Hua Zheng a, Gianluca Giuliani a and Aldo Bonasera a,b a)Cyclotron Institute, Texas A&M University b)LNS-INFN, Catania-Italy. 1 Coulomb Correction to the.

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Presentation transcript:

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

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

Cosmic microwave background radiation 3 Phys Rev 98, 1699 (1955) Specific heat of Au Quantum nature phenomena C. Tournmanis’s lecture

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

Nuclear collision 5 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)

Methods to determine density 6 SAHA’s equation Coalescence modelTwo particles correlationGuggenheim approach Quantum fluctuation

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

Methods to determine the density 8 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, (2012) K. Hagel, R. Wada, L. Qin, J.B. Natowitz et al., PRL 108, (2012)

Methods to determine the density 9 Two particles correlation 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)

Methods to determine the density 10 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, (2013) L.G. Moretto et al., J. Phys. G: Nucl. Part. Phys. 38, (2011) J.B. Natowitz et al., Int. J. Mod. Phys. E Vol 13, No1, 269 (2004)

Conventional thermometers  The slopes of kinetic energy spectra (Tkin)  Discrete state population ratios of selected clusters (Tpop)  Double isotopic yield ratios (Td) 11 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.

New thermometer 12 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

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

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

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

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

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

18 Density and temperature of bosons from quantum fluctuations

19 H. Zheng, G. Giuliani and A. Bonasera, NPA 892 (2012) Multiplicity fluctuation using Landau’s O(m 6 ) phase transition theory

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, 6 th ed. (Springer, Berlin, 2008) H. Zheng, G. Giuliani and A. Bonasera, arXiv: , PRC 88, (2013)

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

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

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

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

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

Summary 27  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

Thank you! 28