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Zbigniew Chaj ę cki National Superconducting Cyclotron Laboratory Michigan State University

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

Probing the symmetry energywith heavy ions

Zbigniew Chajęcki

National Superconducting Cyclotron Laboratory Michigan State University

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

Outline

- 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

Nuclear 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 cosmos
- nuclear reactions that drive stars and stellar explosions?

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

- 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...

E/A (,) = E/A (,0) + d2S()

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

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

EOS: symmetric matter and neutron matter

- Crucial to obtain
- stellar radii
- moments of interia
- maximum masses
- neutron star cooling rates
- crustal vibration frequencies

E/A (,) = E/A (,0) + d2S()

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

1

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

stiff

Neutron matter EOS

E/A [MeV]

soft

The density dependence of symmetry energy is largely unconstrained.

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

Probes of the symmetry energy

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

E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A

stiff

soft

>0

<0

symmetry energy

S()= 12.5·(ρ/ρ0)2/3 + Sint·(ρ/ρ0)

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

International Collaboration

Symmetry Energy Project Collaboration

Determination of the Equation of State of Asymmetric Nuclear MatterNSCL 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 WieleczkoRuđer Bosković Institute, Zoran Basrak, China Institute of Atomic Energy: Yingxun Zhang, Zhuxia Li Brazil: Sergio Souza, Raul Donangelo, Brett Carlson

E/A (,) = E/A (,0) + d2S()

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

RIBF

FRIB

MSU

GSI

?

FAIR

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

Modeling heavy-ion collisions : transport models

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

- BUU - Boltzmann-Uehling-Uhlenbeck
- Simulates two nuclei colliding

Micha Kilburn

- 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)

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

Probing Symmetry Energy:Experimental Observables

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

n/p yield ratios

F2

F1

stiff

F3

gi

soft

S(r)=12.5(r/ro)2/3+17.6(r/ro)

ImQMD

F1=2u2/(1+u)

F2=u

F3=u

soft

Y(n)/Y(p)

soft

u =

stiff

stiff

- 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

=0.3

Uasy (MeV)

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

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

t/3He yield ratios

L-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

Probing Symmetry Energy with n’s and p’s

Density dependence of the symmetry energy with emitted neutrons and protons

& Investigation of transport model parameters.

Famiano, Coupland, Youngs

NSCL experiments 05049 & 09042

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

Measurement of n/p spectral ratios: probes the pressure due to asymmetry term at 0.

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.

gi

Esym=12.7(r/ro)2/3+19(r/ro)

Double Ratios

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

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

soft

stiff

minimize systematic errors

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

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

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

Experimental observable: Isospin dependenceProjectile

124Sn

Target

112Sn

stiff

soft

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

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 dependenceS()= 12.5·(ρ/ρ0)2/3 + Sint·(ρ/ρ0)

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

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

52Ca

48Ca

Stiff EoS

L-W Chen et al., PRL90 (2003) 162701

Soft EoS

Soft EoS (γ=0.5)

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

fasteremission times

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

Sym.En. and correlations

Soft EoS

Stiff EoS

L-W Chen et al., PRL90 (2003) 162701

Stiff EoS

Soft EoS

Soft

Stiff

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

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

proton-proton correlations

Theoretical CF: Koonin-Pratt equation

S.E. Koonin,

PLB70 (1977) 43

S.Pratt et al.,

PRC42 (1990) 2646

… 2-particle wave function

… source function

(p,p) correlation function

(p,p) correlation function

S-wave interraction

Coulomb

uncorrelated

|q| = 0.5 |p1 - p2|

|q| = 0.5 |p1 - p2|

p1

Experimental correlation function:

x1

r

x2

p2

few fm

P(p1,p2)

P(p1)P(p2)

|q| = 0.5 |p1 - p2|

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

NSCL experiments 05045: HiRA + 4 detector

November 2006

= High Resolution Array

beam

- 4π detector => impact parameter + reaction plane
- HiRA => light charge particle correlations (angular coverage 20-60º in LAB,
- 63 cm from target (= ball center))

Reaction systems:

40Ca + 40Ca @ 80 MeV/u

48Ca + 48Ca @ 80 MeV/u

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

Telescope

4x CsI(Tl) 4cm

Si-E 1.5 mm

Si-DE 65mm

pixel

32 strips v.(front)

32 strips h. (back)

32 strips v. (front)

Beam

- ASIC readout

- 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

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

Detector performance

High resolution at low relative momentum

good PID

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

Initial 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

Comparing data to pBUU

Backward angle

Forward angle

BUU Pararameters

No dependence on symmetry energy

Rostock in-medium reduction

Producing clusters

BUU does reasonably well

Except at forward angles -

Spectator source

Where evaporation and secondary decays are important!

Micha Kilburn

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

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

52Ca

48Ca

Stiff EoS

L-W Chen et al., PRL90 (2003) 162701

Soft EoS

Soft EoS (γ=0.5)

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

fasteremission times

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

n-p correlation function

(n,p) correlation function

(n,p) correlation function

S(x)

S(x)

x

x

0

0

Theoretical CF: Koonin-Pratt equation

p1

S.E. Koonin,

PLB70 (1977) 43

S.Pratt et al.,

PRC42 (1990) 2646

x1

r

… 2-particle wave function

… source function

x2

p2

few fm

q = 0.5(p1 - p2)

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

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

52Ca

48Ca

Stiff EoS

L-W Chen et al., PRL90 (2003) 162701

Soft EoS

Soft EoS (γ=0.5)

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

fasteremission times

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

Possible emission configurations (stiff sym. pot.)

n

n

n

n

p

p

p

p

Catching up

Catching up

qx<0

qx>0

Moving away

Moving away

qx<0

qx>0

(n,p) correlation function

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

qx<0

qx>0

S(x)

x

0

q = 0.5(pp - pn)

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

52Ca

48Ca

Stiff EoS

L-W Chen et al., PRL90 (2003) 162701

Soft EoS

Soft EoS (γ=0.5)

Stiff EoS (γ=2)

p’s emitted after n’s

later emission times

p’s and n’s emitted at similar time

fasteremission times

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

Sensitivity to particle emission (soft sym. pot.)

n

n

p

p

Experimentally, we measure the CF, not the source distribution!

Moving away

Catching up

qx<0

qx>0

(n,p) correlation function

qx<0

qx>0

S(x)

x

0

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

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

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

Relating asymmetry in the CF to space-time asymmetry

Stiff EoS

Soft EoS

(n,p) correlation function

qx<0

qx>0

S(x)

<x>

x

0

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

Clasically, average separation b/t protons and neutrons

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

=0

Protons emitted later

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

High density probe: pion production

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.

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

soft

stiff

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

Summary

- 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

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

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

Bob Charity

Jon ElsonLee Sobotka

Washington University, St. Louis

Abdou Chbihi GANIL, Caen, France

Romualdo DesouzaSylvie Hudan

Indiana University, Bloomington

Mike Famiano Western Michigan University, Kalamazoo

Giuseppe Verde INFN, Catania, Italy

Mark Wallace LANL

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

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