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Zbigniew Chaj ę cki National Superconducting Cyclotron Laboratory Michigan State University

Probing reaction dynamics with two-particle correlations. Zbigniew Chaj ę cki National Superconducting Cyclotron Laboratory Michigan State University. Outline. p-p correlations (work with M. Kilburn, B. Lynch and collaborators) NSCL 03045 Experiment transport theory (BUU)

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Zbigniew Chaj ę cki National Superconducting Cyclotron Laboratory Michigan State University

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

  2. Outline • 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 function (p,p) correlation function |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. - NuSYM 2011, June 17-20, 2011

  4. Femtoscopy (p,p) correlation function (p,p) correlation function S-wave interraction S(r) S(r) S-wave interraction r1/2 Coulomb Coulomb r r uncorrelated uncorrelated 0 0 |q| = 0.5 |p1 - p2| |q| = 0.5 |p1 - p2| 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 Z. Ch. - NuSYM 2011, June 17-20, 2011

  5. NSCL experiments 05045: HiRA + 4 detector = 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. - NuSYM 2011, June 17-20, 2011

  6. Momentum and rapidity dependence C(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

  7. Fits to the data C(q) Koonin-Pratt Equation Brown, Danielewicz, PLB398 (1997) 252 Danielewicz, Pratt, PLB618 (2005) 60 Two ways of characterizing the size of the p-p source S(r) - Gaussian shape Imaged S(r) (Brown, Danielewicz) Z. Ch. - NuSYM 2011, June 17-20, 2011

  8. Fits to the data C(q) Koonin-Pratt Equation Brown, Danielewicz, PLB398 (1997) 252 Danielewicz, Pratt, PLB618 (2005) 60 Two ways of characterizing the size of the p-p source S(r) - Gaussian shape Imaged S(r) (Brown, Danielewicz) Both methods give consistent fits Z. Ch. - NuSYM 2011, June 17-20, 2011

  9. Fits to the data r1/2 Source distribution : S(r) x103 Correlation function C(Q) Z. Ch. - NuSYM 2011, June 17-20, 2011

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

  11. 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 KilburnNSCL/MSU • 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. - NuSYM 2011, June 17-20, 2011

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

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

  14. 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 Stiff EoS (γ=2) Soft EoS (γ=0.5) p’s and n’s emitted at similar time fasteremission times p’s emittedafter n’s later emission times Stiff Z. Ch. - NuSYM 2011, June 17-20, 2011

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

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

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

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

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

  20. 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) Classically, 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 Voloshin et al., PRL 79:4766-4769,1997Lednicky et al., PLB 373:30-34,1996 Z. Ch. - NuSYM 2011, June 17-20, 2011

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

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

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

  24. pBUU: Averaged emission time Danielewicz, Bertsch, NPA533 (1991) 712 momentum dependent WITHOUT CLUSTERS WITH CLUSTERS 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) Z. Ch. - NuSYM 2011, June 17-20, 2011

  25. Summary • 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 Z. Ch. - NuSYM 2011, June 17-20, 2011

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