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Understanding Internal Energy of Fragment Patterns: Thermodynamics and Temperature Measurements

This text explores the internal energy of fragment patterns through thermodynamics and temperature measurements using correlation function techniques, such as LP-LP/IMF-LP method and impact parameter selected excited states. It discusses the results, internal excitation of the fragments, and other applications in nuclear physics. The text is written in English.

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Understanding Internal Energy of Fragment Patterns: Thermodynamics and Temperature Measurements

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  1. Space time characterization IIWhat have we learned about the internal energy of the fragment pattern ?Thermodynamics • Temperature measurements using correlation function techniquesLP-LP/IMF- LP • Method : determination of relative population unbound states • Impact parameter selected excited states • Results • Internal excitation of the fragments using correlation function techniquesIMF- LP • Method description : background simulation • Representative results • Determination of the thermal component • Hard photons : Mg-Mimf correlations • Other applications • 3-body correlation in Borromean halo nuclei • Spin determination

  2. Temperature measurements from excited states unstable nuclei MSU Position-sensitive hodoscope • Idea: • The unstable complex cluster should be emitted early in the decay --> the temperature is expected to be close to the initial temperature of the fragmenting system • Hypothesis : at least local equilibrium • Advantages • Small sensitivity to collective dynamical effects : rotational, translational, expansion • Direct emission • Etc. • Technique : Correlation function to reconstruct the unstable nuclei Pochodzalla et al., PRC35 1695, 1987

  3. Results of the excited states Nayak et al., PRC45 132, 1992

  4. Impact parameter selected excited state F. Zhu et al., PR C52 784–797 (1995)

  5. Temperature vs impact parameter / Ein H.F. XI et al., PRC58 R2636 (1998) • Explanation of the THeLi : • Excluding volume • Emission time of 3He • See thermometry F. St-Laurent et al., PLB 202, 190 (1988) Constant temperature over a large range of impact parameter / Ein Serfling et al., PRL 80, 3928 (1998)

  6. explanation of low peak energy alpha particle spectrum ? • Experimental kinetic energy spectrum of a is enhanced in the sub barrier compared to statistical calculations. • sequential a particles from 5He and other clusters ? R.J. Charity et al., PRC63 024611

  7. Excitation energy of the primary fragments Kr + Nb @ 45A MeV Dwarf Ball/Wall • IMF-LCP Vrel Correlations 1+R(Vrel) = Nc/Nnc • Background Parameterization A-1/(BVrel+C) • Evaporated p, d, t, 3He, a • size, E*pr primary fragments • Thermal Contribution N. Marie et al., PRC 58, 256 (1998) S. Hudan et al., PhD thesis and PRC67, 064613 (2003) P. Staszel et al., PRC63, 064610 (2001)

  8. Excitation energy of the fragments Data Simulation Xe + Sn @ 50A MeV, Indra Collaboration TAMU-GANIL

  9. Evaporated LCP multiplicities <E> (MeV) <M> Zimf Zimf

  10. Evaporated LCP multiplicities

  11. Excitation energy of the primary fragments Primary fragment mass hypothesis

  12. Application 1 : Proportion of thermal contribution • Excitation energy saturates at 3 AMeV • Mev/Mtot fractionreflects <E*/A> of the primary fragments • The majority of LCP are not evaporated by excited primary fragments

  13. Application 2 : Constraint to statistical calculations Direct comparison to primary fragments produced by SMM, before their decay and Coulb. Total evaporated charge ( z=1, 2 ) It was not compared to MMMC since in this model the secondary decay is included in the final partition

  14. Data-AMD ComparisonS. Hudan et al., PhD thesis and A. Ono & S. Hudan PRC66, 014603 (2002) Charge distribution for Xe + Sn at 50 and 100 A MeV Xe+Sn 50 A MeV, 0<b<4 Xe+Sn 50 A MeV, 0<b<4 Reasonable agreement in the limit of the number of simulated events (a huge cpu time )

  15. Application 3 : Direct comparison to AMD before cooling Xe + Sn @ 50 AMeV AMD

  16. Characteristics of the Quasi-Projectile Carmen Escano PhD thesis (in preparation) Stage Josiane Moisan

  17. Zbig > 40 30 < Zbig < 40 25 < Zbig < 30 Stage Josiane Moisan Alpha 20 < Zbig < 25 10 < Zbig < 20 5 < Zbig < 10

  18. Zbig > 40 30 < Zbig < 40 25 < Zbig < 30 Stage Josiane Moisan Proton 20 < Zbig < 25 10 < Zbig < 20 5 < Zbig < 10

  19. Evaporated protons Carmen Escano PhD thesis (in preparation) Preliminary results : Quasi-Projectile Central collisions

  20. Nuclear breakup Dominates, small b Electromagnetic dissociation

  21. Spin determination of particle unstable levels with particles correlations 8Be : p-7Li 8B : p-7Be W.P. Tan et al., PRC69, 061304 (R) (2004)

  22. NI + AU 30A MeV NI + AU 45A MeV thermal 1+R g-IMF central collisions: correlation factors as a function of a threshold on the photon energy direct NI + AU 45A MeV • The photon energy spectra: two componentexponential fit • thermal photonsource nucleus-nucleus c.o.m. velocity • direct photonsource nucleon-nucleon c.o.m. velocity E 1+R g-IMF Black: IMF’s velocity in W1 Red: IMF’S velocity in W2 W2 E W1 • The 45A MeV data strongly support the hypothesis of prompt multifragmentation, while the 30A MeV data are compatible with a late statistical decay of a heavy composite system. This indicates a transition between the two mechanisms just in the region of the Fermi energy 0.07 0.14 0.28  c.o.m beam

  23. Conclusions and perspectives • Correlation function is powerful tool to reconstruct stable or unstable nuclei  it can be applied to structure study of exotic nuclei far from stability • Temperatures extracted from excited states saturate around 4-5 MeV for a large range of impact parameter and incident energy (up to 200 A MeV). • Experimental study of the Xe + Sn system from the onset of multifragmentation: the fragments are excited and their E* saturates at 3A MeV. • For a fermi gas a = A/8 --> T = 5 MeV comparable to T excited-state  T=5 consistent with the limiting temperature below which primary frag deexcite only through evaporation • The proportion of thermal LCP does not exceed 35% and decreases with Einc. • Reaction mechanism (HIC) is not able to heat the fragments more than 3A MeV.  a comparison to the proportion of the fast source component extracted from imaging source technique may provides a good cross check to the two method • Comparison with a statistical and dynamical model calculation : • The assumption that the system is in equilibrium at low densities reproduces the primary fragments excitation energies. • BUT it fails to predict the evolution of the evaporative LCP with the incident energy. • AMD predict almost the total energy spectra of protons (78% of total emission) • But it fails to reproduce the thermal contribution (22%). • Questions : • Why are the excitation energies of the spectator fragments at 100 AMeV and the participant fragments at 50 AMeV the same ? Thermal energy saturation ? Same production mechanism ? Or … ?

  24. 4p solid angle Quasi complete information Estimation of E*of all fragments, Thermal component Quantitative estimation Small solid angle Temperature measurements Precise reconstruction of fragments Structure : spin, exotic nuclei Qualitative partial information Do we need 4p hodoscope ? Few hodoscopes inside a 4p ?

  25. Xe+Sn Xe+Sn Xe+Sn HIPSE DATA Comparison between HIPSE model and INDRA data : Fragment-fragment correlations in central collisions Relative velocity and relative angle Of the three biggest fragments Taken two by two Selection : Ztot >80%, Pztot>80%, flow angle> 30 degree In HIPSE, clusters are formed from the very first instant of the reaction [simultaneous fragmentation] up to several thousand of fm/c (during the desexcitation [sequential decay]. In fact, the in-flight decay is performed to preserve space-time correlations. The good reproduction of Fragment-Fragment correlations indicates that the HIPSE scenario is compatible with data Figure from A. Van Lauwe, Ph.D. Thesis-LPC Caen (2003)

  26. Deducing the timescale of multifragmentation using thermal photons (Eg25 MeV) as a “clock” and the -IMF correlation factors as experimental tool The chronometer:density oscillation from BNV simulations of the reaction dynamics and location in time of the main processes First compression direct photon production Expansion prompt IMF emission (at t=t0 the system enters the spinodal region) If the system survives: Second compression thermal photon production, HHS formation, statistical IMF’s thermal photons hot heavy surviving system The experimental tool: -IMFcorrelation factors 1+ R-IMF = Values  1 signal anticorrelation i.e. in a significant fraction of events the emission of fragments inhibits the photon production (0 if the system always disintegrates before and 1 for independent emission)  mmIMF  m mIMF MEDEA + MULTICS at Laboratori Nazionali del Sud

  27. Evolution of the multifragmentation of the Xe+Sn system from 25-150 AMeV Abdou CHBIHI for the INDRA and ALADIN collaborations Experiments performed @ GANIL and GSI with INDRA • Global feature of the fragment emission • Experimental characteristics of fragment production in central collisions (size and E*pr) • Comparison to statistical and dynamical calculations • Characteristics of the Quasi-Projectile @ 100 AMeV Preliminary results

  28. V. Serfling et al., PRL80 3928 (1998)

  29. V. Serfling et al., PRL80 3928 (1998) H.F. XI et al., PRC58 R2636 (1998) F. St Laurent et al., PLB 202, 190, 1988

  30. Primary fragment reconstruction method N. Marie et al., PRC 58, 256 (1998) S. Hudan et al., PhD thesis and PRC67, 064613 (2003) Xe + Sn @ 32 A MeV • IMF-LCP Vrel Correlations 1+R(Vrel) = Nc/Nnc • Background Parameterization A-1/(BVrel+C) • Evaporated p, d, t, 3He, a • size, E*pr primary fragments • Thermal Contribution

  31. Temperature measurements from excited states unstable nuclei • Idea: • The unstable complex cluster should be emitted early in the decay --> the temperature is expected to be close to the initial temperature of the fragmenting system • Hypothesis : at least local equilibrium • Advantages • Small sensitivity to collective dynamical effects : rotational, translational, expansion • Direct emission • Etc. • Technique : Correlation function to reconstruct the unstable nuclei

  32. Temperature measurements from excited states unstable nuclei Position-sensitive hodoscope Pochodzalla et al., PRC35 1695, 1987

  33. Conclusions • Experiments : • Experimental study of the Xe + Sn system from the onset of multifragmentation • The fragments are excited and their E* saturates at 3 A MeV. • The proportion of thermal LCP does not exceed 35% and decreases with Einc. • Reaction mechanism (HIC) is not able to heat the fragments more than 3A MeV.  Strong constraints on the statistical and dynamical models. • Comparison with a statistical and dynamical model calculation : • The assumption that the system is in equilibrium at low densities reproduces the primary fragments excitation energies. • BUT it fails to predict the evolution of the evaporative LCP with the incident energy. • AMD predict almost the total energy spectra of protons (78% of total emission) • But it fails to reproduce the thermal contribution (22%). • Questions : • Why are the excitation energies of the spectator fragments at 100 AMeV and the participant fragments at 50 AMeV the same ? Thermal energy saturation ? Same production mechanism ? Or … ?

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