Zbigniew Chajęcki

National Superconducting Cyclotron Laboratory

Michigan State University

Probing reaction Probing reaction dynamics with two-dynamics with two-particle correlationsparticle correlations

Z. Ch. - NuSYM 2011, June 17-20, 2011 2

OutlineOutline

p-p correlations (work with M. Kilburn, B. Lynch and collaborators)

NSCL 03045 Experiment

transport theory (BUU)

neutron and proton emission times and symmetry energy

(particle emission chronology)

transport theory

Summary

Z. Ch. - NuSYM 2011, June 17-20, 2011 3

Experimental correlation functionExperimental correlation function

few fm

x1

x2

p1

p2

Experimental correlation function:

r

|q| = 0.5 |p1 - p2|

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

P(p1)P(p2)

|q| = 0.5 |p1 - p2|

Z. Ch. - NuSYM 2011, June 17-20, 2011 4

FemtoscopyFemtoscopy

few fm

x1

x2

p1

p2

… 2-particle wave function

… source function

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

r

|q| = 0.5 |p1 - p2|

(p,p) correlation function

0 r

S(r)

uncorrelated

Coulomb

S-wave interraction

|q| = 0.5 |p1 - p2|

uncorrelated

Coulomb

S-wave interraction

(p,p) correlation function

0 r

S(r)

r1/2

Z. Ch. - NuSYM 2011, June 17-20, 2011 5

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

- 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. - NuSYM 2011, June 17-20, 2011 7

Momentum and rapidity Momentum and rapidity dependencedependenceC

(q)

Measured correlation functions depend on rapidity and the transverse momentum of the pair

Next step: extract the sizes

Z. Ch. - NuSYM 2011, June 17-20, 2011 8

Fits to the dataFits to the dataC

(q)

Brown, Danielewicz, PLB398 (1997) 252Danielewicz, Pratt, PLB618 (2005) 60

Koonin-Pratt Equation

Two ways of characterizing the size of the p-p source

1) S(r) - Gaussian shape

2) Imaged S(r) (Brown, Danielewicz)

Z. Ch. - NuSYM 2011, June 17-20, 2011 9

Fits to the dataFits to the data

Brown, Danielewicz, PLB398 (1997) 252Danielewicz, Pratt, PLB618 (2005) 60

C(q

)

Koonin-Pratt Equation

Two ways of characterizing the size of the p-p source

1) S(r) - Gaussian shape

2) Imaged S(r) (Brown, Danielewicz)

Both methods give consistent fits

Z. Ch. - NuSYM 2011, June 17-20, 2011 10

Fits to the dataFits to the dataSource distribution : S(r) x103Correlation function C(Q)

r1/2

Z. Ch. - NuSYM 2011, June 17-20, 2011 11

Fit resultsFit resultsSmall rapidity:reflect the participant zone of the reaction

Large rapidity:reflect the expanding, fragmenting and evaporating projectile-like residues

Higher velocity protons are more strongly correlated than their lower velocity counterparts, consistent with emission from expanding and cooling sources

Sensitivity to the initial size

Z. Ch. - NuSYM 2011, June 17-20, 2011 12

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)

• BUU - Boltzmann-Uehling-Uhlenbeck

• Simulates two nuclei colliding

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

Micha KilburnNSCL/MSU

Z. Ch. - NuSYM 2011, June 17-20, 2011 13

Comparing data to theory Comparing data to theory (pBUU)(pBUU)

BUU Pararameters No dependence on symmetry

energy Rostock in-medium reduction Producing clusters

BUU does reasonably wellExcept at larger rapidities -

Spectator sourceWhere evaporation and

secondary decays are important!

.

Micha Kilburn, NSCL/MSU

Z. Ch. - NuSYM 2011, June 17-20, 2011 14

Averaged emission time of particles in transport theory

Z. Ch. - NuSYM 2011, June 17-20, 2011 15

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

Stiff EoS Soft

EoS

L-W

Chen e

t al., PR

L90

(2

00

3)

16

27

01

52Ca 48Ca

Stiff

Soft

Stiff EoS (γ=2)

p’s and n’s emitted at similar time

faster emission times

Soft EoS (γ=0.5)

p’s emittedafter n’s

later emission times

Z. Ch. - NuSYM 2011, June 17-20, 2011 16

n-p correlation functionn-p correlation function

few fm

x1

x2

p1

p2

… 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. - NuSYM 2011, June 17-20, 2011 17

Emission of pEmission of p’’s and ns and n’’s: Sensitivity to 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. - NuSYM 2011, June 17-20, 2011 18

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

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

qx<0

qx>0

qx>0

Z. Ch. - NuSYM 2011, June 17-20, 2011 19

Emission of pEmission of p’’s and ns and n’’s: Sensitivity to 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. - NuSYM 2011, June 17-20, 2011 20

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

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

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

Z. Ch. - NuSYM 2011, June 17-20, 2011 21

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

(n,p) correlation function

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

qx<0

qx>0

Protons emitted later

0x

S(x)

<x>

=0

Stiff EoS Soft

EoS

Classically, average separation b/t protons and neutrons

Voloshin et al., PRL 79:4766-4769,1997Lednicky et al., PLB 373:30-34,1996

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IBUU: more calculationsIBUU: more calculations

Stiff AsyEoS

Soft AsyEoS

L-W

Chen e

t al., PR

L90

(2

00

3)

16

27

01

Figure obtained from calculations with momentum-independent potential

Calculations with momentum-dependent nuclear potential

L-W Chen et al., PRC69 (2004) 054606

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IBUU: averaged emission IBUU: averaged emission timetime

Momentum independent

Momentum dependent (isoscalar)

Momentum dependent (isoscalar & isovector)

52Ca+48Ca @ 80 MeVA

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IBUU vs pBUU: Averaged emission IBUU vs pBUU: Averaged emission timetime

IBUU pBUU52Ca+48Ca @ 80 MeVA

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pBUU: Averaged emission pBUU: Averaged emission timetime

Danielewicz, Bertsch, NPA533 (1991) 712

No effect of symmetry energy on averaged emission time of particles

Clusters affect the space-time picture of the HIC (t-3He correlations could show possible sensitivity to the relative emission time analogously to n-p correlations)

WITHOUT CLUSTERS WITH CLUSTERS

momentum dependent

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Two particle correlations provide a unique probe to study the space-time extend of the source

add constrains on the in-medium cross-section

importance of the clusters, symmetry energy

validate theoretical models

The average relative emission time of n’s and p’s potentially sensitive to the symmetry energy and can be “measured” with two particle correlations

Transport models Predictions are model dependent

Collaboration between theorists and experimentalists beneficial for both sides

SummarySummary