Reaction Dynamics in Near-Fermi-Energy Heavy Ion Collisions

1. Reaction Dynamics in Near-Fermi-Energy Heavy Ion Collisions Jiansong Wang and NIMROD Collaboration Texas A&M University, TX, USA Institute of Modern Physics, Lanzhou China

2. Outline • Motivation • Experimental set up • Goshal-like test • The impact parameter dependence of Coalescence radii • Summary

3. Nucl-ex/0410024 P. Chomaz Motivation • Hot topics of HI collisions at intermediate energy: Isospin Physics and Liquid-Gas Phase Transition • Goshal like tests in these Fermi energy collisions are of interest. • Ghoshal et al. find the independence of entrance channel on compound nuclei at low energy collisions • Is it still true in these collisions at near fermi energy? • Studying the impact parameter dependence of the interaction zones is of interest too • What is the properties of the nuclear matter in the interaction zone? • What is the relationship between the Coalescence radius and the interaction zone

4. NIMROD(Neutron Ion Multidetector for Reaction Oriented Dynamics)

5. Selecting the Violent Collisions • There are many variables to select the centrality, Such as Transverse Energy of LCP, Multiplicity, Flow Angle etc. • In our case, total multiplicity of neutron and charged particle is used to select the most violent collisions

6. Reaction systems • 35MeV/u 64Zn+92Mo • 40MeV/u 40Ar+112Sn • 47MeV/u 64Zn+92Mo • 55MeV/u 27Al+124Sn

7. Energy spectra of particle emitted from spherical thermal source • Surface emission • Volume emission

8. Moving Source Fits Target-like Source (surface emission) Mid-Rapidity Source (volume emission) Projectile-like Source (surface emission) PRC39(1989)p497, R. Wada et al. PRC57(1998)p1305, D. Prindle et al

9. An example of moving fit

10. Temperature Determination • Double Ratio Isotope Temperature (S. Albergo et al., Nuovo Cimento A 89(1985)p1) • Assumptions in the model: • Free nucleons and composite fragments are contained within a certain volume • The thermal and chemical equilibrium are reached • The yield follows the Maxwell distribution • The experimental yield of a fragment is proportional to the density inside the volume • All detected fragment originate from a single source • For the isotopes of d,t,he3,he4, The formula of temperature for a certain velocity zone is as the following,

11. Time (fm/c) Time Evolution of Temeprature • the temperature evolution curves rises to a maximum and then decreases. • Maximum temperatures of 10-15 MeV are observed at times in the range of 95 to 110 fm/c. • Freezing out at the time corresponding Vsurf=3.5 cm/ns, temperatures at these time are very similar to the limiting temperatures.

12. Excitation Energy • The excitation energy remaining in the TLF source was determined using calorimetric technique

13. Comparison of initial properties of the hot nuclei • For each individual system, deviations from those averages are seen to be relatively small • The neutron multiplicity for the 55 MeV/u 27Al + 124Sn reaction is an exception • The calculated values (SMM-- Δ, GEMINI--□) of the multiplicities and average energies show quite similar trends in comparison with those of the experiments, • suggesting that the statistical picture has some validity

14. Cut events into 4 bins • The total multiplicity of charged particles and neutron particles is used to select the collision as an impact parameter sensitive paramter • We divide the total HM events into 4 parts corresponding the small impact parameter (central collisions) to the larger ones (peripheral collisions) respectively

15. Results of three source fits • Multiplicity decrease from central bin to peripheral bin. • Temperatures and velocities of NN source keep similar for different bins while they are reasonably changing from central events to peripheral events

16. How to study the dynamic in the early stage of nuclear reaction • the kinetic energy of the emitted particle is used as a clock with a dynamic model calculation

17. Coalescence Model I : determining P0 • In Coalescence Model, the density of composite particle momentum space with Z protons and N neutrons is directly related to the density of free neutrons and protons momentum space as the following formula, (T. Butler and C.A.Pearson, PRL7(1961)69, PhysRev129(1963)p836, A Mekjian PRL38(1977)p640 • Because of the difficulty to measure the neutron spectra, we assume the neutron has the same shape of momentum distribution and the yield is related to the isospin of the system, then the equation become as the following,

18. Coalescence Model II: determining size of the system • In Mekjian thermal Coalescence model, assuming the chemical equilibrium is reached and the particle are emitted at the freeze-out density. The relationship of coordinate volume and momentum volume is as the following, EB and s is the binding energy and spin of the composite particle and T is the temperature of the source A. Mekjian et al. PRL77(1977)p640, PRC17(1978)p1051

19. Vsurf Evolution of the t/3He Ratios

20. Evolution of HHe Isotope Ratio Temperature

21. Evolution of coalescence Parameter P0 • Coalescence Parameter P0 changes with surface velocity for different particle and different bins • Peaks at Vsurf about 5 cm/ns

22. Evolution of the Coalescence Radii • Coalscence Radii of different particle for reaction ZnMo47

23. Nucleon density (r) “Spectators” RA a “Participants” r(fm) “Spectators” l b impact Glauber Model • Sampling the positions of the nucleons according to Woods-Saxon density • Sampling an impact parameter • Calculate the distance d between the nucleon in projectile and that in target • If d < R_interaction, these two nucleons are counted as participant nucleons

24. Results of Glauber model simulation Impact Parameter (fm)

25. Relationship Between Coalescence Radii and the Participant number • Total multiplicity of LCP and neutron is sensitive to the impact parameter • Coalescence analysis can give the reasonable size of the overlapped zone in heavy ion reaction

26. Summary • The very similar hot nuclei are indeed produced for the central HI collisions at near fermi energy. • The dynamic evolution of the interaction zone from the central to the peripheral collisions are very similar. • The Radius from the coalescence analysis is well correlated with the impact parameter.

27. The End Thank you !