A MODEL FOR PROJECTILE FRAGMENTATION

1. A MODEL FOR PROJECTILE FRAGMENTATION Gargi Chaudhuri Variable Energy Cyclotron Centre, INDIA Collaborators: S. Mallik, VECC, India S. Das Gupta, McGill University, Canada

2. CONTENTS • Different Stages of Projectile Fragmentation • Our Model • Results • Comparison with different experimental data • Summary

3. PROJECTILE FRAGMENTATION (Different Stages) • Collision of the projectile & target nuclei above certain energy (> 100 MeV/n) • (COLLISION) • Part of the projectile goes into the participant & remaining part • (projectile spectator or PLF) gets sheared off (ABRASION) • Hot, abraded PLF (As, Zs) expands to about 3V0 – 4V0.(V0-normal nuclear volume) & breaks up into many fragments (MULTIFRAGMENTATION) • The excited fragments de-excite by sequential decay (EVAPORATION)

4. Pictorial Scenario Projectile fragmentation PLF Projectile Target Abrasion Multi-fragmentation Evaporation

5. Abrasion Stage Calculation ( for different impact parameter b ) Ref: S. Mallik, G.Chaudhuri & S. Das Gupta Phys. Rev. C 83 (2011) 044612 • Overlapping volume V(b) (participant region)of projectile & target • using straight-line geometry • PLF Size : average number of proton (<ZS>) and neutron (<NS> ) Vs(b)=V0-V(b) PLF size for different reactions Probability of formation of PLF (Ns ,Zs) using minimal distribution • Abrasion Cross section • We use animpact parameter dependent • temperature profile T(b) for the PLF

6. Temperature of PLF • T is independent of projectile beam energy • T depends on impact parameter (b). It depends upon the wound of the original projectile which is (1.0 – As/A0) Simplest parametrization As(b)/A0 T independent of As/Ao For all reactions From many sets of experimental data

7. Multi-fragmentation Stage Ref: C. B. Das , S. Das Gupta et al. , Phys . Rep. 406 (2005) 1 PLF(As,Zs) Canonical Thermodynamical Model (CTM) High excitation energy Breaking into composites and nucleons Density fluctuation Expansion EvaporationStage :-(based on Monte-Carlo Simulation) Thermodynamic Equilibrium @freeze-out Evaporation Model Cold Secondary fragments Hot primary fragments production Hot primary fragments Weisskopf’s evaporation theory Decay Channels:- p, n, α, d, t, 3He, γ Ref: G.Chaudhuri & S.Mallik Nucl. Phys. A 849 (2011) 190

8. Canonical Thermodynamical Model (CTM) Canonical Partition function of PLF AS (ZS ,NS) ni,j=No of fragments with i neutrons & j protons Baryon & charge conservation constraints ωi,j=Partition function of the fragment ni ,j Computationally difficult ! Crux of the model An exact computational method which avoids Monte Carlo by exploiting some properties of the partition function Recursion relation Possible to calculate partition function of very large nuclei within seconds Most important feature of our model

9. CTM contd… Partition function of the fragment ni ,j Cross-section after multi-fragmentation stage:- translational intrinsic Intrinsic part of the partition function Liquid drop model Fermi-gas model multifragmentation abrasion Average no. of composites {i,j} or Multiplicity

10. Model summary……….. Freeze-out volume=3V0 Projectile size (A0,Z0 ) & target size (At, Zt ) Abrasion Model As(b) Zs(b) CTM + evaporation observables PLF size Results……… Comparison with experimental data • Different • Target-projectile combinations • Incident energy • Observables

11. Comparison of theoretical and experimental temperature profile Zbound = ZS - No. of Z=1 fragments Experiment:- 600 MeV/nucleon (ALADIN @GSI) 107Sn and 124Sn on natural Sn Experimental Temperature Profile By isotope thermometry method Good agreement solid lines  model Squares with error bars  data

12. Variation of IMF multiplicity with Zbound Experiment :- 600 MeV/nucleon (ALADIN @GSI) 107Sn and 124Sn on natural Sn IMF size: 3 ≤ Z ≤ 20 dashed lines  model solid lines  data Nice agreement with data

13. Differential Charge Distribution in Projectile Fragmentation (At different Zbound intervals) Experiment:- 600 MeV/nucleon (ALADIN) • Lower Zbound range • higher T of PLFbreaks into many fragments of very small charge. • Steeper Charge distribution • Higher Zbound range • Lower T of PLFfragmentation • is less, both low & high Z fragments • “U” shaped Charge distribution dashed lines  model solid lines  data

14. Largest Cluster in Projectile Fragmentation Experiment :- 600 MeV/nucleon (ALADIN @GSI) 107Sn and 124Sn on natural Sn Average size of largest cluster Probability that zmis the largest cluster Nice agreement with experiment dashed lines  model solid lines  data

15. Charge Distribution in Projectile Fragmentation 58Ni+9Be 140 MeV/nucleon (MSU) 136Xe+208Pb 1 GeV/nucleon (GSI) The trend is nicely reproduced for all the reactions Experimentally Different Beam Energy Theoretically Same Temperature Profile 58Ni+181Ta 140 MeV/nucleon (MSU) 129Xe+27Al 790 MeV/nucleon (GSI) dashed lines  model solid lines  data Ref: S. Mallik, G.Chaudhuri & S. Das Gupta Phys. Rev. C 84 (2011) 054612

16. Isotopic Distribution in Projectile Fragmentation 58Ni+9Be 140 MeV/nucleon (MSU Experiment) Circles joined by dotted lines  model Squares with error bars data Nice agreement with data

17. SUMMARY • The model for projectile fragmentation is grounded in traditional concepts of heavy-ion reaction (abrasion) plus the well known model of multifragmentation (Canonical Thermodynamical Model). • The model is in general applicable and implementable above a certain beam energy. • Universal temperature profile (depending on impact parameter) is introduced as input for different target-projectile combinations & widely varying energy of the projectile. • The modelis able to successfully reproduce a wide variety of experimental observables like charge & mass distribution, isotopic distributions, IMF multiplicity, size of largest cluster . • Microscopic BUU calculations is being done in order to estimate the size & excitation of the initial PLF at different impact parameters. • The work is in progress…….

18. Thank You

19. Fluctuation in number of IMFs for small Projectile like fragments:- Sn124+Sn119 Sn107+Sn119 Zbound=ZS- No. of Z=1 fragment Experiment :- Zbound=Integer (Due to event by event measurement) Theoretical Calculation :- Zbound=Non-integer (Due to average no. of fragment calculation) Black solid lines  data Red dotted lines  direct calculation

20. Fluctuationcontd… Zbound=3 AX3 BX3+neutron(s) AX4 BX3+neutron(s)+proton AX5 BX3+neutron(s)+2 protons …… Sn124+Sn119 Sn107+Sn119 <MIMF>=1 Zbound=5 AX5 BX5+neutron(s) AX5 BX3+CHe2 +neutron(s) …… <MIMF>=1 Zbound=4 MIMF=1 AX4 BX4+neutron(s) AX4 CHe2+DHe2 +neutron(s) …… MIMF=0 <MIMF> is calculated by modifying the CTM with experimental decay scheme of different energy levels. Black solid lines  data Red dotted lines  direct calculation Blue triangles  modified calculation