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
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