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

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

The The Superconducting Superconducting Solenoid Rare Isotope Line at TAMUSolenoid Rare Isotope Line at TAMU

BigSol Line results: Rare Isotope Production ( Sept.-Oct. 2003)

Example of Z-A distribution of fragments from64Ni(25MeV/u)+64NiB=1.473,IBigSol=79.3 AAngular acceptance: 1.5-3.0 deg.

A

Z

Z

ANeutron-Rich fragments from64Ni (25MeV/u) + 64Ni (4.0mg/cm2)B=1.900 Tm, IBigSol=102.5 Aibeam = 1 pnA, 4 hour runAngular acceptance: 1.5-3.0 deg.

-1p+1n

-2p+2n

-4p

CoFe

MnCr

Experimental work at Texas A&M: deep inelastic collisions below the Fermi energy: 86Kr(25MeV/nucleon) + 64Ni,124Sn PRL 91, 022701 (2003) 86Kr(15MeV/nucleon) + 64Ni,124Sn PRC 84, 064607 (2011) 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 :

Collisions between Heavy Ions at Fermi Energies (10<E/A < 40MeV)

b: impact parameterθ: scattering angle

Approaching phase:

Target (Zt,At)

θ

b

Projectile (Zp,Ap) • 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-likefragment (PLF) or quasi-projectile

excited target-likefragment (TLF) orquasi-target

Grazing angle, θgr: nuclei in touching configuration

The Process of N/Z Transport * and Equilibration

112 Sn50 62

124 Sn50 74

86Kr36 50

86Kr36 50

N/Z = 1.40

N/Z = 1.48

N/Z = 1.40

N/Z = 1.24

Projectile

Target

Excited Projectile-likeFragment (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)

*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 Vsym(ρ)

Pauli principle imposed (via a phase-space ‘constraint’ algorithm )

Fragment recognition algorithm (Rmin = 3.0 fm)

• Neutrons• Protons

CoMD Evolution of 86Kr Nucleus: t = 0-500 fm/c Δt = 10 fm/c

z 86Kr36 50

CoMD Calculations: 86Kr (15 MeV/nucleon) + 124Sn

CoMD: Constraint Molecular Dynamics; M. Papa, A. Bonasera, Phys. Rev. C 64, 024612 (2001)

• Neutrons• Protons

86Kr36 50

124Sn50 74

Peripheral Collision

b = 10 fm t = 0-300 fm/c Δt = 10 fm/c

zz

b = 8 fm t = 0-300 fm/c Δt = 10 fm/c

86Kr36 50

124Sn50 74

z

Semi-Peripheral Collision

z

Si Telescope Er ΔE

PPAC1 Start T,X,Y

Production Target

D1D2WienFilter

Q1Q2

Q3

Q4Q5

Dispersive Image

FinalAchromatic Image Rotatable Arm

Reaction Angle: 0-12o (selectable)

PPAC2 Stop T, X,Y

MARS Acceptances:Angular: 9 msrMomentum: 4 %

Βρ = mυ/Q

Separation Stage I

Separation Stage II

D3

MARS Recoil Separator and Setup for Heavy-Residue / RIB Studies*

K500Beam

*G. A. Souliotis et al., Nucl. Instr. Methods B, 266, 4692 (2008) and references therein

Extracted physical quantities: Velocity, Energy loss, Total Energy Mass-to-charge ratio: A/Q B ~ A/Q Atomic Number Z Z ~ ΔE1/2 Ionic charge Q Q ~ f(E, , B)

Mass number A A = Qint A/Q

 

Reconstructed: Fragment Yield Distribution Y(Z, A, υ)

Experimental Details

Reactions studied with MARS:

Δθ = 2.2-5.8o 86Kr22+ (15 MeV/u, 5 pnA) + 64Ni, 58Ni (gr~ 6o) Δθ = 5.6-9.2o 86Kr + 124Sn, 112Sn (gr~ 9o)

Experimental Mass Distributions: 86Kr (15 MeV/u) + 64,58Ni*

Large cross sectionsof n- pickup products

-6p

- 3p

-2p-1p

-5p

34Se

33As

30Zn31Ga

32Ge

35Br

-4p

23

86Kr + 64Ni (15 MeV/u)

86Kr + 58Ni (15 MeV/u)

*G. A. Souliotis et al., Phys. Rev. C 84, 064607 (2011)

Comparison of calculations with data: 86Kr (15 MeV/nucleon) + 64NiComparison of calculations with data: 86Kr (15 MeV/nucleon) + 64Ni

* P.N. Fountas, G.A. Souliotis et al., in preparation

86Kr + 64Ni (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)

35Br 34Se

33As 32Ge

31Ga 30Zn

*data: G.A. Souliotis et al., PRC 84, 064607 (2011)

Comparison: Data, Calculations: 86Kr (15 MeV/nucleon) + 64NiComparison: Data, Calculations: 86Kr (15 MeV/nucleon) + 64Ni

*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)

86Kr + 64Ni (15 MeV/u)* CoMD/SMM

----- CoMD/GEMINI35Br 34Se

33As 32Ge

31Ga 30Zn

* P.N. Fountas, G.A. Souliotis et al., in preparation

Scaling of Yield Ratios: 15MeV/nucleon data*

R21 (N,Z) = Y2/Y1

R21 = C exp ( α N )

•86Kr+64Ni,58Ni data at 4o (gr=6.0o)

•86Kr+124Sn,112Sn data at 7o (gr=9.0ο)

*G. A. Souliotis et al., in preparation

Isoscaling Parameter α : 15MeV/u data**

○ 86Kr+64Ni,58Ni ( 4o data)

R21 = C exp ( α N )

● 86Kr+124Sn,112Sn (7o data)

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)

Velocity, TKEL, E* vs Z 15MeV/u data**

○ 86Kr+64Ni,58Ni ( 4o data)

● 86Kr+124Sn,112Sn (7o data)

Peripheral collision:tinteraction short

Semi-peripheral collisions:tinteraction longer

**G. A. Souliotis et al., (in preparation)

Residues: 86Kr (15 MeV/u) + 64,58Ni

-------- DIT

-------- CoMD (asy-stiff)

-------- CoMD (asy-soft)86Kr+ 64Ni

86Kr+58Ni

• MARS Isoscaling data*

Δ(Z/A)2 = (Z/A)21

- (Z/A)2 2

= α T / (4 Csym )

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: T2 = K0 (/o) 2/3 *

K0 : inv. lev. dens. param. at o (K0 = 12 )Assume QP at normal density =o

Csym =23 MeV

Residues: 86Kr (15 MeV/u) + 124,112Sn

-------- DIT

-------- CoMD (asy-stiff)

-------- CoMD (asy-soft)86Kr+ 124Sn

86Kr+112Sn

• MARS Isoscaling data*

Δ(Z/A)2 = (Z/A)21

- (Z/A)2 2

= α T / (4 Csym )

α,V,TKEL, E* vs Z 25MeV/u data**

● 86Kr+124Sn,112Sn (4o data)

Peripheral collision:tinteraction short

Semi-peripheral collisions:tinteraction long

**G. A. Souliotis et al., PLB 588, 35 (2004)

Residues: 86Kr (25 MeV/u) + 124,112Sn

-------- DIT

-------- CoMD (asy-stiff)

-------- CoMD (asy-soft)86Kr+ 124Sn

86Kr+112Sn

• 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 )

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

FAUST/Q-Triplet Setup at TAMU*FAUST/Q-Triplet Setup at TAMU*

* Paul Cammarata et al, ( SJYgroup )

● 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

* 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).

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:

END of Talk :

Additional material here:

Peripheral Collisions: 86Kr + 124Sn

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

np

ρoverlap = ρprojectile + ρtarget

ρoverlap ~ 1/4 ρo124Sn

50 74

86Kr36 50

Peripheral collision:tinteraction

short

np

R =10 fmρoverlap ~ 1.0-1.5 ρo

124Sn50 74

86Kr36 50

Semi-peripheral collision:tinteraction

longer

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

Velocity, E*, TKEL vs Z correlations: 15MeV/u data

υmin => E*/A ~2.0 MeV

● 40Ar+64Ni,58Ni (4o data)

GS files in “ar07” : anal_mars_ar_jun07 vz_iso_arni_tex.fit vz_iso_arni_figure.tex => *.ps

Residues: 40Ar (15 MeV/u) + 64,58Ni

-------- DIT

-------- CoMD (linear)-------- CoMD (a-soft)-------- CoMD (a-stiff)-------- CoMD (Vsym = 0)

40Ar+ 64Ni

40Ar+58Ni

Csym(ρ)

• 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

TKEL correlations (I): All available MARS data

О 86Kr(15MeV/u)+64,58Ni (4o data)

GS files in “kr07” : anal_mars_kr_jun07 azel_xxxx_tex.fit azel_xxxx_figure.tex => *.ps

● 86Kr(15MeV/u)+124,112Sn (7o data)

▲ 40Ar(15MeV/u)+64,58Ni (4o data)

TKEL correlations (II): All available MARS data

О 86Kr(15MeV/u)+64,58Ni (4o data)

GS files in “kr07” : anal_mars_kr_jun07 azelv_xxxx_tex.fit azelv_xxxx_figure.tex => *.ps

● 86Kr(15MeV/u)+124,112Sn (7o data)

▲ 40Ar(15MeV/u)+64,58Ni (4o data)

υrel / υrel,max

40Ar +64Ni

largest cross sectionswith the n-rich 64Ni target

Nuclide cross sections from: 40Ar (15MeV/nucleon) + 64Ni, 58Ni, 27Al

40Ar +58Ni

40Ar +27Al

38S σ = 20 mb

K Ar

Cl S

P Si

(+1p)

(-1p)

(-4p)(-3p)

(-2p)

Mass Distributions: 86Kr (15 MeV/u) + 64Ni*

Large cross sectionsof n- pickup products

-4p

- 3p

-2p-1p

-5p

34Se

33As

30Zn31Ga

32Ge

35Br

-4p

23

86Kr + 64Ni (15 MeV/u)

86Kr + 64Ni (25 MeV/u)*

----- DIT/GEMINI

----- EPAX

*G. A. Souliotis et al., Phys. Lett. B 543, 163 (2002)

The Superconducting Solenoid Rare Isotope Line at TAMU:

Schematic diagram of the setup for heavy-residue studies from DIC:

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.

28+ 27+

Y

X

Angular acceptance: 3.0-6.0 deg.

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) :

E/A (MeV/u)

ZZ

E/A (MeV/u)

136Xe “elastic”

B=1.325 Tm, Angular acceptance: 1.5-3.0 deg.

136Xe+124Sn 136Xe+232Th

136Xe “elastic”

up to + 6 p

END of Talk

( ΙI )

Quad Triplet :

Ion Optics calculations with COSY-Infinity (M. Berz et al.)

θ0= 30 mr φ0 =30 mr

Quadrupole Triplet: 1st order optics

Target

PPAC1t,X,Y

Rays through QTS: 46Ar18+(14.7 MeV/u) Bρ=1.400 Tm

x-z plane

y-z plane

Beam

Q1 Q2 Q3PPAC2, ΔE,E

Ion Optics calculations with COSY-Infinity (M. Berz et al.)

θ0= 30 mr φ0 =30mr

Quadrupole Triplet: 3d order optics

Target

PPAC1t,X,Y

x-z plane

y-z plane

Beam

Q1 Q2 Q3

Rays through QTS: 46Ar18+(14.7 MeV/u) Bρ=1.400 Tm

PPAC2, ΔE,E

Ion Optics calculations with COSY-Infinity (M. Berz et al.)

θ0= 30 mr φ0 =30mr

Quadrupole Triplet: 3d order optics

Target x-z plane

y-z plane

Q1 Q2 Q3

Rays through QTS: 46Ar18+(14.7 MeV/u) Bρ=1.400 Tm

0.0% Δp/p

2.5% Δp/p

5.0% Δp/p

Beam

PPAC1t,X,Y

PPAC2, ΔE,E