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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. - PowerPoint PPT Presentation
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Andreas HeinzAndreas HeinzWright Nuclear Structure Laboratory, Wright Nuclear Structure Laboratory,
Yale UniversityYale University
for the for the CHARMSCHARMS Collaboration Collaboration
Symposium on Nuclear Structure and Reactions in the Era of Radioactive Beams, ACS meeting, Boston, August 20-22, 2007
Fission of Spherical Radioactive Ion Beams Fission of Spherical Radioactive Ion Beams A New Tool to Study the Dissipative A New Tool to Study the Dissipative
Properties of Nuclear MatterProperties of Nuclear Matter
CHARMSCHARMSCCollaboration for ollaboration for HHigh-igh-AAccuracy Experiments on Nuclear ccuracy Experiments on Nuclear RReaction eaction MMechanisms with echanisms with
Magnetic Magnetic SSpectrometerspectrometers
P. ArmbrusterP. Armbruster11, A. , A. BacquiasBacquias11, , L. GiotL. Giot11, V. Henzl, V. Henzl1,121,12, D. Henzlova, D. Henzlova1,121,12, A. Keli, A. Kelićć11, S. , S. LukićLukić11, , R. PleskaR. Pleskačč11, , M.V. RicciardiM.V. Ricciardi11, , K.-H. SchmidtK.-H. Schmidt11, O. Yordanov, O. Yordanov11, J. Benlliure, J. Benlliure22, J. Pereira, J. Pereira2,122,12, E. Casarejos, E. Casarejos22, M. , M.
FernandezFernandez22, T. Kurtukian, T. Kurtukian22, C.-O. Bacri, C.-O. Bacri33, M. Bernas, M. Bernas33, L. Tassan-Got, L. Tassan-Got33, L. Audouin, L. Audouin33, C. St, C. Stééphanphan33, A. , A. BoudardBoudard44, S. Leray, S. Leray44, C. Volant, C. Volant44, C. Villagrasa, C. Villagrasa44, B. Fernandez, B. Fernandez44, J.-E. Ducret, J.-E. Ducret44, J. Ta, J. Taïïebeb55, , C. SchmittC. Schmitt66, ,
B. JuradoB. Jurado77, F. Reymund, F. Reymund88, P. Napolitani, P. Napolitani88, D. Boilley, D. Boilley88, A. Junghans, A. Junghans99, A. Wagner, A. Wagner99, A. Kugler, A. Kugler1010, V. , V. WagnerWagner1010, A. Krasa, A. Krasa1010, A. Heinz, A. Heinz1111, P. Danielewicz, P. Danielewicz1212, L. Shi, L. Shi1212, T. Enqvist, T. Enqvist1313, K. Helariutta, K. Helariutta1414, A. , A.
IgnatyukIgnatyuk1515, A. Botvina, A. Botvina1616, P.N. Nadtochy, P.N. Nadtochy11
11GSI, Darmstadt, GermanyGSI, Darmstadt, Germany22Univ. Santiago de Compostela, Sant. de Compostela, SpainUniv. Santiago de Compostela, Sant. de Compostela, Spain
33IPN Orsay, Orsay, FranceIPN Orsay, Orsay, France44DAPNIA/SPhN, CEA Saclay, Gif sur Yvette, FranceDAPNIA/SPhN, CEA Saclay, Gif sur Yvette, France
55DEN/DMS2S/SERMA/LENR, CEA Saclay, Gif sur Yvette , FranceDEN/DMS2S/SERMA/LENR, CEA Saclay, Gif sur Yvette , France66IPNL, Universite Lyon, Groupe Materie Nucleaire 4, Villeurbanne, FranceIPNL, Universite Lyon, Groupe Materie Nucleaire 4, Villeurbanne, France
77CENBG, Bordeau-Gradignan, FranceCENBG, Bordeau-Gradignan, France88GANIL, Caen FranceGANIL, Caen France
99Forschungszentrum Rossendorf, Dresden, GermanyForschungszentrum Rossendorf, Dresden, Germany1010Nuclear Physics Institute, Rez, Czech RepublicNuclear Physics Institute, Rez, Czech Republic
1111Wright Nuclear Structure Laboratory, Yale University, New Haven, USAWright Nuclear Structure Laboratory, Yale University, New Haven, USA1212NSCL and Physics and Astronomy Department, Michigan State University, East Lansing, USANSCL and Physics and Astronomy Department, Michigan State University, East Lansing, USA
1313CUPP Project, Pyhasalmi, FinlandCUPP Project, Pyhasalmi, Finland1414Univeristy of Helsinki, Helsinki, FinlandUniveristy of Helsinki, Helsinki, Finland
1515IPPE Obninsk, RussiaIPPE Obninsk, Russia1616Institute for Nuclear Research, Russian Academy of Sciences, Moscow, RussiaInstitute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia
OutlineOutline
• Dissipation of nuclear matter
• Radioactive beams – choose deformation and fissility
• Results – experimental evidence of the influence of ground-state deformation
• Summary
Dissipation
Dissipation in nuclear physicsDissipation in nuclear physics
colleqcoll
coll EEdt
dE
Energy in collective degrees of freedom
Energy in single-particle degrees of freedom
Transport theories
Reduced dissipation coefficient
Dissipation
o How can it be measured?
o What is its magnitude?
o Does it depend on temperature, deformation, isospin, …?
Fission and DissipationFission and Dissipation
Centroid of the probability distribution!
Bjornholm, Lynn; Rev. Mod. Phys. 52, 725 (1980)
Motion is governed by:
dissipation
phase space
Analogy: Brownian Motion
Fokker-Planck
Langevin Diffusion Friction
Saddle point
Fission Time ScaleFission Time Scale
D. Hilscher, Ann. Phys. Fr. 17 (1992) 471
Consequence of dissipation:
→ fission slows down!
Escape RateEscape 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!
Fission and DissipationFission and Dissipation
Scission
Deformation
Energy
Compound Nucleus
Saddle point
Ground state
τCN-Saddle τSaddle-Scission
Fiss
ion
barr
ier
Fluctuating Forces:
increases time scale
decreases excitation energy by particle evaporation
Friction
What is the influence of the compound nucleus deformation on the transient time?
Not to scale!
Dissipation: ObservablesDissipation: 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
Measuring a Temperature DifferenceMeasuring a Temperature Difference
Deformation
En
er
gy
Compound Nucleus
Saddle point
Ground state
τCN-Saddle
τSaddle-Scission
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!
→ Measure the temperature of the compound nucleus.
→ Measure the temperature at the saddle!
Not to scale!
Two-step Projectile FragmentationTwo-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!
ExperimentExperiment
Projectile Fragmentation
Production of nuclei near N=126
Fragmentation Fission
Induce fission of spherical fissile nuclei at high excitation energies.Inverse kinematics: large detection
efficiency!
Investigated NucleiInvestigated NucleiP
roto
n nu
mbe
r
Neutron number
238U @ 1 A GeV on 9Be: projectile fragmentation
x - investigated nuclei
Deformed nuclei
Spherical nuclei
Heavy nuclei near N=126:
Highly fissile
45 secondary beams with |β2| ≤ 0.15
238U ground state:β2 ≈ 0.23
Fission Fragment Charges and Fission Fragment Charges and Compound Nucleus Excitation EnergyCompound Nucleus Excitation Energy
The sum of the fission fragment charges is a measure of the energy of the compound nucleus!
Abrasion-Ablasion modelData
Deformation Induced by Projectile Deformation Induced by Projectile FragmentationFragmentation
215Ac
Nearly spherical pre-fragments!
Saddle point: β2 ≈ 0.6 - 0.8
Access to compound nuclei which are:
highly excited
highly fissile
nearly spherical
215Ac
P.N. Nadtochy
Temperature DifferenceTemperature Difference
Deformation
En
er
gy
Compound Nucleus
Saddle point
Ground state
τCN-Saddle
τSaddle-Scission
Not to scale!
Energy difference we want to measure:
Compound nucleus excitation energy
→ use Z1+Z2
Saddle point excitation energy
→ use width of the charge distribution
Charge Width as a ThermometerCharge Width as a Thermometer
Asymmetric mass split
Symmetric mass split
Asymmetric mass split
Bjornholm, Lynn; Rev. Mod. Phys. 52, 725 (1980)
Mass (charge) asymmetry η
Pote
nti
al Populatio
n
2
2
2
2
2
fissA
saddle
fiss
fissZ
dVd
T
A
Z
A. Ya. Rusanov et al. Phys. At. Nucl. 60, 683 (1977)
Fission WidthsFission Widths
Z1+Z2 – gate on CN excitation energy!
Results IResults I CN excitation energy
Statistical Model
Kramers
β = 4.5 x 1021 s-1
Calculations: Abrasion-Ablation model (ABRABLA)
Results IIResults II
• Compound nucleus temperature up to 5.5 MeV• Saddle point temperature up to 3 MeV• This work: <τtrans> = (3.30.7)x10-21 s• 238U: <τtrans> = (1.70.4)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?
Multi-dimensional Langevin Calculations
Example: 248Cf
2-body dissipation
P.N. Nadtochy et al., PRC 75 (2007)
E*=30 MeV
E*=150 MeV
→ strong influence on the stationary fission rate!
SummarySummary• 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!
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