Nuclear Geometry in High Energy Nuclear Collisions

Transcription

1 Nuclear Geometry in High Energy Nuclear Collisions Wei Zhou School of Physics, Shan Dong University May 20, / 23

2 Outline 1 Some Definition and Experiment issue 2 Nuclear Geometry 3 Glauber Model in Nuclear-Nuclear Collisions 4 Summary and Outlook 2/ 23

3 Outline 1 Some Definition and Experiment issue 2 Nuclear Geometry 3 Glauber Model in Nuclear-Nuclear Collisions 4 Summary and Outlook 3/ 23

4 Some Definition b: impact parameter the distance between two nuclear N part : number of participants nucleons which have encountered at least one binary collision. N bin (N coll ): number of binary collisions inelastic nucleon-nucleon scattering. 4/ 23

5 Experiment issue In experiment, b,n part and N bin can not be measured directly. Their values can be derived by mapping the measured data. dn dn ch (a) 50% 40% 30% 20% 10% 5% Nch PHENIX STAR PHENIX and STAR have different method to determine the centrality in Nuclear-Nuclear collision. In this talk, we will inlustrate the relation between the centrality, b, N part and N bin. 5/ 23

6 Outline 1 Some Definition and Experiment issue 2 Nuclear Geometry 3 Glauber Model in Nuclear-Nuclear Collisions 4 Summary and Outlook 6/ 23

7 Nucleon s Density in Nuclear 1 There are two popular density profiles: Sharp Sphere n A (r) = { n0 r R 0 r > R n 0 = 0.17fm 3,R = ( 3A 4πn 0 ) 1/3 Woods-Saxon n A (r) = n exp( r R d ) n 0 = 0.17fm 3, R = (1.12A 1/3 0.86A 1/3 )fm, d = 0.54fm Both densities should be normalized to the number of nucleons: d 3 rn A (r) = A 7/ 23

8 Nucleon s Density in Nuclear 2 Sharp Sphere: Woods-Saxon: ] ] n[fm 0.18 n[fm = 0.17fm n 0 R = 6.5fm = 0.17fm n 0 R = 6.369fm d = 0.54fm b[fm] b[fm] The nucleon s density in Au(197) Nuclear. The difference between these two profiles is in the peripheral region. 8/ 23

9 Thickness Function 1 The probability of one nucleon can be found at ( b,z): ρ( b,z), ρ( b,z)d bdz = 1 The probability of one nucleon can be found at b: t( b) = ρ( b,z)dz, t( b)d b = 1 Thickness function The density of nucleons at b: T( b) = n( b,z)dz, n( b)d b = A So, we have this relation: t( b) = T( b) A 9/ 23

10 Thickness Function 1 The relation between thickness function T and impact parameter b of Au(197) nuclei: ] -2 T[fm ] -2 T[fm b[fm] b[fm] Sharp Sphere Woods-Saxon 10/ 23

11 Thickness Function 2 In nuclear collision A+B: The probability of one nucleon-nucleon pair can be found when the impact parameter is b: t AB = t A ( s + b)t B ( s)d s, d bt AB = 1 Thickness function in A+B collision: T AB = T A ( s + b)t B ( s)d s, d bt AB = AB It means the density of nucleon-nucleon pairs in A+B collision when impact parameter is b. As above, we have this relation: t AB ( b) = T AB( b) AB 11/ 23

12 Thickness Function 2 The relation between thickness function T AB and impact parameter b in Au+Au collision: ] -2 T AB [fm ] -2 T AB [fm b[fm] b[fm] Sharp Sphere Woods-Saxon 12/ 23

13 Outline 1 Some Definition and Experiment issue 2 Nuclear Geometry 3 Glauber Model in Nuclear-Nuclear Collisions 4 Summary and Outlook 13/ 23

14 Assumptions A nuclear-nuclear collision can be considered to be a series of multiple nucleon-nucleon scattering. The difference between the nucleon and its excited states in successive scattering can be neglected. That means all the inelastic cross-sections of nucleon-nucleon collisions are same. The inelastic cross-section of pp collision: s 56GeV 130GeV 200GeV 5.5TeV σ pp 37mb 41mb 42mb 60mb 14/ 23

15 Glauber Model 1 The probability of n nucleon-nucleon collisions happens in A+B collision: ( ) P(n, AB [ b) = t n AB( n [ b)σ pp] 1 t AB ( ] AB n b)σ pp The total probability of inelastic collision of A+B collision when impact parameter is b: AB n=1 Here we use: P(n, [ b) = 1 1 t AB ( ] AB b)σ pp 1 e T AB ( b)σ pp lim (1 µ n n )n = e µ, AB 1, t AB ( b) = T AB( b) AB 15/ 23

16 Glauber Model 2 The total inelastic cross-section of A+B collision: { σ AB (tot) = d b 1 [1 t AB ( ] } AB b)σ pp d } b {1 e T AB( b)σ pp Then we have: centrality = σab ( b) σ AB (tot) Now, we have derived the relation between impact parameter b and centrality in nuclear-nuclear collision. 16/ 23

17 Glauber Model 2 The relation between impact parameter b and centrality in Au+Au collision at s = 130GeV : centrality(%) b[fm] The nucleon s density profile is Woods-Saxon. 17/ 23

18 Glauber Model 3 Number of binary collisions of A+B collision when the impact parameter is b: N bin ( b) = AB n=1 n P(n, b) = AB t AB ( b)σ pp = T AB ( b)σ pp For one nucleon in nuclear A, the probability of it can have collision with the nucleons in nuclear B: B ( B n )(t B( b)σ pp ) n (1 t B ( b)σ pp ) B n = 1 [1 T B( b)σ pp ] B B n=1 Then we can derive the number of participants in A+B collision: N part ( b) = N parta + N partb = + d s T A ( s){1 [1 T B( s b)σ pp ] B } B d s T B ( s){1 [1 T A( s + b)σ pp ] A } A 18/ 23

19 Glauber Model 3 The relation between Npart, Nbin and impact parameter b in Au+Au collision at s = 130GeV : # Npart Nbin b[fm] The nucleon s density profile is Woods-Saxon. 19/ 23

20 The Monte Carlo Glauber Model Other method to determine b,nbin and Npart in A+B collision: Nuclear A Nuclear B Each possible nucleons are distributed about point (0,0,0) each nucleon is randomly distributed using Woods-Saxon profile, R + 0 d 3 rn(r) = A all nucleons are separated by d > d min where d min = 0.4 is characteristic of the length of the repulsive nucleon-nucleon force. nucleon-nucleon pair is determined to interact if they are separated by the transverse q σpp distance r π nucleons are distributed about point (b,0,0) each nucleon is randomly distributed using Woods-Saxon profile, R + 0 d 3 rn(r) = B all nucleons are separated by d > d min where d min = 0.4 is characteristic of the length of the repulsive nucleon-nucleon force. This process is iterated for an arbitrary number of events, with the impact parameter b for each event randomly chosen from a flat distribution. Then the distributions dσ/dn bin,dσ/dn part and dσ/db are determined. 20/ 23

21 Comparison between two Models Mapping of multiplicity classes to the optical Glauber calculations. Mapping of multiplicity classes to the Monte-Carlo Glauber calculations. The results of two models are consist to each other especial in central collisions. 21/ 23

22 Outline 1 Some Definition and Experiment issue 2 Nuclear Geometry 3 Glauber Model in Nuclear-Nuclear Collisions 4 Summary and Outlook 22/ 23

23 Summary and Outlook We first introduce two profiles to describe the nucleon s distribution in nuclei. We gives the detail description of the optical glauber model. The comparison between the result of two glauber models is presented. This study can be used in the extension of our combination model to nuclear-nuclear collisions. 23/ 23