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!