george a. souliotis laboratory of physical chemistry, department of chemistry,

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