Nuclear Reactions With Rare Isotope Beams

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Nuclear Reactions With Rare Isotope Beams

• New facilities new capabilities.
• Stable beams (A?100) N/Z1.24 -1.48
• CCF N/Z1.14 1.64, E/Alt180 MeV.
• RIA N/Z1.06 1.72, E/Alt360 MeV.
• Isospin dependence of EOS
• Density dependence of the symmetry term.
• Constraints on symmetry from nuclear structure
  and from microscopic theory.
• Relevance to dense astrophysical environments.
• Prospects for experimental determination.
• Dynamics at extreme isospin asymmetry
• Isospin dependence of the liquid-gas phase
  transition.
• Fission barriers far from the valley of
  stability.
• Nuclear level densities far from the valley of
  stability.

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Isospin Dependence of the Nuclear Equation of
State
PAL Prakash et al., PRL 61, (1988) 2518. Colonna
et al., Phys. Rev. C57, (1998) 1410.
E/A (?,?) E/A (?,0) ?2?S(?) ? (?n- ?p)/
(?n ?p) (N-Z)/A

• Potentially significant change in the
  incompressibility of asymmetric matter.

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Constraints on asymmetry term from nuclear
structure
Symmetry term for 18 currently used Skyrme
interactions that reproduce 132Sn-100Sn mass
difference

• The density dependence of symmetry term is poorly
  constrained by nuclear properties near the valley
  of stability.

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Sensitivity of nuclear properties to density
dependence of S(?)
B.A. Brown (2000)
radius shift vs. pressure at ? 0.1 fm-3

• Pressure from asymmetry term dictates the
  difference between proton and neutron matter
  radii in heavy nuclei near valley of stability.
• Away from valley of stability the difference
  between neutron and proton Fermi energies is also
  important.

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Constraints on S(?) from microscopic models
BHF Varia- tional

• Microscopic theory provides incomplete guidance
  regarding the extrapolation away from saturation
  density.

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Relevance to Dense Astrophysical Environments
Symmetry energy dependencies

• Proton and electron fractions throughout the
  star.
• Thickness of the inner crust.
• Frequency change accompanying star quakes.
• Density profile within the star.
• Role of Kaon condensates and mixed quark-hadron
  phases in the stellar interior.

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Observable consequences

• Macroscopic properties
• Neutron star radii, moments of inertia and
  central densities.
• Maximum neutron star masses and rotation
  frequencies.

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Observable Consequences, continued

• Energy release in supernova collapse and cooling
  .
• Neutrino signal from collapse.
• Feasibility of URCA processes for proto-neutron
  star cooling if fp gt 0.1.
• pe ? n? n ? pe?
• Viability of supernova explosions.

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Determination of EOS from HI Collisions

• Many factors influence EOS
• Density and momentum dependence of mean fields.
• Use of HI collisions brings a sensitivity to
  in-medium nucleon-nucleon cross section.
• Experiments have placed constraints upon the EOS
  for symmetric matter.
• Eliminates very stiff and very soft EOSs.

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Relevance to Neutron Star EOS
Danielewicz, Prakash (2000)

• Strong sensitivity to uncertainty in the density
  dependence of the asymmetry term.

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Isospin Dependence of theMean Field for the
Asymmetry Term

• Sign of mean field opposite for protons and
  neutrons.
• Shape is influenced by incompressibility.
• These parameterizations are developed by Prakash
  and Lattimer for neutron star calculations.

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Isospin Dependence of EoS

• Fundamental property of nuclear matter.
• External relevance
• Neutron stars, supernovae

 

• Observables depend on isospin of the system and
  of the measured particle.

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Fusion/Binary Collision Boundary
M.Colonna et al., Phys. Rev. C57, 1410 (1998)

• Fusion occurs to larger impact parameters with
  soft asymmetry term.
• Measurements can be performed at rare Isotope
  facilities.
• Intensities of 105 ions/s are sufficient
• Example 103Sn112Sn, 136Sn124Sn collisions can
  be measured at RIA.
• More than an 80 increase in asymmetry at RIA and
  about 50 increase in asymmetry at CCF over the
  range of stable Sn isotopes.

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Pre-equilibrium neutron/proton emission rates

• Asymmetry of emitted nucleons much greater than
  that of dense bound matter for the soft asymmetry
  term.
• Measurements can be performed at rare isotope
  facilities.
• Intensities of 105 ions/s are sufficient at
  E/A50 MeV and intensities of 104 ions/s are
  sufficient at higher incident energies
• Example 103Sn112Sn, 136Sn124Sn collisions can
  be measured at RIA.
• More than an 80 increase in asymmetry at RIA and
  about 50 increase in asymmetry at CCF over the
  range of stable Sn isotopes.

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Pre-equilibrium Energy Spectra

• Emission of energetic neutrons is favored
  relative to energetic protons for the soft
  asymmetry term.

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Collective Flow - Nuclear EOS

• Flow Effects
• Transverse Directed Flow,
• Radial Flow,
• Squeeze-Out or elliptical flow.
• reflect internal pressure.

• Microscopic origins of pressure
• Nuclear Incompressibility,
• Momentum dependence of nuclear mean field,
• nucleon-nucleon scattering by the residual
  interaction.

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Neutron/proton transverse flow

• Comparisons of neutron to proton flow provide
  information about the density dependence of the
  symmetry term.
• Measurements can be performed with intensities of
  104 105 ions/s at rare isotope facilities.
• Example 103Sn112Sn, 136Sn124Sn collisions can
  be measured at RIA 50-80 increase in asymmetry
  over that achievable with stable beams.

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Isospin dependence of liquid-gas phase transition

• Astrophysical sites
• Matter passes through the L.G.P.T. during the
  collapse and during the later explosion.
• Vaporization of infalling nuclei at the shock
  front plays a major role dampening the shock.
• The inner crust of a neutron star is the site of
  various low density phase transitions.
• EOS at subnuclear density and boundary of mixed
  phase region important to understanding star
  quakes.

H. Muller and B. Serot, Phys. Rev. C52, 2072
(1995).

• Properties
• Gas is relatively neutron-rich.
• Region of mixed phase decreases with isospin
  asymmetry.

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Status of multifragmentation investigations

• Conditions for multifragmentation understood.
• Conditions consistent with mixed phase.
• Some systems are not in equilibrium.
• Other systems well described by equilibrium
  models the accuracy of this description under
  investigation.

AuAu, E/A35 MeV
E/A7.0 MeV
E/A6.0 MeV
E/A5.0 MeV
E/A5.8 MeV
E/A4.8 MeV
E/A3.8 MeV
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Fission Far From ? Stability

• Fission terminates r- process pathway
• Neutron induced.
• Beta delayed.
• Fission cycling?

Cameron (1985)
solar
calculated

• Fission barriers far from stability
• Measurements of fission yields on isotope chain.
• Obtain relationship between constrained mass
  surface and ground state properties as function
  of isospin.
• Improve extrapolations to extreme asymmetries.

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Nuclear Structure with a Broad Angle Lens

• Level density parameters are modulated by neutron
  shell structure.
• Minima in a(Z,A) occur at closed shells.
• Maxima correspond to deformed nuclei.
• How does the level density vary with neutron
  excess towards the r-process pathway?
• 180Tl, 180Er, 182Pb, 216Pb, 108Zr, 108Te beams
  have required intensities. Can explore
  1.08ltN/Zlt1.7 for A108. Measurements near 132Sn
  are feasible.

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Scientific Objectives

• Density dependence of symmetry term of nuclear
  EOS
• Poorly understood aspect of bulk nuclear matter.
• Closely related to neutron star structure and
  stability.
• Dynamics at extreme asymmetry relevant to nuclear
  astrophysics
• Phase transitions in low density asymmetric
  matter.
• Fission of extremely asymmetric systems
• Level densities far from beta stability.
• These objectives are attainable with RIA.
• High energies are essential for EOS studies and
  multi-fragmentation.
• Significant work can be done at the NSCL Coupled
  Cyclotron Facility.

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Observable consequences

• Macroscopic properties
• Neutron star radii, moments of inertia and
  central densities.
• Maximum neutron star masses and rotation
  frequencies.