Zbigniew Chajęcki

National Superconducting Cyclotron Laboratory

Michigan State University

B. Lynch, B. Tsang, M. Kilburn, D. Coupland, M.

Youngs

Probing the symmetry Probing the symmetry energyenergy

with heavy ionswith heavy ions

Z. Ch. - WWND 2011, Feb 6-13, 2011 2

OutlineOutline

Symmetry energy

Probing Symmetry Energy with heavy ions

n/p , t/3He spectrum

isospin diffusion

correlations

neutron and proton emission time and symmetry energy (particle emission chronology)

pion production

Summary

Z. Ch. - WWND 2011, Feb 6-13, 2011 3

E/A (,) = E/A (,0) + 2S()

= (n- p)/ (n+ p) = (N-Z)/A

Nuclear Equation of StateNuclear Equation of State

Examples of possible research areas in NSCL/FRIB

Astrophysics Nuclear structure Nuclear reactions mass and size of neutron stars nature of neutron stars and dense nuclear matter origin of elements heavier than iron in the cosmosnuclear reactions that drive stars and stellar explosions?

Neutron skin thickness GMR PDR Isobaric Analog States nature of the nuclear

force that binds protons and neutrons into stable nuclei and rare isotopes

etc...

n/p ratios t/³He ratios Isospin diffusion Isoscalingproton-proton correlations etc...

Z. Ch. - WWND 2011, Feb 6-13, 2011 4

EOS: symmetric matter and neutron EOS: symmetric matter and neutron mattermatter

Brown, Phys. Rev. Lett. 85, 5296 (2001)

Neutron matter EOS

The density dependence of symmetry energy is largely unconstrained.

E/A (,) = E/A (,0) + 2S()

= (n- p)/ (n+ p) = (N-Z)/A

1

E/A

[MeV

]

Crucial to obtain

stellar radii

moments of interia

maximum masses

neutron star cooling rates

crustal vibration frequencies

stiff

soft

Z. Ch. - WWND 2011, Feb 6-13, 2011 5

Probes of the symmetry Probes of the symmetry energyenergy

• To maximize sensitivity, reduce systematic errors:– Vary isospin of detected particle– Vary isospin asymmetry

=(N-Z)/A of reaction.• Low densities (<0):

– Neutron/proton spectra and flows– Isospin diffusion– Correlations

• High densities (20) :– Neutron/proton spectra and flows + vs. - production– Correlations

symmetry energy

<0>0

E/A (,) = E/A (,0) + 2S() = (n- p)/ (n+ p) = (N-Z)/A

S() = 12.5·(ρ/ρ0)2/3 + Sint· (ρ/ρ0)

stiff

soft

Z. Ch. - WWND 2011, Feb 6-13, 2011 6

InternationaInternational l

CollaboratioCollaborationn

RIBFFRIB

MSU

GSI

FAIR

?

Facility Probe Beam En. [MeV]

Year Density

MSU n,p,t,3He 50-140 2009 < 0

GSI n,p,t,3He 400 2010/2011 2.5 0

MSU iso-diffusion 50 2010/2011 < 0

RIKEN iso-diffusion 50 2010 < 0

MSU 140 2012-2014 1-1.5 0

RIKEN n,p,t,3He,

200-300 2014 2 0

GSI n,p,t,3He 800 2014 2-3 0

FRIB n,p,t,3He,

200 2018- 2-2.5 0

FAIR K+,K- 800-1000 2018 3 0

E/A (,) = E/A (,0) + 2S()

= (n- p)/ (n+ p) = (N-Z)/A

Symmetry Energy Project Symmetry Energy Project CollaborationCollaboration

Determination of the Equation of State of Asymmetric Nuclear Matter NSCL MSU, USA: B. Tsang & W. Lynch, Gary Westfall, Pawel Danielewicz, Edward Brown, Andrew Steiner Rutgers University: Jolie Cizewski Smith College : Malgorzata Pfabe University of Texas, El Paso: Jorge Lopez Texas A&M University : Sherry Yennello Western Michigan University : Michael Famiano RIKEN, JP: Hiroshi Sakurai, Shunji Nishimura, Yoichi Nakai, Atsushi Taketani Kyoto University: Tetsuya MurakamiRikkyo University, JP: Jiro Murata, Kazuo Ieki Tohoku University: Akira Ono GSI DE: Wolfgang Trautmann, Yvonne Leifels, Marcus Bleicher Daresbury Laboratory, UK: Roy Lemmon INFN LNS Catania, IT: Giuseppe Verde, Angelo Pagano, Paulo Russotto, Massimo di Toro, Maria Colonna, Aldo Bonasera, Vincenzo Greco SUBATECH FR: Christoph Hartnack GANIL FR: Abdou Chbihi, John Frankland, Jean-Pierre Wieleczko Ruđer Boskovic Institute, Zoran Basrak, China Institute of Atomic Energy: Yingxun Zhang, Zhuxia Li Brazil: Sergio Souza, Raul Donangelo, Brett Carlson

Z. Ch. - WWND 2011, Feb 6-13, 2011 7

Modeling heavy-ion collisions : transport Modeling heavy-ion collisions : transport modelsmodels

• Parameter space

• not only about the symmetry energy

• also important to understand e.g. an effect of cross section (free x-section, in-medium x-section), reduced mass

• Production of clusters: d,t, 3He (alphas)

QuickTime™ and a decompressor

are needed to see this picture.

• BUU - Boltzmann-Uehling-Uhlenbeck

• Simulates two nuclei colliding

Danielewicz, Bertsch, NPA533 (1991) 712 B. A. Li et al., PRL 78 (1997) 1644

Micha Kilburn

Z. Ch. - WWND 2011, Feb 6-13, 2011 8

Probing Symmetry Energy:Probing Symmetry Energy:

Experimental ObservablesExperimental Observables

Z. Ch. - WWND 2011, Feb 6-13, 2011 9

n/p yield ratios

-100

-50

0

50

100

0 0.5 1 1.5 2

Li et al., PRL 78 (1997) 1644

Vasy

(MeV)

/ο

NeutronProton

F1=2u2/(1+u)

F2=u

F3=u

F1F2

F3

u =

stiff

soft

Uas

y (M

eV)

=0.3

• n and p potentials have opposite sign

• n and p energy spectra depend on the symmetry energy and softer density dependence emits more neutrons at low density

•More n’s are emitted from the n-rich system and softer iso-EOS

ImQMD

Y(n

)/Y

(p)

S()=12.5(/o)2/3 +17.6(/o)i

soft

stiff

soft

stiff

Z. Ch. - WWND 2011, Feb 6-13, 2011 10

t/3He yield ratiosL-W Chen et al., PRC 69 (2004) 054606

t/3He ratio sensitive to the symmetry energy (similarly as n/p)

- advantage: easier to measure

However, the magnitude of the ratio depends also on the details within the symmetry energy potential

Z. Ch. - WWND 2011, Feb 6-13, 2011 11

Probing Symmetry Energy with n’s and p’sProbing Symmetry Energy with n’s and p’s

Density dependence of the symmetry energy with emitted neutrons and protons& Investigation of transport model parameters.

Proj Target E/A Range

40Ca 124Sn 140

> 0

40Ca 112Sn 140

48Ca 124Sn 140

48Ca 112Sn 140

124Sn 124Sn 50, 120 < 0

> 0

112Sn 112Sn 50, 120

Famiano, Coupland, Youngs

NSCL experiments 05049 & 09042NSCL experiments 05049 & 09042

Z. Ch. - WWND 2011, Feb 6-13, 2011 12

Measurement of n/p spectral ratios: probes the Measurement of n/p spectral ratios: probes the pressure due to asymmetry term at pressure due to asymmetry term at 00..

• Probe expulsion of neutrons from bound neutron-rich system by symmetry energy.

• Has been probed by direct measurements of neutrons vs. proton emission rates in central Sn+Sn collisions.

Esym=12.7(/o)2/3 + 19(/o)i

minimize systematic errors

124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)

Double Ratios

•Double ratio removes the sensitivity to neutron efficiency and energy calibration.

soft

stiff

Z. Ch. - WWND 2011, Feb 6-13, 2011 13

Isospin diffusion is measured with fragments emitted from the neck region. Probe the symmetry energy at subsaturation densities in semi-peripheral

collisions, e.g. 124Sn + 112Sn at b=6 fm Isospin “diffuse” through low-density neck region

Symmetry energy drives system towards equilibrium.

=(N-Z)/A

• stiff EOS small diffusion; |Ri|>>0

• soft EOS fast equilibrium; Ri0

Projectile

Target

124Sn

112Sn

soft

stiff

Experimental Experimental observable: observable:

Isospin dependenceIsospin dependence

Ri ( ) =2⋅ −(bothn-rich +bothp-rich) / 2

bothn-rich −bothp-rich

Z. Ch. - WWND 2011, Feb 6-13, 2011 14

Isospin diffusion is measured with fragments emitted from the neck region.

Probe the symmetry energy at subsaturation densities in semi-peripheral collisions, e.g. 124Sn + 112Sn at b=6 fm

Isospin “diffuse” through low-density neck region

Symmetry energy drives system towards equilibrium.

• stiff EOS small diffusion; |Ri|>>0

• soft EOS fast equilibrium; Ri0

Experimental observable: Isospin Experimental observable: Isospin dependencedependence

Projectile Target E/A lab range

124,118,112Sn 124,118,112Sn 50 NSCL < 0124,112,108Sn 124,112Sn 50 RIKEN

S() = 12.5·(ρ/ρ0)2/3 + Sint· (ρ/ρ0)

Ri (X) =2⋅X−(XA+A + XB+B) / 2

XA+A −XB+B

X =lnY( 7Li)Y( 7Be)

⎛

⎝⎜⎞

⎠⎟

Z. Ch. - WWND 2011, Feb 6-13, 2011 15

Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn

Stiff EoS Soft

EoS

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

faster emission times

Soft EoS (γ=0.5)

L-W

Chen e

t al., PR

L90

(2

00

3)

16

27

01

52Ca 48Ca

Z. Ch. - WWND 2011, Feb 6-13, 2011 16

Sym.En. and correlationsSym.En. and correlations

Stiff EoS

Soft EoS

L-W

Chen e

t al., PR

L90

(2

00

3)

16

27

01

Stiff

Stiff EoS

Soft

Soft EoS

n-n, p-p, n-p correlations sensitive to the symmetry energy

Z. Ch. - WWND 2011, Feb 6-13, 2011 17

proton-proton correlationsproton-proton correlations

few fm

x1

x2

p1

p2

€

C(p1, p2 ) =P(p1, p2 )

P(p1)P(p2 )=

real event pairs

mixed event pairs

Experimental correlation function:

P(p1) - single particle distribution

P(p1, p2 ) - two particle distribution

r

|q| = 0.5 |p1 - p2|

(p,p) correlation functionP(p1,p2)

P(p1)P(p2)

|q| = 0.5 |p1 - p2|

( ) ( ) ( )rSrrdq q

rrrr

23C ∫ Φ=

( )rqr

rΦ

( )rS r… 2-particle wave function

… source function

Theoretical CF: Koonin-Pratt equationS.E. Koonin, PLB70 (1977) 43S.Pratt et al., PRC42 (1990) 2646

|q| = 0.5 |p1 - p2|

(p,p) correlation function

uncorrelated

Coulomb

S-wave interraction

Z. Ch. - WWND 2011, Feb 6-13, 2011 18

NSCL experiments 05045: HiRA + 4NSCL experiments 05045: HiRA + 4 detectordetector November 2006November 2006

- 4π detector => impact parameter + reaction plane

- HiRA => light charge particle correlations (angular coverage 20-60º in LAB,

-63 cm from target (= ball center))

beam

= High Resolution Array

Reaction systems:

40Ca + 40Ca @ 80 MeV/u

48Ca + 48Ca @ 80 MeV/u

Z. Ch. - WWND 2011, Feb 6-13, 2011 19

32 strips v. (front)

Beam

Si-E 65 m

32 strips v.(front)

Si-E 1.5 mm

pixel

32 strips h. (back)

4x CsI(Tl) 4cm

• up to 20 Telescopes • 62.3 x 62.3 mm2 active area• strip pitch 2 mm• 1024 Pixels per telescope

@ 63 cm from target => Δθ<0.2º

•ASIC readout

Telescope

Z. Ch. - WWND 2011, Feb 6-13, 2011 20

Detector performanceDetector performance

good PIDHigh resolution at low relative momentum

Z. Ch. - WWND 2011, Feb 6-13, 2011 21

Initial size effectInitial size effect

R=r0 A1/3

R(40Ca) = 4.3 fm

R(48Ca) = 4.6 fm

R 48Ca+ 48Ca > R 40Ca+ 40Ca

Z. Ch. - WWND 2011, Feb 6-13, 2011 22

Comparing data to pBUU Comparing data to pBUU

BUU PararametersNo dependence on symmetry

energyRostock in-medium reductionProducing clusters

BUU does reasonably wellExcept at forward angles -

Spectator sourceWhere evaporation and

secondary decays are important!

Forward angle

Backward angle

Micha Kilburn

Z. Ch. - WWND 2011, Feb 6-13, 2011 23

Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn

Stiff EoS Soft

EoS

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

faster emission times

Soft EoS (γ=0.5)

L-W

Chen e

t al., PR

L90

(2

00

3)

16

27

01

52Ca 48Ca

Z. Ch. - WWND 2011, Feb 6-13, 2011 24

n-p correlation functionn-p correlation function

few fm

x1

x2

p1

p2

( ) ( ) ( )rSrrdq q

rrrr

23C ∫ Φ=

( )rqr

rΦ

( )rS r… 2-particle wave function

… source function

Theoretical CF: Koonin-Pratt equationS.E. Koonin, PLB70 (1977) 43S.Pratt et al., PRC42 (1990) 2646

r

0 x

S(x)

(n,p) correlation function

0 x

S(x)

(n,p) correlation function

q = 0.5(p1 - p2)

Z. Ch. - WWND 2011, Feb 6-13, 2011 25

Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn

Stiff EoS Soft

EoS

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

faster emission times

Soft EoS (γ=0.5)

L-W

Chen e

t al., PR

L90

(2

00

3)

16

27

01

52Ca 48Ca

Z. Ch. - WWND 2011, Feb 6-13, 2011 26

Possible emission configurations (stiff Possible emission configurations (stiff sym. pot.)sym. pot.)

nCatching up

p

np

np

Catching up

Moving awayMoving away

np

0 x

S(x)

(n,p) correlation function

q = 0.5(pp - pn)

qx<0

qx<0

qx>0( ) ( ) ( )rSrrdq q

rrrr

23C ∫ Φ=

q=pp -pn =(qx, qy=0, qz=0); r =(x, y=0,z=0)

qx<0

qx>0

qx>0

Z. Ch. - WWND 2011, Feb 6-13, 2011 27

Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn

Stiff EoS Soft

EoS

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

faster emission times

Soft EoS (γ=0.5)

L-W

Chen e

t al., PR

L90

(2

00

3)

16

27

01

52Ca 48Ca

Z. Ch. - WWND 2011, Feb 6-13, 2011 28

Sensitivity to particle emission (soft Sensitivity to particle emission (soft sym. pot.)sym. pot.)

np

np

Catching upMoving away

0

x

S(x)

(n,p) correlation function

qx = 0.5(px,p - px,n)

qx<0 qx>0

qx<0

qx>0

( ) ( ) ( )rSrrdq q

rrrr

23C ∫ Φ=Experimentally, we measure the CF, not the source distribution!

€

C(p1, p2 ) =P(p1, p2 )

P(p1)P(p2 )=

real event pairs

mixed event pairs

P(p1) - single particle distribution

P(p1, p2 ) - two particle distribution

q=pp -pn =(qx, qy=0, qz=0); r =(x, y=0,z=0)

Z. Ch. - WWND 2011, Feb 6-13, 2011 29

Not expected if n,p emitted from the same source (no n-p differential flow)

Relating asymmetry in the CF to space-time Relating asymmetry in the CF to space-time asymmetryasymmetry

x t( ) = xp −xn( )−V tp −tn( )

(n,p) correlation function

qx = 0.5(px,p - px,n)

qx<0

qx>0

C qx( ) = dxΦ r

q x( )∫2S x t( )( )

x < 0ifx p < x n

tp > tn

⎛

⎝

⎜⎜ Protons emitted later

0x

S(x)

<x>

=0

Stiff EoS Soft

EoS

Clasically, average separation b/t protons and neutrons

Z. Ch. - WWND 2011, Feb 6-13, 2011 30

High density probe: pion High density probe: pion productionproduction

• Double ratio involves comparison between neutron rich 132Sn+124Sn and neutron deficient 112Sn+112Sn reactions.

• Double ratio maximizes sensitivity to asymmetry term.– Largely removes sensitivity

to difference between - and + acceptances.

R− / 132Sn+124 Sn( ) / 112Sn+112 Sn( )

=Y −( )

132+124/Y +( )

132+124⎡⎣

⎤⎦

Y −( )112+112

/Y +( )112+112

⎡⎣

⎤⎦

Yong et al., Phys. Rev. C 73, 034603 (2006)

soft

stiff

Facility Probe Beam En. [MeV]

Year Density

MSU 140 2012-2014 1-1.5 0

Z. Ch. - WWND 2011, Feb 6-13, 2011 31

The density dependence of the symmetry energy is of fundamental importance to nuclear physics and neutron star physics.

Observables in HI collisions provide unique opportunities to probe the symmetry energy over a wide range of density especially for dense asymmetric matter

Calculations suggest a number of promising observables that can probe the density dependence of the symmetry energy.

Need more guidance from theory regarding observables beyond normal nuclear matter density

The availability of intense fast rare isotope beams at a variety of energies at FRIB & FAIR allows increased precisions in probing the symmetry energy at a wide range of densities

– Experimental programs are being developed to do such measurements at MSU/FRIB, RIKEN/RIBF and GSI/FAIR

SummarySummary

Z. Ch. - WWND 2011, Feb 6-13, 2011 32

Acknowledgments

• Brent Barker, Dan Brown, Zbigniew Chajecki, Dan Coupland, Pawel Danielewicz, Vlad Henzl, Daniela Henzlova, Clemens Herlitzius,

Micha Kilburn, Jenny Lee, Sergei Lukyanov, Bill Lynch, Andy Rogers, Alisher Sanetullaev, Zhiyu Sun, Betty Tsang, Andrew

Vander Molen, Gary Westfall, Mike Youngs

• NSCL-MSU

Abdou Chbihi GANIL, Caen, France

Mike Famiano Western Michigan University, Kalamazoo

Giuseppe Verde INFN, Catania, Italy

Mark Wallace LANL

Washington University, St. Louis

Romualdo DesouzaSylvie Hudan Indiana University, Bloomington

Bob CharityJon ElsonLee Sobotka