1. Zbigniew Chajęcki National Superconducting Cyclotron Laboratory Michigan State University Probing reaction dynamics with two-particle correlations

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

3. Z. Ch. - NuSYM 2011, June 17-20, 2011 3 Experimental correlation function few fm x1x1 x2x2 p1p1 p2p2 Experimental correlation function: r |q| = 0.5 |p 1 - p 2 | (p,p) correlation function P(p 1,p 2 ) P(p 1 )P(p 2 ) |q| = 0.5 |p 1 - p 2 |

4. Z. Ch. - NuSYM 2011, June 17-20, 2011 4 Femtoscopy few fm x1x1 x2x2 p1p1 p2p2 … 2-particle wave function … source function Theoretical CF: Koonin-Pratt equation S.E. Koonin, PLB70 (1977) 43 S.Pratt et al., PRC42 (1990) 2646 r |q| = 0.5 |p 1 - p 2 | (p,p) correlation function 0 r S(r) uncorrelated Coulomb S-wave interraction |q| = 0.5 |p 1 - p 2 | uncorrelated Coulomb S-wave interraction (p,p) correlation function 0 r S(r) r 1/2

5. Z. Ch. - NuSYM 2011, June 17-20, 2011 5 NSCL experiments 05045: HiRA + 4  detector - 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: 40 Ca + 40 Ca @ 80 MeV/u 48 Ca + 48 Ca @ 80 MeV/u

6. Z. Ch. - NuSYM 2011, June 17-20, 2011 6 Initial size effect R=r 0 A 1/3 R( 40 Ca) = 4.3 fm R( 48 Ca) = 4.6 fm R 48Ca+ 48Ca > R 40Ca+ 40Ca Koonin-Pratt Equation Brown, Danielewicz, PLB398 (1997) 252 Danielewicz, Pratt, PLB618 (2005) 60

7. Z. Ch. - NuSYM 2011, June 17-20, 2011 7 Momentum and rapidity dependence C(q) Measured correlation functions depend on rapidity and the transverse momentum of the pair Next step: extract the sizes

8. Z. Ch. - NuSYM 2011, June 17-20, 2011 8 Fits to the data C(q) Brown, Danielewicz, PLB398 (1997) 252 Danielewicz, 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)

9. Z. Ch. - NuSYM 2011, June 17-20, 2011 9 Fits to the data Brown, Danielewicz, PLB398 (1997) 252 Danielewicz, 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

10. Z. Ch. - NuSYM 2011, June 17-20, 2011 10 Fits to the data Source distribution : S(r) x10 3 Correlation function C(Q) r 1/2

11. Z. Ch. - NuSYM 2011, June 17-20, 2011 11 Fit results Small 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

12. Z. Ch. - NuSYM 2011, June 17-20, 2011 12 Modeling heavy-ion collisions : transport models 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, 3 He (alphas) BUU - Boltzmann-Uehling-Uhlenbeck Simulates two nuclei colliding Danielewicz, Bertsch, NPA533 (1991) 712 B. A. Li et al., PRL 78 (1997) 1644 Micha Kilburn NSCL/MSU

13. Z. Ch. - NuSYM 2011, June 17-20, 2011 13 Comparing data to theory (pBUU) BUU Pararameters No dependence on symmetry energy Rostock in-medium reduction Producing clusters BUU does reasonably well Except at larger rapidities - Spectator source Where evaporation and secondary decays are important!. Micha Kilburn, NSCL/MSU

14. Z. Ch. - NuSYM 2011, June 17-20, 2011 14 Averaged emission time of particles in transport theory

15. Z. Ch. - NuSYM 2011, June 17-20, 2011 15 Emission of p’s and n’s: Sensitivity to SymEn Stiff EoS Soft EoS L-W Chen et al., PRL90 (2003) 162701 52 Ca 48 Ca 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 emitted after n’s later emission times

16. Z. Ch. - NuSYM 2011, June 17-20, 2011 16 n-p correlation function few fm x1x1 x2x2 p1p1 p2p2 … 2-particle wave function … source function Theoretical CF: Koonin-Pratt equation S.E. Koonin, PLB70 (1977) 43 S.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(p 1 - p 2 )

17. Z. Ch. - NuSYM 2011, June 17-20, 2011 17 Emission of p’s and n’s: Sensitivity to SymEn 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 et al., PRL90 (2003) 162701 52 Ca 48 Ca

18. Z. Ch. - NuSYM 2011, June 17-20, 2011 18 Possible emission configurations (stiff sym. pot.) n Catching up p n p n p Moving away n p 0 x S(x) (n,p) correlation function q = 0.5(p p - p n ) q x <0 q x >0  q=  p p -  p n =(q x, q y =0, q z =0); r =(x, y=0,z=0) q x <0 q x >0

19. Z. Ch. - NuSYM 2011, June 17-20, 2011 19 Emission of p’s and n’s: Sensitivity to SymEn 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 et al., PRL90 (2003) 162701 52 Ca 48 Ca

20. Z. Ch. - NuSYM 2011, June 17-20, 2011 20 Sensitivity to particle emission (soft sym. pot.) n p n p Catching upMoving away 0 x S(x) (n,p) correlation function q x = 0.5(p x,p - p x,n ) q x <0q x >0 q x <0 q x >0 Experimentally, we measure the CF, not the source distribution!  q=  p p -  p n =(q x, q y =0, q z =0); r =(x, y=0,z=0)

21. 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 asymmetry (n,p) correlation function q x = 0.5(p x,p - p x,n ) q x <0 q x >0 Protons emitted later 0 x S(x) =0 Stiff EoS Soft EoS Classically, average separation b/t protons and neutrons Voloshin et al., PRL 79:4766-4769,1997 Lednicky et al., PLB 373:30-34,1996

22. Z. Ch. - NuSYM 2011, June 17-20, 2011 22 IBUU: more calculations Stiff AsyEoS Soft AsyEoS L-W Chen et al., PRL90 (2003) 162701 Figure obtained from calculations with momentum-independent potential Calculations with momentum -dependent nuclear potential L-W Chen et al., PRC69 (2004) 054606

23. Z. Ch. - NuSYM 2011, June 17-20, 2011 23 IBUU: averaged emission time Momentum independent Momentum dependent (isoscalar) Momentum dependent (isoscalar & isovector) 52 Ca+ 48 Ca @ 80 MeVA

24. Z. Ch. - NuSYM 2011, June 17-20, 2011 24 IBUU vs pBUU: Averaged emission time IBUUpBUU 52 Ca+ 48 Ca @ 80 MeVA

25. Z. Ch. - NuSYM 2011, June 17-20, 2011 25 pBUU: Averaged emission time 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- 3 He correlations could show possible sensitivity to the relative emission time analogously to n-p correlations) WITHOUT CLUSTERSWITH CLUSTERS momentum dependent

26. Z. Ch. - NuSYM 2011, June 17-20, 2011 26  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 sidesSummary