleon) + 64 Ni *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) 86 Kr + 64 Ni (15 MeV/u)* CoMD/SMM ----- CoMD/GEMINI 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn * P.N. Fountas, G.A. Souliotis et al., in preparation

16. Scaling of Yield Ratios: 15MeV/nucleon data* R 21 (N,Z) = Y 2 /Y 1 R 21 = C exp ( α N ) 86 Kr+ 64 Ni, 58 Ni data at 4 o (  gr =6.0 o ) 86 Kr+ 124 Sn, 112 Sn data at 7 o (  gr =9.0 ο ) *G. A. Souliotis et al., in preparation

17. Isoscaling Parameter α : 15MeV/u data** ○ 86 Kr+ 64 Ni, 58 Ni ( 4 o data) R 21 = C exp ( α N ) ● 86 Kr+ 124 Sn, 112 Sn ( 7 o data) α = 4 C sym /T ( (Z/A) 1 2 – (Z/A) 2 2 ) 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)

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

19. Residues: 86 Kr (15 MeV/u) + 64,58 Ni -------- DIT -------- CoMD (asy-stiff) -------- CoMD (asy-soft) 86 Kr+ 64 Ni 86 Kr+ 58 Ni MARS Isoscaling data* Δ(Z/A) 2 = (Z/A) 2 1 - (Z/A) 2 2 = α T / (4 C sym ) DIT: Deep Inelastic Transfer: L. Tassan-Got, Nucl. Phys. A 524, 121 (1991) CoMD: Constraint Molecular Dynamics * G.A. Souliotis et al. (in preparation) Fermi gas: T 2 = K 0 (  /  o ) 2/3  * K 0 : inv. lev. dens. param. at  o (K 0 = 12 ) Assume QP at normal density  =  o C sym =23 MeV

20. Residues: 86 Kr (15 MeV/u) + 124,112 Sn -------- DIT -------- CoMD (asy-stiff) -------- CoMD (asy-soft) 86 Kr+ 124 Sn 86 Kr+ 112 Sn MARS Isoscaling data* Δ(Z/A) 2 = (Z/A) 2 1 - (Z/A) 2 2 = α T / (4 C sym )

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

22. Residues: 86 Kr (25 MeV/u) + 124,112 Sn -------- DIT -------- CoMD (asy-stiff) -------- CoMD (asy-soft) 86 Kr+ 124 Sn 86 Kr+ 112 Sn MARS Isoscaling data: G.A.Souliotis et al. PRC 68, 024605 (2003) Δ(Z/A) 2 = (Z/A) 2 1 - (Z/A) 2 2 = α T / (4 C sym )

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

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

25. ● 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 V sym (ρ) found in the Δ vs TKEL correlation * TAMU Cyclotron Upgrade, see : http://cyclotron.tamu.edu Summary and Conclusions Extension of experimental studies using neutron-rich RIBs from TAMU RIB Upgrade*, SPES at Legnaro, SPIRAL-II at GANIL and other facilities 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).

26. Collaborators M. Veselsky, S. Galanopoulos, Z. Kohley, A. McIntosh, L.W. May, B.C. Stein, S.J. Yennello Special thanks to: A. Bonasera, TAMU and INFN, Catania, Italy, A. Botvina, FIAS, Frankfurt, Germany 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 Acknowledgements:

27. END of Talk : Additional material here:

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

29. Isoscaling: 40 Ar (15MeV/nucleon) + 64 Ni, 58 Ni 40 Ar + 64 Ni, 58 Ni (data inside  gr =6.2 ο ) R 21 = C exp ( α N ) α = 4 C sym /T ( (Z/A) 1 2 – (Z/A) 2 2 ) 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

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

31. Residues: 40 Ar (15 MeV/u) + 64,58 Ni -------- DIT -------- CoMD (linear) -------- CoMD (a-soft) -------- CoMD (a-stiff) -------- CoMD (Vsym = 0) 40 Ar+ 64 Ni 40 Ar+ 58 Ni C sym (ρ) MARS Isoscaling data* Δ(Z/A) 2 = (Z/A) 2 1 - (Z/A) 2 2 = a T / (4 C sym ) GS files in “ar07” : anal_mars_ar_jun07 azel1_arni_tex.fit azel1_arni_figure.tex => *.ps

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

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

34.  40 Ar + 64 Ni largest cross sections with the n-rich 64 Ni target Nuclide cross sections from: 40 Ar (15MeV/nucleon) + 64 Ni, 58 Ni, 27 Al  40 Ar + 58 Ni  40 Ar + 27 Al 38 S σ = 20 mb KAr Cl S P Si (+1p) (-1p) (-4p)(-3p) (-2p)

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

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

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

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

39. END of Talk ( ΙI ) Quad Triplet :

40. Ion Optics calculations with COSY-Infinity (M. Berz et al.) θ 0 = 30 mr φ 0 =30 mr Quadrupole Triplet: 1 st order optics Target PPAC1 t,X,Y Rays through QTS: 46 Ar 18+ (14.7 MeV/u) Bρ=1.400 Tm x-z plane y-z plane Beam Q1Q2Q3 PPAC2, ΔE,E

41. Ion Optics calculations with COSY-Infinity (M. Berz et al.) θ 0 = 30 mr φ 0 =30mr Quadrupole Triplet: 3 d order optics Target PPAC1 t,X,Y x-z plane y-z plane Beam Q1Q2Q3 Rays through QTS: 46 Ar 18+ (14.7 MeV/u) Bρ=1.400 Tm PPAC2, ΔE,E

42. Ion Optics calculations with COSY-Infinity (M. Berz et al.) θ 0 = 30 mr φ 0 =30mr Quadrupole Triplet: 3 d order optics Target x-z plane y-z plane Q1Q2Q3 Rays through QTS: 46 Ar 18+ (14.7 MeV/u) Bρ=1.400 Tm 0.0% Δp/p 2.5% Δp/p 5.0% Δp/p Beam PPAC1 t,X,Y PPAC2, ΔE,E