Andreas Heinz Wright Nuclear Structure Laboratory, Yale University for the CHARMS Collaboration

1. Fission of Spherical Radioactive Ion Beams A New Tool to Study the Dissipative Properties of Nuclear Matter Andreas Heinz Wright Nuclear Structure Laboratory, Yale University for the CHARMS Collaboration Symposiumon Nuclear Structure and Reactions in the Era of Radioactive Beams, ACS meeting, Boston, August 20-22, 2007

2. CHARMSCollaboration for High-Accuracy Experiments on Nuclear Reaction Mechanisms with Magnetic Spectrometers P. Armbruster1, A. Bacquias1, L. Giot1, V. Henzl1,12, D. Henzlova1,12, A. Kelić1, S. Lukić1, R. Pleskač1, M.V. Ricciardi1, K.-H. Schmidt1, O. Yordanov1, J. Benlliure2, J. Pereira2,12, E. Casarejos2, M. Fernandez2, T. Kurtukian2, C.-O. Bacri3, M. Bernas3, L. Tassan-Got3, L. Audouin3, C. Stéphan3, A. Boudard4, S. Leray4, C. Volant4, C. Villagrasa4, B. Fernandez4, J.-E. Ducret4, J. Taïeb5, C. Schmitt6, B. Jurado7, F. Reymund8, P. Napolitani8, D. Boilley8, A. Junghans9, A. Wagner9, A. Kugler10, V. Wagner10, A. Krasa10, A. Heinz11, P. Danielewicz12, L. Shi12, T. Enqvist13, K. Helariutta14, A. Ignatyuk15, A. Botvina16, P.N. Nadtochy1 1GSI, Darmstadt, Germany 2Univ. Santiago de Compostela, Sant. de Compostela, Spain 3IPN Orsay, Orsay, France 4DAPNIA/SPhN, CEA Saclay, Gif sur Yvette, France 5DEN/DMS2S/SERMA/LENR, CEA Saclay, Gif sur Yvette , France 6IPNL, Universite Lyon, Groupe Materie Nucleaire 4, Villeurbanne, France 7CENBG, Bordeau-Gradignan, France 8GANIL, Caen France 9Forschungszentrum Rossendorf, Dresden, Germany 10Nuclear Physics Institute, Rez, Czech Republic 11Wright Nuclear Structure Laboratory, Yale University, New Haven, USA 12NSCL and Physics and Astronomy Department, Michigan State University, East Lansing, USA 13CUPP Project, Pyhasalmi, Finland 14Univeristy of Helsinki, Helsinki, Finland 15IPPE Obninsk, Russia 16Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia

3. Outline • Dissipation of nuclear matter • Radioactive beams – choose deformation and fissility • Results – experimental evidence of the influence of ground-state deformation • Summary Dissipation

4. Dissipation in nuclear physics Transport theories Energy in collective degrees of freedom Energy in single-particle degrees of freedom Dissipation Reduced dissipation coefficient • How can it be measured? • What is its magnitude? • Does it depend on temperature, deformation, isospin, …?

5. Fission and Dissipation Saddle point Centroid of the probability distribution! Motion is governed by: • dissipation • phase space • Analogy: Brownian Motion • Fokker-Planck • Langevin Diffusion Friction Bjornholm, Lynn; Rev. Mod. Phys. 52, 725 (1980)

6. Fission Time Scale Consequence of dissipation: → fission slows down! D. Hilscher, Ann. Phys. Fr. 17 (1992) 471

7. Escape Rate Bohr-Wheeler (1939): Transition-state method Quasi-stationary (Kramers 1940): Fission width is reduced due to trajectories back into the well. Transient time: Time the system needs to adjust to the potential under the influence of a fluctuating force. C. Schmitt Topic of this talk!

8. τCN-Saddle τSaddle-Scission Fission and Dissipation • Fluctuating Forces: • increases time scale • decreases excitation energy by particle evaporation Compound Nucleus Saddle point Friction Energy What is the influence of the compound nucleus deformation on the transient time? Fission barrier Scission Ground state Deformation Not to scale!

9. Dissipation: Observables • Time: Particle multiplicities (neutron clock) → impossible to distinguish pre- and post-saddle neutrons! • Fission cross sections → reduction of fission width • Energy loss up to saddle due to particle evaporation → thermometer D. Hilscher, Ann. Phys. Fr. 17 (1992) 471

10. Measuring a Temperature Difference Compound Nucleus the energy the nucleus looses on its way to the saddle point (via evaporation): The longer the motion to the saddle takes the more energy will be lost by particle evaporation! Saddle point Energy → Measure the temperature of the compound nucleus. → Measure the temperature at the saddle! Ground state Deformation Not to scale! τCN-Saddle τSaddle-Scission

11. Two-step Projectile Fragmentation Step 1: Projectile fragmentation → prepare exotic beams Step 2: Projectile-fission → measure the charge of the two fission fragments • Advantages: • High excitation energy (up to several hundred MeV) • Low angular momentum (< 20 ħ) • Selection of fissility and ground-state deformation!

12. Induce fission of spherical fissile nuclei at high excitation energies. Experiment Projectile Fragmentation Fragmentation Fission Production of nuclei near N=126 Inverse kinematics: large detection efficiency!

13. Investigated Nuclei 238U @ 1 A GeV on 9Be: projectile fragmentation x - investigated nuclei • Heavy nuclei near N=126: • Highly fissile • 45 secondary beams with |β2| ≤ 0.15 • 238U ground state: β2 ≈ 0.23 Deformed nuclei Spherical nuclei Proton number Neutron number

14. Fission Fragment Charges and Compound Nucleus Excitation Energy Data Abrasion-Ablasion model The sum of the fission fragment charges is a measure of the energy of the compound nucleus!

15. Deformation Induced by Projectile Fragmentation • Nearly spherical pre-fragments! • Saddle point: β2 ≈ 0.6 - 0.8 • Access to compound nuclei which are: • highly excited • highly fissile • nearly spherical 215Ac 215Ac P.N. Nadtochy

16. Temperature Difference Compound Nucleus Saddle point Energy difference we want to measure: Compound nucleus excitation energy → use Z1+Z2 Saddle point excitation energy → use width of the charge distribution Energy Ground state Deformation Not to scale! τCN-Saddle τSaddle-Scission

17. Charge Width as a Thermometer A. Ya. Rusanov et al. Phys. At. Nucl. 60, 683 (1977) Asymmetric mass split Symmetric mass split Asymmetric mass split Population Potential Mass (charge) asymmetry η Bjornholm, Lynn; Rev. Mod. Phys. 52, 725 (1980)

18. Fission Widths Z1+Z2 – gate on CN excitation energy!

19. Results I CN excitation energy Calculations: Abrasion-Ablation model (ABRABLA) Statistical Model Kramers β = 4.5 x 1021 s-1

20. Results II • Compound nucleus temperature up to 5.5 MeV • Saddle point temperature up to 3 MeV • This work: <τtrans> = (3.30.7)x10-21 s • 238U: <τtrans> = (1.70.4)x10-21s B. Jurado et al., PRL 93, 072501(2004) • β= (4.5 ±0.5) x 1021 s-1 • Over-damped motion at small deformation and high excitation energies?

21. Multi-dimensional Langevin Calculations Example: 248Cf 2-body dissipation E*=30 MeV E*=150 MeV → strong influence on the stationary fission rate! P.N. Nadtochy et al., PRC 75 (2007)

22. Summary • First experimental evidence of the influence of deformation on the transient time. • Radioactive beams allow to control ground-state deformation and fissility. • Charge sum and width as a measure of the energy lost due to pre-saddle particle emission. • Shape does matter!