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Dynamics of Mid-Peripheral Collisions: Analyzing PLF Decay and Isotropy in Fragment Emission

This study investigates the decay dynamics of projectile-like fragments (PLF*) in mid-peripheral collisions, focusing on the different statistical and dynamical behaviors during forward and backward emission. Utilizing experimental setups, we analyze variations in charge splits, relative velocities, and fragment alignment, revealing a significant dependency on whether decay occurs forward or backward. Findings suggest that backward emission is more aligned and exhibits higher asymmetry, challenging traditional statistical models. The correlations derived from the velocities and energy distributions provide a deeper understanding of anisotropy in nuclear fragmentation.

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Dynamics of Mid-Peripheral Collisions: Analyzing PLF Decay and Isotropy in Fragment Emission

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  1. Mid-peripheral collisions : PLF* decay T TLF* P PLF* vL > vH forward vH > vL backward 1 fragment Sylvie Hudan, Indiana University Statistical behavior  isotropy  vH > vL vL > vH

  2. Experimental setup LASSA : Mass resolution up to Z=9 7  lab  58 Beam Ring Counter : Si (300 m) – CsI(Tl) (2cm) 2.1  lab  4.2 1 unit Z resolution Mass deduced† † : Modified EPAX K. Sümmerer et al., Phys. Rev. C42, 2546 (1990) 48 Projectile 114Cd + 92Mo at 50 A.MeV Miniball/Miniwall  Detection of charged particles in 4p

  3. Events with two fragments from a PLF* ZL ZH vL > vH, forward PLF* ZH vH > vL , backward ZL

  4. Anisotropy of PLF* decay Different charge splits more asymmetric split for the backward case Different relative velocities higher vrel for the backward case Different alignments more alignment for the backward case 6  NC 10 B. Davin et al., Phys. Rev. C65, 064614 (2002)

  5. Asymmetry of the breakup :Sensitivity to vPLF* vPLF* vL > vH vH > vL 9.2 x80 x100 x20 8.9 x10 x2 8.6 x1 8.3 E*,J 6  NC 10 B. Davin et al., Phys. Rev. C65, 064614 (2002) • More asymmetric Z distribution for the backward case • Higher asymmetry at high vPLF* (low E*,J) • For all vPLF* , asymmetry for the backward case  An other degree of freedom? vprojectile = 9.45 cm/ns

  6. To summarize… • The forward and backward cases are different : • Forward emission is consistent with standard statistical emission • Backward emission is consistent with dynamical decay • Different charge split dynamical has higher asymmetry • Different alignment  dynamical is more aligned • Different relative velocity for the same ZL dynamical has higher vrel • Different Z distribution for a given (E*,J)

  7. Well-defined PLF* : ZPLF* and vPLF* dynamical statistical vL > vH vH > vL dynamical • Same correlation expected if vPLF* and E* correlated • More dissipation and fluctuations as ZPLF* decreases • For a given size, less dissipation for the dynamical case

  8. Opening channels 1 fragment (x 0.1) vL > vH vH > vL  Dynamical emission opensat higher vPLF* , i.e. lower E* • Up to 10% of the cross-section in the 2 fragment decay

  9. Asymmetry and Coulomb barrier 35  ZPLF* 39 • Higher asymmetry for the dynamical case • Coulomb barrier lower • Dynamical case appears at lower E*

  10. Energy in the fragments • More kinetic energy in the 2 fragments for the dynamical case • For a given vPLF*, difference of  20-30 MeV

  11. A statistical picture : Viola systematics Comparison statistical / Viola At large vPLF*, statistical  Viola  Deviation for low vPLF*  Temperature ? Comparison dynamical / Viola  For all vPLF*, dynamical >>Viola More compact shape needed for the dynamical case

  12. Estimation of the temperature Measured Estimated (Viola systematic) Statistical case : vL > vH • Temperatures between 0 and 10-12 MeV • These temperatures are consistent with T=7 MeV from the isotopes in LASSA (for 30  ZPLF*  46)

  13. To summarize… • vPLF* as a good observable : • Samecorrelation(vPLF*)-vPLF* for statistical and dynamical cases • Dynamical case appears at higher vPLF*Coulomb barrier effect •  vPLF*(TKE)dynamical > (TKE)statistical by  20-30 MeV • Statistical  Viola at high vPLF* and deviation with increasing vPLF* Temperature • Dynamical case always underestimated by Viola

  14. A law : energy conservation ZH ZL + + PLF* E* , BEPLF* TKEH , BEH TKEL , BEL TKEevap , BEevap For a selected vPLF* E* • Kinetic energy in the fragments  Higher for the dynamical case • Q value • Evaporated particles

  15. “Missing” energy : Q value? (MeV) • Same Q value in both cases for all vPLF*

  16. “Missing” energy : evaporation? vL > vH statistical vH > vL dynamical Multiplicity of Z=2 emitted forward to the PLF*(in LASSA) • Higher average multiplicities for the statistical case • Deviation of 10-20%

  17. Energy conservation : balance Fixed vPLF* fixed for Z=2 Suggests a longer time scale in the statistical case

  18. A picture of the process Time Saddle-point Scission-point Initial kinetic energy? Q Coulomb Collective TKE “Extra” energy Fluctuations of TKE (Q+Coulomb)-TKE correlation

  19. TKE : width of the distribution • More fluctuations in the dynamical case consistent with an additional kinetic energy at the scission-point

  20. Conversion : Q + Coulomb to TKE Statistical TKE  Q + Coulomb Dynamical TKE  Q + Coulomb + E0

  21. Conclusions : building a coherent picture Correlation (vPLF*)-vPLF* vPLF* good selector for E* Correlation vPLF* - Mevap Multiplicities of evaporated Z=2 scission,dynamical < scission,statistical Different TKE for all vPLF* Initial TKE at scission Different TKEfor all vPLF* for the dynamical case is Correlation TKE-(Q+Coulomb) larger than the statistical case We observed… We interpreted…

  22. Collaboration • S. Hudan , B. Davin, R. Alfaro, R. T. de Souza, H. Xu, • L. Beaulieu, Y. Larochelle, T. Lefort, V. Viola and R. Yanez • Department of Chemistry and Indiana University Cyclotron Facility, • Indiana University, Bloomington, Indiana 47405 • R. J. Charity and L. G. Sobotka • Department of Chemistry, Washington University, St. Louis, Missouri 63130 • T. X. Liu, X. D. Liu, W. G. Lynch, R. Shomin, W. P. Tan, M. B. Tsang, • Vander Molen, A. Wagner, H. F. Xi, and C. K. Gelbke • National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, • Michigan State University, East Lansing, Michigan 48824

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