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Hua Zheng a , Gianluca Giuliani a and Aldo Bonasera a,b

Coulomb Correction to the Density and the Temperature of Fermions and Bosons from Quantum Fluctuations. Hua Zheng a , Gianluca Giuliani a and Aldo Bonasera a,b a)Cyclotron Institute, Texas A&M University b)LNS-INFN, Catania-Italy. Outline. Motivation Methods to determine density

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Hua Zheng a , Gianluca Giuliani a and Aldo Bonasera a,b

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  1. Coulomb Correction to the Density and the Temperature of Fermions and Bosons from Quantum Fluctuations Hua Zhenga, Gianluca Giuliania and Aldo Bonaseraa,b a)CyclotronInstitute, Texas A&M University b)LNS-INFN, Catania-Italy. IWNDT2013, College Station, Tx

  2. Outline • Motivation • Methods to determine density • Conventional thermometers • New thermometer • Application to F&B • Coulomb correction to F&B • Summary

  3. Quantum nature phenomena Specific heat of Au Cosmic microwave background radiation Phys Rev 98, 1699 (1955) C. Tournmanis’s lecture http://asd.gsfc.nasa.gov/arcade/cmb_spectrum.html

  4. Trapped Fermions/Bosons systems Li6 Rb87 PRL 105, 040402 (2010) PRL 96, 130403 (2006)

  5. Nuclear collision Measured in experiment event by event: Mass (A) Charge (Z) Yield Velocity Angular distribution Time correlation The physical quantities in EoS: Pressure (P) Volume (V) or Density ( ) Temperature (T)

  6. Methods to determine density SAHA’s equation Coalescence model Two particles correlation Guggenheim approach Quantum fluctuation

  7. Methods to determine the density SAHA’s equation It is justified for very low density region and high temperature S. Albergo et al., IL NUOVO CIMENTO, vol 89 A, N. 1 (1985) S.Shlomo, G. Ropke, J.B. Natowitz et al., PRC 79, 034604(2009)

  8. Methods to determine the density Coalescence model A. Mekjian, PRL Vol 38, No 12 (1977), PRC Vol 17, No 3 (1978) T.C. Awes et al., PRC Vol 24, No 1 (1981) L. Qin, K. Hagel, R. Wada, J.B. Natowitz et al., PRL 108, 172701(2012) K. Hagel, R. Wada, L. Qin, J.B. Natowitz et al., PRL 108, 062702(2012)

  9. Methods to determine the density Two particles correlation R S.E. Koonin, Phys. Lett Vol 70B, No 1 (1977) S. Pratt, M.B. Tsang, PRC Vol 36, No 6 (1987) W.G. Gong, W. Bauer, C.K. Gelbke and S. Pratt, PRC Vol 43, No 2 (1991)

  10. Methods to determine the density Fisher’s model Guggenheim approach E.A. Guggenheim, J. Chem. Phys Vol 13, No7 (1945) T. Kubo, M. Belkacem. V. Latora, A. Bonasera, Z. Phys. A. 352, 145 (1995) P. Finocchiaro et al., NPA 600, 236 (1996) J.B. Elliott et al., PRL Vol 88, No4 (2002), J.B. Elliott et al., PRC 87, 054622 (2013) L.G. Moretto et al., J. Phys. G: Nucl. Part. Phys. 38, 113101 (2011) J.B. Natowitz et al., Int. J. Mod. Phys. E Vol 13, No1, 269 (2004)

  11. Conventional thermometers • The slopes of kinetic energy spectra (Tkin) • Discrete state population ratios of selected clusters (Tpop) • Double isotopic yield ratios (Td) S. Albergo et al.,IL Nuovo Cimento, Vol 89A, N. 1 (1985) M. B. Tsang et al., PRC volume 53, (1996), R1057 J. Pochodzalla et al., CRIS, 96, world scientific, p1 A. Bonasera et al., IL Nuovo Cimento, Vol 23, p1, 2000 A. Kelic, J.B. Natowitz, K.H. Schmidt, EPJA 30, 203 (2006) All of them are based on the Maxwell-Boltzmann distribution. No quantum effect has been considered so far.

  12. New thermometer A new thermometer is proposed in S. Wuenschel, et al., Nucl. Phys. A 843 (2010) 1 based on momentum fluctuations A Quadrupole is defined in the direction transverse to the beam axis Its variance is LHS: analyze event by event in experiment RHS: analytic calculation by assuming one distribution When a classical Maxwell-Boltzmann distribution of particles at temperature was assumed

  13. Density and temperature of fermions from quantum fluctuations Quadrupole fluctuations: Fermi Dirac distribution High T Low T 1 Multiplicity fluctuations: Wolfgang Bauer, PRC, Volume 51, Number 2 (1995) H. Zheng, A. Bonasera, PLB, 696(2011) 178-181 H. Zheng, A. Bonasera, PRC 86, 027602 (2012)

  14. Density and temperature of fermions from quantum fluctuations Testing the method Density: • CoMD simulations: • Experimental data H. Zheng, A. Bonasera, PLB, 696(2011) 178-181 H. Zheng, A. Bonasera, PRC 86, 027602 (2012)

  15. Density and temperature of fermions from quantum fluctuations Li6 S32+Sn112 PRL 105, 040402 (2010) B. C. Stein et al, arXiv: 1111.2965v1 H. Zheng, G. Giuliani and A. Bonasera, NPA 892 (2012) 43-57

  16. Density and temperature of bosons from quantum fluctuations Quadrupole fluctuations: Bose-Einstein distribution Multiplicity fluctuations: Density: H. Zheng, G. Giuliani and A. Bonasera, NPA 892 (2012) 43-57

  17. Density and temperature of bosons from quantum fluctuations H. Zheng, G. Giuliani and A. Bonasera, NPA 892 (2012) 43-57

  18. Density and temperature of bosons from quantum fluctuations

  19. Multiplicity fluctuation using Landau’s O(m6) phase transition theory H. Zheng, G. Giuliani and A. Bonasera, NPA 892 (2012) 43-57

  20. The results of Fermions and bosons We introduce the Coulomb correction

  21. Coulomb correction Similar to the density determination of the source in electron-nucleus scattering The distribution function is modified B. Povh et al., Particles and Nuclei, 6th ed. (Springer, Berlin, 2008) H. Zheng, G. Giuliani and A. Bonasera, arXiv: 1305.5494, PRC 88, 024607 (2013)

  22. Coulomb correction Need one more condition H. Zheng, G. Giuliani and A. Bonasera, arXiv: 1305.5494, PRC 88, 024607 (2013)

  23. Coulomb correction for Bosons (T<Tc) H. Zheng, G. Giuliani and A. Bonasera, PRC 88, 024607 (2013)

  24. Coulomb correction for Bosons (T<Tc) H. Zheng, G. Giuliani and A. Bonasera, PRC 88, 024607 (2013) R.P. Smith et al., PRL 106, 250403 (2011)

  25. Coulomb correction results for Fermions H. Zheng, G. Giuliani and A. Bonasera, arXiv: 1305.5494

  26. Coulomb correction results for Bosons Deuteron is over bound in the model. The densities of deuteron may be over estimated. H. Zheng, G. Giuliani and A. Bonasera, PRC 88, 024607 (2013) K. Hagel, R. Wada, L. Qin, J.B. Natowitz et al., PRL 108, 062702(2012

  27. Summary • We reviewed the methods to determine density and three conventional thermometers • A new thermometer to take into account the quantum effects of fermions and bosons is proposed • Some evidences of quantum nature of fermions and bosons are found in the model and experimental data • Coulomb correction to the temperature and the density of fermions and bosons from quantum fluctuations is discussed

  28. Thank you!

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