Andreas Heinz

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

Symposium on 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. Kelic1, S. Lukic1,
  R. Pleskac1, 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
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!
tCN-Saddle
tSaddle-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 (lt 20 h)
• Selection of fissility and ground-state
  deformation!

12
Experiment
Projectile Fragmentation
Fragmentation Fission
Production of nuclei near N126
Inverse kinematics large detection efficiency!
13
Investigated Nuclei
238U _at_ 1 A GeV on 9Be projectile fragmentation
x - investigated nuclei

• Heavy nuclei near N126
• Highly fissile
• 45 secondary beams with ß2 0.15
• 238U ground state ß2 0.23

Deformed nuclei
Spherical nuclei
Proton number
Neutron number
14
Fission Fragment Charges and Compound Nucleus
Excitation Energy
Abrasion-Ablasion model
Data
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 ß2 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 Z1Z2 Saddle
point excitation energy ? use width of the charge
distribution
Energy
Ground state
Deformation
Not to scale!
tCN-Saddle
tSaddle-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 ?
Bjornholm, Lynn Rev. Mod. Phys. 52, 725 (1980)
18
Fission Widths
Z1Z2 gate on CN excitation energy!
19
Results I
CN excitation energy
Statistical Model
Kramers ß 4.5 x 1021 s-1
Calculations Abrasion-Ablation model (ABRABLA)
20
Results II

• Compound nucleus temperature up to 5.5 MeV
• Saddle point temperature up to 3 MeV
• This work ltttransgt (3.3?0.7)x10-21 s
• 238U ltttransgt (1.7?0.4)x10-21s
• B. Jurado et al., PRL 93, 072501(2004)
• ß (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
E30 MeV
E150 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!