Diapositive 1

1
Fusion-evaporation cross section. Density
dependence of symmetry energy
Exotic nuclei and neutron stars meeting IPN
Orsay, september 18, 2006

• Nuclear physic thematic of the meeting
• low-density equation of state
• symmetry energy
• limiting temperature for equation of state
• pairing interaction and gaps
• excitations in the crust of neutron stars
• isovector optical potential
• hypernuclei
• heavy element nucleosynthesis

subjects addressed in this talk
2
Nuclear collisions

• General context
• Our main goals are the following the nuclear
  matter properties under constraint,
• particularly the density dependence of the
  symmetry term
• microscopic properties like viscosity, transport
  properties, symmetry term,
• in medium n-n cross section could be addressed
  by the use of dynamical studies
• macroscopic properties can be inferred by
  studying the deexcitation of hot nuclei, level
• density parameter, limiting T, Emax, Coulomb
  barrier
• So far these properties were studied with stable
  beams.
• With availabilities of radioactive beams those
  studies can be extended.

3
Nuclear collisions with RIB
Availability of RIB gt new dimension in the
exploration of the phase diagram

• Topics regarding RIB (Spiral-Spiral 2)
• Level density temperature and density
  dependence
• Limiting temperature and Coulomb instabilities
• n-p asymmetry and decay channel at drip lines
• Reaction mechanism and thermodynamic equilibrium
• Transport properties and symmetry energy
• Our requirements
• largest possible N/Z range
• sufficient bombarding energy and intensities
  106-8 pps
• a new generation of 4p detector (A, Z, E) and
  neutron detection(?)

Fazia
4
Subjects addressed, in connection with astrophysic

• Level density parameter evolution with isospin
  and temperature
• presentation of a specific experiment currently
  in preparation at Ganil
• with both stable and radioactive beams
• Limiting temperature isopin effect
• toward a better knowledge of hot light nuclei,
  control of the secondary decay
• in multifragmentation
• Symmetry energy term evolution with density and
  isospin
• some recent results obtain by comparison with
  model

5
INDRAVamos_at_Spiral The physic case
Exploration of the deexcitation properties of hot
nuclei formed by fusion reactions with the N/Z
from the p drip line to stable nuclei
Ar Ni -gt Pd
Spiral beam

• Event by event complete information
• Fusion residue detection and identification by
  the Vamos spectrometer (Z, A, E)
• LCP in coincidence measured by the 4p INDRA
  multidetector (Mult, Z, A, E)
• neutron multiplicity by A conservation
• Complete study of the properties of the c.n.
  (cross section, mass asymmetry effects,
• deexcitation properties, thermodynamics)
• gt access to the level density parameter

6
Level density parameters

• Level density parameter is closely connected to
  the nuclear EOS
• importance in both nuclear structure and
  deexcitation of hot nuclei
• Many parameters influence the level density
  parameter
• pairing and shell effects
• surface effects
• deformation and angular momentum
• temperature
• isospin
• level density parameter vanish at high E,
  limiting T ?
• (rupture of the balance between surface, coulomb
  and bulk energies)
• and with extreme isospin composition? gtdirect
  link with EOS

our present goal
7
Level density parameter N/Z dependence
Very scarce information is available Extrapolation
s starting from stable nuclei lead to empirical
parameterisations of the form
aaA/expß(N-Z)2 Two of them give important
variations for a(N/Z) With SPIRAL beams, Ganil
offers a great chance to perform precise
measurements on a large range of isotopes Such
kind of basic thermodynamical properties are of
fundamental interest
extrapolation according to R.J. Charity Phys.
Rev. C67-044611 (2003) S.I. Al-Quraishi Phys.
Rev. C63-065803 (2001)
8
Limiting temperature and Coulomb instabilities
Limiting temperature and Coulomb instabilities
evolution with chemical composition
Basically the same experimental device as before,
we just change the beam E

• Better knowledge of hot light nuclei
• Statistical decay of hot light nuclei (C-Ca)
  Tlim, E max ?
• control of the secondary decay in
  multifragmentation (characterization of the
  freeze-out stage)
• Studying the decay of isobars populated at the
  same E

9
Transport properties and symmetry energies

• Transport models predict fluctuations of large
  amplitude in the density matter during
• the dynamic phase of the collisions
• We can observe these fluctuations by measuring
  isotopic distribution in the mid velocity region
• Competition between (incomplete) fusion and
  deep-inelastic reactions gt information
• on the density behaviour of the symmetry energy,
  the viscosity and in medium
• n-n cross section
• Comparison with theory gives access to transport
  properties such as the dependence of the
• symmetry term with density

asy stiff
asy soft
saturation density
10
BNV calculation 124Sn64Ni _at_ 10 A.MeV b7fm
Maria Colonna stochastic BNV calculations
(private communication)
asy soft gt
asy stiff gt
Less repulsion at low density (neck), the
probability for surviving increases. The presence
or not of this neck could put some constraint on
the symmetry term via model comparison
11
Present experimental results on isospin
(N/Z)CP for Z1-4

• Forward N/Z ratio smaller and varies more with
  dissipation than mid-rapidity
• Isopin diffusion visible for NiAu
• not for NiNi as expected (reference)
• BNV used as a clock
• For NiAu at 52 A MeV maximum measured
  dissipation corresponds to b5 fm in BNV
  calculations.
• for b5 fm tint130 fm/c10 fm/c
• Comparison with BNV
• better overall agreement with
• asy-stiff EOS
• for NiAu system at 52 A MeV the isospin
  equilibration is reached at 130 fm/c10 fm/c

NiAu
Symmetric system taken as reference
NiNi
Emmanuelle Galichet et al. in preparation
12
Summary and conclusion

• We develop a long term program concerning
  thermodynamic of hot nuclei
• in relation with their chemical composition.
• This program enters the study of phase transition
  and nuclear EOS
• for asymmetric matter
• As a first step, with RIB, we can perform a
  systematic study on a large range
• of (light) hot exotic nuclei which are produced
  in multifragmentation.
• We can extract fundamental basic properties like
• level density
• limiting temperature
• symmetry energy term
• equilibration of various degrees of freedom
• decay modes and emission barriers
• A better knowledge of these nuclear properties is
  also necessary in astrophysic

13
More
14
Level density parameters
Level densities govern the statistical decay of
excited nucleus gt basic ingredients for
statistical models

• Up to now fusion-evaporation reactions were
  studied through inclusive
• measurements (A or Z of residues or light
  particle spectra)
• For the very first time we will be able to have
  information
• on the residue and all the evaporated particles
  in coincidence
• all decay chains will be measured, disentangled
  and weighed
• For example
• ArNi -gt pxnRh
• ArNi -gt axnRu
• ArNi -gt 2pxn2nRu
• ArNi -gt pd(x1)nRu
• ArNi -gt 2pdynTc
• .
• E spectra for all evaporated particles will be
  measured
• with INDRA

15
Level density parameters exp constraints
For comparison with statistical model
1st constraint ECIN spectra of all evaporated
particles
2nd constraint all exit channels for the same
residue of c.n.
16
Level density parameters extraction
Fit experimental multichance emission spectra
with GEMINI simulations for example Cannot fit
with constant level density parameter a a depend
on A and E which decrease all along the
evaporation chain. An effective aeff is
necessary into Gemini calculations Starting from
experimental slopes we constrain an aeff which
then evolves with E, in the model, all along the
deexcitation chain.
Then by iteration we find level densities and
level density parameters consistent with data
INDRA is able to measure such kind of variation
on the slope of all evaporated particles But
now information on the dependence of a with N/Z
is also necessary