Thessaloniki

1
Thessaloniki T?SS??????? Solún Salonico Salonique
Salonik 315 B.C.
2
ARISTOTLE UNIVERSITY ???S???????? ??????S?????
75 000 students 14 Faculties 53 Departments
3
Section of Nuclear Particle Physics
Theory Group
Experimental Group
C. KoutroulosG. LalazissisS. MassenC. PanosC.
MoustakidisR. FossionK. ChatzisavvasS.
KaratzikosV. PrassaB. PsonisZagreb, Sofia,
Catania, Munich, Hamburg, Oak Ridge, Mississippi,
Giessen
M. Chardalas S. DedoussisC. EleftheriadisM.
ZamaniA. Liolios M. ManolopoulouE. SavvidisA.
IoannidouK. PapastefanouS. StoulosM.
FragopoulouC. LamboudisTh. PapaevagelouParis
(CEA), Dubna, CERN (CAST, n-TOF)
4
Covarinat density functional theory isospin
dependence of the effective nuclear force

• Georgios A. Lalazissis
• Aristotle University of Thessaloniki, Greece

Collaborators T. Niksic (Zagreb), N. Paar
(Darmstadt), P. Ring (Munich), D. Vretenar
(Zagreb)
5
Table of Isotopes
Evolution of the Table of Isotopes
Evolution of the Table of Isotopes
1940 - 2000
Future ?
A large portion of this table is less than ten
years old !
Large gaps on the heavy neutron rich side !
6
Structure and stability of exotic nuclei with
extreme proton/neutron asymmetries
Formation of neutron skin and halo structures
Isoscalar and isovector deformations
Mapping the drip-lines
Structure of superheavy elements
Evolution of shell structure
EOS of asymmetric nuclear matter and neutron
matter
Need for improved isovector channel of the
effective nuclear interaction.
7
DFT very successful because being effective
theories, adjusted to experiment, include
globally a large number of important effects,
which go beyond simple Hartree theory, such as
Brueckner correlations, ground state
correlations, vacuum polarizations, exchange
terms etc.
Mean field
Eigenfunctions
Interaction
8
Why relativistic?
Large spin-orbit term in nuclear physics
(magic numbers)
Success of relativistic Brueckner calculations
(Coester
line)
Weak isospin dependence of spin-orbit
(isotopic shifts)
Pseudospin symmetry (nuclear
spectra)
Relativistic saturation mechanism
Nuclear magnetism (magnetic
moments)
(moments of inertia)
Simplicity and elegance
Non-relativistic kinematics !!!
9
Covariant density functional theory
system of Dirac nucleons coupled by the exchange
mesons and the photon field through an effective
Lagrangian.
(J?,T)(0,0)
(J?,T)(1-,0)
(J?,T)(1-,1)
Rho-meson isovector field
Omega-meson short-range repulsive
Sigma-meson attractive scalar field
10
Covariant density functional theory
No sea approximation
i runs over all states in the Fermi sea
Dirac operator
11
EFFECTIVE INTERACTIONS (NL1, NL2, NL3, NL-Z2, )
model parameters meson masses m?, m?, m?,
meson-nucleon coupling constants g?, g?, g?,
nonlinear self-interactions coupling constants
g2, g3, ...
The parameters are determined from properties of
nuclear matter (symmetric and asymmetric) and
bulk properties of finite nuclei (binding
energies, charge radii, neutron radii, surface
thickeness ...)
Effective density dependence
through a non-linear potential Boguta and
Bodmer, NPA. 431, 3408 (1977)
NL1,NL3,TM1..
through density dependent coupling constants
Here, the meson-nucleon couplings
T.W.,DD-ME..
are replaced by functions depending on the
density r(r)
12
number of param.
How many parameters ?
7 parameters
symmetric nuclear matter
E/A, ?0
finite nuclei (NZ)
E/A, radii spinorbit for free

Coulomb (N?Z)

a4
K8
density dependence T0
T1
rn - rp
13
groundstates of Ni-Sn
Ground states of Ni and Sn isotopes
G.L., Vretenar, Ring, Phys. Rev. C57, 2294 (1998)
combination of the NL3 effective interaction for
the RMF Lagrangian, and the Gogny interaction
with the parameter set D1S in the pairing channel.
Neutron densities
One- and two-neutron separation energies
surface thickness
surface diffuseness ?
14
Shape coexistence in the N28 region
G.L., Vretenar, Ring, Stoitsov, Robledo, Phys.
Rev. C60, 014310 (1999)
RHB description of neutron rich N28 nuclei.
NL3D1S effective interaction.
Strong suppression of the spherical N28 shell
gap.
1f7/2 -gt fp core breaking
Shape coexistence
Ground-state quadrupole deformation
Average neutron pairing gaps
15
Neutron single-particle levels for 42Si, 44S, and
46Ar against of the deformation. The energies
in the canonical basis correspond to
qround-state RHB solutions with constrained
quadrupole deformation.
Total binding energy curves
SHAPE COEXISTENCE
Evolution of the shell structure, shell gaps and
magicity with neutron number!
16
Proton emitters I
Nuclei at the proton drip line
Vretenar, G.L., Ring, Phys.Rev.Lett. 82, 4595
(1999)
characterized by exotic ground-state decay modes
such as the direct emission of charged
particles and ? -decays with large Q-values.
Ground-state proton emitters
Self-consistent RHB calculations -gt separation
energies, quadrupole deformations, odd-proton
orbitals, spectroscopic factors
G.L., Vretenar, Ring Phys.Rev. C60, 051302 (1999)
17
Proton drip-line in the sub-Uranium region
Possible ground-state proton emitters in this
mass region?
Proton drip-line for super-heavy elements
How far is the proton-drip line from the
experimentally known superheavy nuclei?
G.L. Vretenar, Ring, PRC 59 (2004) 017301
18
Pygmy 208-Pb
Paar et al, Phys. Rev. C63, 047301 (2001)
208Pb
Exp GDR at 13.3 MeV
208Pb
Exp PYGMY centroid at 7.37 MeV
In heavier nuclei low-lying dipole states appear
that are characterized by a more distributed
structure of the RQRPA amplitude.
Among several single-particle transitions, a
single collective dipole state is found below 10
MeV and its amplitude represents a coherent
superposition of many neutron particle-hole
configurations.
19
Neutron radii
RHB/NL3
Na
20
2. MODELS WITH DENSITY-DEPENDENT MESON-NUCLEON
COUPLINGS
A. THE LAGRANGIAN
B. DENSITY DEPENDENCE OF THE COUPLINGS
the meson-nucleon couplings g?, g?, g? -gt
functions of Lorentz-scalar bilinear forms of
the nucleon operators. The simplest choice
a) functions of the vector density
b) functions of the scalar density
21
PARAMETRIZATION OF THE DENSITY DEPENDENCE
MICROSCOPIC Dirac-Brueckner calculations of
nucleon self-energies in symmetric and
asymmetric nuclear matter g?
saturation density
PHENOMENOLOGICAL
g?(r)
g?(r)
g?(r)
S.Typel and H.H.Wolter, NPA 656, 331 (1999)
Niksic, Vretenar, Finelli, Ring, PRC 66, 024306
(2002)
22
Fit DD-ME2
Nuclei used in the fit for DD-ME2
()
()
Nuclear matter
E/A-16 MeV (5), ro1,53 fm-1 (10) K 250
MeV (10), a4 33 MeV (10)
23
(No Transcript)
24
Neutron Matter
25
Nuclear Matter Properties
DD-ME2 DD-ME1 TW-99 NL3 NL3
?? (fm-3) 0.152 0.152 0.153 0.149 0.150
?/? (MeV) -16.14 -16.20 -16.25 -16.25 -16.31
K (MeV) 250.89 244.5 240.0 271.8 258.5
J (MeV) 32.3 33.1 32.5 37.9 38.3
m/m 0.572 0.578 0.556 0.60 0.595
26
Masses 900 keV
rms-deviations masses Dm 900 keV
radii Dr 0.015 fm
G.L., Niksic, Vretenar, Ring, PRC 71, 024312
(2005)
DD-ME2
27
(No Transcript)
28
SH-Elements
Superheavy Elements Qa-values
Exp Yu.Ts.Oganessian et al, PRC 69,
021601(R) (2004)
DD-ME2
29
(No Transcript)
30
IS-GMR
Isoscalar Giant Monopole IS-GMR
The ISGMR represents the essential source of
experimental information on the nuclear
incompressibility
Blaizot-concept
constraining the nuclear matter compressibility
RMF models reproduce the experimental data only
if
250 MeV K0 270 MeV
T. Niksic et al., PRC 66 (2002) 024306
31
IV-GDR
Isovector Giant Dipole IV-GDR
the IV-GDR represents one of the sources of
experimental informations on the nuclear matter
symmetry energy
constraining the nuclear matter symmetry energy
the position of IV-GDR is reproduced if
32 MeV a4 36 MeV
T. Niksic et al., PRC 66 (2002) 024306
32
(No Transcript)
33
Relativistic (Q)RPA calculations of giant
resonances
Sn isotopes DD-ME2 effective interaction Gogny
pairing
Isoscalar monopole response
34
Conclusions

• Covariant Density Functional Theory provides a
  unified description of properties for ground
  states and excited states all over the periodic
  table
• The present functionals have 7-8 parameters.
• The density dependence (DD) is crucial
• NL3 is has only DD in the T0 channel
• DD-ME1, have also DD in the T1 channel
• better neutron radii
• better neutron EOS
• better symmetry energy
• consistent description
  of GDR and GMR

35
-----Open Problems ------
Open Problems
Simpler parametrizations - point coupling
- simpler pairing Improved energy
functional - Fock terms and tensor forces
- why is the first order pion-exchange
quenched? - is vacuum polarization important
in finite nuclei?