Influence of Vibration and Deformation
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1 Influence of Vibration and Deformation C60 of Nuclei ON the ELLIPTIC FLOW Peter Filip (IP SAS, Bratislava) XXI Baldin Seminar, Sept. Dubna 2012 Elliptic Flow Initial eccentricity Deformation effects GMC simulations Vibrations of nuclei Summary
2 Elliptic Flow: v2 initial state Azimuthal asymmetry Asymmetry in Spatial distribution leads to asymmetry in Momentum distribution Asymmetry Effect depends on the COLLISION ENERGY
3 Elliptic Flow: v2 energy dependence Fig: A.Wetzler (2005) from A.Poskanzer talk. RHIC LHC Asymmetry strength: v2 v2: has strength = magnitude <v2> and fluctuations: σv2 Azimuthal Momentum distribution
4 Elliptic flow v2: magnitude & fluctuations Au+Au collisions Magnitude of v2 decreases for central collisions We believe = assume: v2 fluctuation v2 fluctuation width comes from: the initial eccentricity fluctuation (at given Nch or Npart) Peripheral coll. Central coll.
5 Centrality dependence of initial eccentricitry ε: Rotation-ivariant formula Eccentricity Elliptic flow is larger for non-central collisions
6 Elliptic flow at RHIC: partonic expansion nucl-ex/ nucl-ex/ π,k,p,φ,λ,ξ,ω Very nice! However: Cu+Cu
7 Elliptic flow v2 strength in Cu+Cu v2 strength = < v2> average v2 value (at given centrality, η) Phys.Rev.C85, Central CuCu non-central v2 strength in Cu+Cu (RHIC at 22.4 GeV/n) is not understood...
8 In this talk Two initial-state effects: influence Elliptic flow. Ground-state deformation Ground-state Vibration (2012) 197-Au
9 Fluctuating Eccentricity: fixed impact param. [b] OGM simulation
10 Deformation of nuclei in MC Glauber: increased Eccentricity fluctuations due to deformation standard fluctuation Phys.Rev.C80, : Deformation effects on σv2 (fluctuation of v2)
11 Deformation influence on v2 strength: self-orientation effect in central UU collisions + cusp + 20% difference in v2 strength + MC Glauber simulation: Phys.Rev.C80, : ε CUSP v2 CUSP
12 Self-orientation effect: for very high Nch multiplicity collisions max. binary NN collisions Nch orientation extremal case:
13 Deformation effects: σv2 / v2 [ Nch ] Assuming hydrodynamical expansion: σv2 /v2 σε / < ε > Optical Glauber Optical Glauber Model σv / v2 2 sensitive to deformation of nuclei Phys.Rev.C80, Full MC Glauber simulation
14 DEFORMATION OF NUCLEI: Most of nuclei are deformed (including Cu, In, Ho, Ho Au) Au: β2 = Ho: β2 = 0.30 Si28: β2 = -0.4 Si-28 Study Nd,Sm,Ho,Si collisions at LHC/Nica/SPS to verify our understanding of the Elliptic flow.
15 Suggestion N.1: Deformation of nuclei: β2 in relativistic Nucleus-Nucleus collisions may allow a more detailed understanding of the elliptic flow phenomenon. stable Samarium isotopes
16 Comparing v2 strength & fluctuations: for spherical & deformed Sm+Sm collisions due to deformation all other fluctuations We know initial eccentricity fluctuation increases for Sm154 collisions Experimentally measured v2 fluctuation: should increase: How much?
17 v2 eccentricity for Sm+Sm (OGM: larger β2 larger ε2 (v2) fluctuations) cusp
18 Other initial-state effect: GROUND-STATE nuclear Vibration (ZPV) What is it? (Zero-Point-Shape-Vibration) present in deformed nuclei? present also in spherical nuclei? Is it stronger or weaker for light nuclei? Does it really exist? has anybody observed Ground-State vibration = GSV? (in molecular physics?) Should we include it in MC simulations of HIC?
19 Bohr and Mottelson on ZPV Nuclear Structure II nuclei do oscilate = vibrate in the ground state amplitude is comparable to static deformation β 2
20 Molecular Physics: C60 Ground-state-shape vibration From J.Ménendez and J.Page: Vibrational spectroscopy of C60 Nuclei may vibrate similarly!
21 Mollecular Ground-state VIBRATION important in: µ cf (1956) Berkeley He3 re 200x smaller vibrating... ψ 2 (ZPE) [ Observation of Coherent Mollecular Quantum vibrations: see Nature 343 (1990) p. 737 ]
22 Bohr and Mottelson on ZP Vibration Nuclear Structure II depends on Nucleus Ground-state vibration = Quantum effect! well known from Molecular physics: C60 and µcf
23 Au (RHIC,GSI) & Pb (SPS,LHC) shape vibrations... How large they are? SHOULD WE INCLUDE (? Cu+Cu?) SHAPE VIBRATION into Elliptic Flow (eccentricity) SIMULATIONS? Does it affect v2 physics at BNL / LHC?
24 Frequency of Shape vibrations: For molecules: f 10 For Nuclei e.g Hg: Hz (microwave) EZPE 2 MeV fv 5 * 1020 Hz Comparing to HIC initial overlap time: 1 / fv 2*10-21 s >> 2*10-23 s = Tinit 6 fm/c Initial overlap is fast collision in frozen vibrational state
25 Ground-state wave function: 196 Hg Nucl.Phys.A403 (1983) p.263 Fluctuating β2 parameter!!! 197 ( <β2> = ) Au similar behavior (proton hole in 198Hg).
26 ZPVibration of deformed nuclei in RHIC enhanced self-orientation (CUSP) effect in central UU? influencing AuAu eccentricity? + cusp + + in Phys.Rev.C80, (ZPE vibrations were neglected) need to be studied to obtain a correct < initial state >
27 Collisions of deformed vibrating nuclei: P(β2, β2) Collision probability distribution of Hg shapes: spherical + spherical (40%) spherical + deformed (45%) deformed + deformed (15%) Hg196
28 Conclusion: Quadrupole vibration of the colliding nuclei expected in Ground state other (β3) ZP vibrations possible: Amplitudes up to β -βο ( for deformed nuclei) in frozen vibrational state: Ho,U may have large β STRONGER CUSP EFFECT in Ultra-Central Collisions During A+A collision: vibration is frozen
29 Vibrational properties of Nuclei (comparing B(E2) transition probability with Qo) some nuclei Vibrate: Ca, Fe, Ni, Zn, Ge, Kr, Sr, Pd, Cd, Sn some nuclei do Not vibrate: Zr, Nd, Sm, Gd, Dy, Er,W, Os W Sn Publication: I. Boboshin et al. Investigation of quadrupole deformation of nucleus and its surface dynamic vibrations International Conf. on Nuclear Data for Science and Technology 2007 (DOI: /ndata:07103)
30 Summary: Ground-state vibration + deformation of nuclei can influence initial state Elliptic Flow v2 in HIC. Enhancement of eccentricity cusp is possible in Ultra-central collisions of prolate vibrating nuclei (U+U) eccentricity in Au+Au may be affected. Comparing v2 in (144Sm+144Sm) and (154Sm+154Sm) was suggested for R-HIC Collisions of Cd (vibrating) nuclei and Nd,Sm (non-vibrating) nuclei may clarify influence of vibrations
31 THANK YOU for Your kind ATTENTION
32 Backup Slide We expect We think Cd to be strongly vibrating (<β2> = +0.16) Sm, 146Nd do Not vibrate (<β2> = +0.16) Cu properties?
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