1. Technical University Munich
Isovector properties of covariant DFT's and their influence on static and dynamic properties of neutron distributions
ISTANBUL-06
Trento ECT*, Aug. 7, 2009
Peter Ring
Technical University Munich
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

2. Content Density dependence in the isovector channel
of covariant density functionals
Neutron skin in various models
Connection to ab-initio calculations ?
Neutron skin and collective phenomena
Conclusions
The basic goal is to find an optimal functional, which
describes the essential facts of nuclear structure
properly and to deduce from it the neutron skin
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

3. Density functional theory
Density functional theory in nuclei:
Density functional theory
Slater determinant
density matrix
Mean field:
Eigenfunctions:
Interaction:
Extensions: Pairing correlations, Covariance
Relativistic Hartree Bogoliubov (RHB)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

4. Walecka model
- the basis is an effective Lagrangian with all relativistic symmetries
- it is used in a mean field concept (Hartree-level)
- with the no-sea approximation
(J,T)=(0+,0)
(J,T)=(1-,0)
(J,T)=(1-,1)
sigma-meson:
attractive scalar field
omega-meson:
short-range repulsive
rho-meson:
isovector field
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

5. Effective density dependence:
The basic idea comes from ab initio calculations
density dependent coupling constants include Brueckner correlations
and threebody forces
non-linear meson coupling NL1,NL3,…
Manakos and Mannel, Z.Phys. 330, 223 (1988)
Bürvenich, Madland, Maruhn, Reinhard, PRC 65, (2002): PC-F1
Niksic, Vretenar, P.R., PRC 78, (2008): DD-PC1
Point-coupling models
with derivative terms: ρ σ ω
gσ(ρ) gω(ρ) gρ(ρ)
gσ(ρ) gω(ρ) gρ(ρ)
+ gradient term
Typel, Wolter, NPA 656, 331 (1999)
Niksic, Vretenar, Finelli, P.R., PRC 66, (2002): DD-ME1
Lalazissis, Niksic, Vretenar, P.R., PRC 78, (2008): DD-ME2
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009 ρ σ ω

6. Neutron skins: Na
NL3
most of the non-linear models (NL1, NL3, …) overestimate the neutron skins
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

7. 2 MeV/fm3 < p0 < 4 MeV/fm3
Symmetry energy
Symmetry energy
saturation density
empirical values:
30 MeV £ a4 £ 34 MeV
2 MeV/fm3 < p0 < 4 MeV/fm3
-200 MeV < DK0 < -50 MeV
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

8. Isovector Giant Dipole Resonance: IV-GDR
the IVGDR represents
one of the sources of
experimental informations
on the nuclear matter
symmetry energy
constraining the nuclear
matter symmetry energy
the position of IVGDR is
reproduced if
32 MeV £ a4 £ 36 MeV
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

9. Ground state properties of finite nuclei
DD-ME1
Ground state properties of finite nuclei
Binding energies, charge isotope shifts, and quadrupole
Deformations of Gd, Dy, and Er isotopes.
Charge isotope shifts in even-A
Pb isotopes.
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

10. rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm
Masses: 900 keV
Lalazissis, Niksic, Vretenar, P.R., PRC 71, (2005)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

11. Relativistic (Q)RPA calculations of giant resonances
Sn isotopes: DD-ME2 effective
interaction + Gogny pairing
Isovector dipole response
protons
neutrons
Isoscalar
monopole
response
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

12. Isoscalar Giant Monopole Resonances in Sn nuclei
R(Q)RPA analysis of
compression modes
and isovector giant
dipole resonances:
The compressibility
and symmetry energy
of nuclear matter:
Phys. Rev. C 68, (2003)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

13. U. Garg: Monopole-resonance and compressibility
U. Garg et al, Proceedings INPC2007), Tokyo, June 3-8, 2007
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

14. comparison with ab initio calculations: DD-ME2 (Lalazissis et al)
ab initio (Baldo et al)
neutron matter
DD-ME2 (Lalazissis et al)
nuclear matter
see talk of X. Vinas
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

15. Fit to ab-initio results
point coupling model is fitted to microscopic nuclear matter:
av = 16,04
av = 16.06
av = 16,08
av = 16,10
av = 16,12
av = 16,14
av = 16.16
ρsat = fm-3
m* = 0.58m
Knm = 230 MeV
DD-PC1
A. Akmal, V.R. Pandharipande, and D.G. Ravenhall, PRC. 58, (1998).
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

16. results for the neutron skin in 208Pb:
rn-rp
nonlinear meson coupling
NL fm
NL fm
density dependent meson exchange
DD-ME fm
DD-ME fm
point coupling models
PC-F fm
DD-PC fm
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

17. can we fit directly the potentials ?
Microscopic
can we fit directly the potentials ?
Y. Akaishi (KEK)
T. Otsuka (Tokyo)
S. Hirose
M. Serra†
M. Serra, T. Otsuka, Y. Akaishi, P. R., and S. Hirose, Prog.Theor.Phys. 113, 1009 (2005)
S. Hirose, M. Serra, P. R, T. Otsuka, and Y. Akaishi, PRC 75, (2007)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

18. G-Matrix representation in r-space:
Tamagaki + Takatsuka potential
various densities:
kf = 1.0 fm-1
kf = 1.4 fm-1
kf = 1.8 fm-1
the most important contributions to
nuclear binding come from
1E and 3E (tensor force)
S. Hirose, M. Serra, P. R, T. Otsuka, and Y. Akaishi, PRC 75, (2007)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

19. OME-potentials are fitted for r > 0.8 fm:
G-Matrix
OME-potential
density kf = 1.4 fm-1:
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

20. comparison with other theories other theories
density dependence
of g for constant masses
hadron field theory
(from rel. Brueckner)
DD-ME1
phenomenological
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

21. Equation of state (symmetric nuclear matter):
EOS symmetric
Masses mm(ρ) and
coupling constants gm(ρ)
for the
meson exchange potentials
G-Matrix
Gogny (GT2)
present model (adjusted to GT2)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

22. Asymmetry energy S2(ρ):
G-Matrix
present model
DD-ME1
empirical values:
30 MeV £ a4 £ 34 MeV
2 MeV/fm3 < p0 < 4 MeV/fm3
-200 MeV < DK0 < -50 MeV
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

23. Equation of state (neutron matter):
EOS neutron matter
DD-ME1
present model FP
Gogny (GT2)
G-Matrix
asymmetry energy
G-Matrix
present model
DD-ME1
no isovector property of the correlated system
has been used for the fit
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

24. Neutron skin and collective phenomena:
Relativistic QRPA with the same functionals
Soft dipole mode (pygmy resonances)
Spin-isospin modes (GT – IAR)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

25. Soft dipole modes and neutron skin
ρ(r,t) = ρ0 (r) + δρ(r,t) δρ r
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

26.
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

27. Dipole-strength in neutron-rich Sn isotopes
Th. Aumann:
Dipole-strength in neutron-rich Sn isotopes
Electromagnetic-excitation cross section
Photo-neutron cross section
stable A
PDR
GDR
Ecentr
[MeV]
sum
rule fraction
[%] Γ
124Sn -
15.3
4.8
116
130Sn
10.1
(0.7)
7.0
(3.0)
15.9
(0.5)
(1.8)
145
(19)
132Sn
9.8
4.0
(3.1)
16.1
(0.8)
4.7
(2.2)
125
(32)
radioactive
PDR
located at 10 MeV
exhausts a few % TRK sum rule
in agreement with theory
GDR
no deviation from systematics
P. Adrich et al., PRL 95 (2005)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

28. PDR strength versus a4, po
Th. Aumann:
Result (averaged 130,132Sn) :
a4 = ± MeV
po = ± 0.8 MeV/fm3
RQRPA – DD-ME
N. Paar et al. (2007)
S(r) : moderate stiffness
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

29. neutron skin deduced from pygmy strength
Rn-Rp δr
Rn – Rp :
130Sn: ± 0.04 fm
132Sn: ± 0.04 fm
LAND
Sn isotopes
A.Krasznahorkay et al.
PRL 82(1999)3216
A. Klimkiewicz, N. Paar, et al,
submitted to PRL
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

30. complex configuration and width :
th: Litvinova et al, PRC 79, (2009)
exp: Adrich et al, PRL 75, (2005)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

31. Spin-Isospin Resonances: IAR - GTR
Z,N
Z+1,N-1
spin flip s
isospin flip t
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

32. Spin-Isospin Resonances: IAR and GTR
charge-exchange excitations
proton-neutron
relativistic QRPA
π and ρ-meson exchange
generate the spin-isospin
dependent interaction terms
the Landau-Migdal zero-range
force in the spin-isospin channel
(g’0=0.55)
S=1 T=1 J = 1+
S=0 T=1 J = 0+
GAMOW-TELLER RESONANCE:
ISOBARIC ANALOG STATE:
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

33. GTR
GT-Resonances
N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, (2004)
experiment
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

34. Isobaric Analog Resonance: IAR
N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, (2004)
experiment
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

35. Neutron skin and IAR/GRT
The isotopic dependence of the energy
spacings between the GTR and IAS
direct information on the
evolution of the neutron skin
along the Sn isotopic chain
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

36. Conclusions 1 ------- Conclusions:
We study the density dependence in the isovector channel
of covariant density functional theory and discuss its
influence on:
- symmetry energy
- neutron skin
- EOS in neutron matter
Phenomenological functionals with high precision
predict for 208Pb: rn-rp = 0.20 fm
Semiphenomenological ab-initio calculations show agreement
Properties of specific collective excitations correlate with the
neutron skins:
- GDR, PDR, Spin-Isospin modes
Predictions for densities much higher than saturation density
are strongly model dependent !
Conclusions
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

37. Colaborators: G. A. Lalazissis (Thessaloniki) E. Litvinova (GSI)
V. Tselyaev (St. Petersburg)
T. Niksic (Zagreb)
N. Paar (Zagreb)
D. Vretenar (Zagreb)
S. Hirose (Tokyo)
M. Serra†
Y. Akaishi (KEK)
T. Otsuka (Tokyo)
ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009