1. W. Udo Schröder University of Rochester, Rochester, NY Proximity Splitting W. Udo Schröder IWNDT 2013 1 International Workshop on Nuclear Dynamics and Thermodynamics Honoring Joseph B. (“Joe”) Natowitz College Station (TX), August 2013

2. Proximity Splitting W. Udo Schröder IWNDT 2013 2 Outline:  Challenges  Mechanical (in)stability, tensile strength  Simple expectations  Expt example: 48 Ca+ 112,124 Sn @45A MeV  Conclusions Outline:  Challenges  Mechanical (in)stability, tensile strength  Simple expectations  Expt example: 48 Ca+ 112,124 Sn @45A MeV  Conclusions M.J. Quinlan, H. Singh, E. Henry, J. Tõke, WUS and CECIL/CHIMERA Collaboration (Univ. Rochester, LNS/Catania,…) 48 Ca+ 124 Sn Reaction. E/A=45 MeV, b= 5 fm, QMD simulation, soft EOS M.J. Quinlan, PhD Thesis, U. Rochester, 2011  Influence of mean field vs. residual interactions (scattering)  EOS/isoEOS compatible with interactions/decay of finite nuclei Method: Statistical vs. dynamical particle emission (, E*/T/ ).  Influence of mean field vs. residual interactions (scattering)  EOS/isoEOS compatible with interactions/decay of finite nuclei Method: Statistical vs. dynamical particle emission (, E*/T/ ). Basic Questions and Challenges in HIR Dynamics

3. Challenges to Studies of “the” EOS/isoEOS Preparation (A, Z, E*, J) of highly excited, equilibrated systems at limits of stability. Understanding of EOS-driven expansion and decay mechanism of finite nuclei. Interest in bulk mean field (EOS), …. But exotic clusters (=instability) evaporated from surface. Competing reaction mechanisms produce similar phenomena (e.g. isotopic distributions), fission, neck rupture, but different sensitivity/response. Proximity Splitting W. Udo Schröder IWNDT 2013 3 Q: Are there additional useful processes, observables?  dynamical processes: aligned dynamical fission/breakup proximity splitting (  a number of recent works, here example Ca+Sn). Superposition of effects of mean field with those of residual interactions (in-medium scattering, “pre-equilibrium”). Secondary evaporation effects/”side feeding.” What can be learnt from dyn. fission/breakup

4. EOS and Tensile Strength Proximity Splitting W. Udo Schröder IWNDT 2013 4 F=Load Force required for nuclear breakup depends on T, A/Z and on transitional nuclear shapes (light vs. heavy nuclei). Available forces: centrifugal, nucleus- nucleus interactions, thermal pressure. J. R. Davis, Tensile Testing, ASM Intern., 2004 Fracture Ductile Metal

5. EOS and Tensile Strength Proximity Splitting W. Udo Schröder IWNDT 2013 5 J. R. Davis, Tensile Testing, ASM Intern., 2004 Fracture Ductile Metal Centrifugal-Force Effect F=Load Force required for nuclear breakup depends on T, A/Z and on transitional nuclear shapes (light vs. heavy nuclei). Available forces: centrifugal, nucleus- nucleus interactions, thermal pressure.

6. Dynamical (Centrifugal) Instabilities Stability criteria for dynamical system, state= {density profile (r), shape par’s, E*,J} Proximity Splitting W. Udo Schröder IWNDT 2013 6 Spherical Triaxial Binary Estimate trends: RLDM at T≠0, Scale E surf with  (E rot (J)/E surf ) crit = f(T) But: No expansion d.o.f. !! Rotating-liquid drop model (g.s.) (Cohen, Plasil, Swiatecki, Ann. Phys. 82 (1974)) Instability = f (shape, J), specific families of nuclear shapes. Angular Momentum J

7. Expectations for Peripheral Ca+Sn Collisions Proximity Splitting W. Udo Schröder IWNDT 2013 7 Angular Momentum (h) Temperature (MeV) Classical transport model (NEM) calculations. Proximity +Coulomb interactions, one- body dissipation. Ca+Sn 45 A MeV typical ranges Interaction Time (L) PLF Temperature (L) PLF Mean Spin (L) Dissipated Energy (L) Can projectile (PLF) sustain E*,J ?

8. Proximity Splitting W. Udo Schröder IWNDT 2013 8 Experiment: 48 Ca + 112,124 Sn @ 45 A MeV Cone 1m 1° 30° CHIMERA Multi-Detector Array (LNS Catania) TARGET BEAM Cone: 688 telescopes Sphere 40,48 Ca+ 112,124 Sn Reaction. E/A=45 MeV M.J. Quinlan, PhD Thesis, U. Rochester, 2011 No neutrons

9. 48 Ca + 112,124 Sn @ 45 A MeV Proximity Splitting W. Udo Schröder IWNDT 2013 9 E(Si)-E(CsI) correlations for different elements for 48 Ca + 124 Sn at laboratory angle θ = 19 o. Angle-integrated isotopic distributions for both targets are approximate Gaussians with similar widths. Heavier target  n rich PLF

10. Proximity Splitting W. Udo Schröder IWNDT 2013 10 Dynamic Splitting of PLF* after Dissipative Rxns 48 Ca+ 112,124 Sn, E/A = 45 MeV Experimental Wilczyński contour diagrams for 48 Ca+ 112 Sn @E/A=45 MeV. Top: PLF energy vs. angle, Bottom: PLF velocity vs. angle. Nucleon exchange model (CLAT). Sequential evaporation: GEMINI. Galilei invariant cross sections a) for heavier PLF remnants b) for lighter remnants (IMFs). Wilczyński Plots Invariant Velocity Plots

11. Proximity Splitting of PLF* after Dissipative Rxns Proximity Splitting W. Udo Schröder IWNDT 2013 11 Prompt projectile splitting in proximity (under the influence) of target. Nuclear surface interactions  aligned asymmetric breakup Evidence for dynamics: 1.Alignment of breakup axis in plane, in direction of flight 2.F/B of heavy/light. 3.Relative velocity ≈2x systematics. 4.Anti-correlation Z: Z 1 + Z 2 ≈ Z PLF* 48 Ca+ 112,124 Sn Reaction Plane

12. Angular Alignment and Coplanarity Proximity Splitting W. Udo Schröder IWNDT 2013 12 Statistical x 4 Angular Distribution of light IMF clusters  tilt (deg.) Distribution of Tilt Angles (of Split-Axis) Orientation of the PLF scission axis  Tilt ≈ 90 0 ±25 0.  Coplanarity Preferred orientation of deformed pre- scission PLF: lighter IMF backwards (towards TLF)  Minimizing energy/L Relative IMF/PLF rem velocity

13. 48 Ca + 124 Sn E/A =45 MeV Multiplicity Correlations Projectile velocity v || = 9 cm/ns Multiplicity distributions indicate semi-peripheral (fast) reactions for More central (smaller L) if IMF is emitted forward Charged-Particle Multiplicity Distributions Proximity Splitting W. Udo Schröder IWNDT 2013 13 Relative IMF/PLF rem velocity

14. IMF/PLF rem Angle-Velocity Correlations Proximity Splitting W. Udo Schröder IWNDT 2013 14 Experiment Simulation NEM/GEMINI Simulation QMD/GEMINI v C = Viola Systematics NEM & QMD simulations: Fragment emission is sequential (via GEMINI) or late in collision. Centrifugal energy boost: Required J values are consistent with J stability limit for Ca. But does not explain F/B alignment and yield asymmetry. Centrifugal energy boost v rel TLF-(IMF+PLF rem ) Int ?

15. 3-Body Driving Potential (Proximity + Coulomb) Proximity Splitting W. Udo Schröder IWNDT 2013 15 rPrP r def L=0 L=80 L=160 L=300 B.R. Binary Reaction F. Complete Fusion I.F. Incomplete Fusion P.S. Projectile Splitting

16. 3-Body Driving Potential (Proximity + Coulomb) Proximity Splitting W. Udo Schröder IWNDT 2013 16 rPrP r def L=0 L=80 L=160 L=300 B.R. Binary Reaction F. Complete Fusion I.F. Incomplete Fusion P.S. Projectile Splitting

17. Isoscaling in Dynamic PLF* Splitting ( 48 Ca+ 112,124 Sn) Proximity Splitting W. Udo Schröder IWNDT 2013 17 PLFs from 2 dissipative reactions split dynamically. Compare cluster yields  ratios. Isoscaling Plot Li, Be, B, C, N Isotones R 12 Ambiguity due to uncertain reconstruction  Isoscaling due to interaction of breakup fragments? Need reaction model to simulate simultaneous observables. Need realistic model to relate {}  C sym (r) Apparent ?

18. Summary & Conclusions Experimental observations (Ca+Sn, 45A MeV) Reaction mechanism changes for semi-peripheral collisions from binary (PLF+TLF) to PLF* splitting in TLF proximity. Estimates: J PLF ~ (20-25)ħ, T PLF ~ 5 MeV. Relative velocity augmented by centrifugal boost. Breakup instability suggests softening of surface,   0 for T  (5-6) MeV Breakup alignment indicates influence of underlying PES (TLF proximity). Potential of dynamical breakup processes to image bulk EOS, tensile strength. Process much faster than (collective) shape evolutions. Isoscaling observed also for competing mechanisms (dynamic splitting). Ground state masses explain isoscaling phenomena. Progress in thermodynamics of finite nuclei (expansion, surface, caloric). Theoretical work needed to derive more rigorous/direct connection between EOS (hot RLDM?) and dynamic processes. Proximity Splitting W. Udo Schröder IWNDT 2013 18

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