1. GCM calculations based on covariant density functional theory
ISTANBUL-06
GCM calculations based on covariant density functional theory
Saclay, April 9, 2008
Peter Ring
Technical University Munich
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

2. Colaborators: E. Lopes (BMW) T. Niksic (Zagreb)
R. Rossignoli (La Plata)
J. Sheikh (Kashmir)
D. Vretenar (Zagreb)
E. Litvinova (GSI)
V. Tselaev (St. Petersburg)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

3. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

4. Content Relativistic density functional theory GCM calculations
Microscopic description of quantum phase transitions
Variation after projection
Particle vibrational coupling
Conclusions
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

5. Covariant density functional theory
The nuclear fields are obtained by coupling
the nucleons through the exchange of effective mesons
through an effective Lagrangian.
(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
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

6. Three relativistic models:
Density dependence
Meson exchange with non-linear meson couplings:
Boguta and Bodmer, NPA. 431, 3408 (1977)
Lalazissis, Koenig, Ring, PRC (1997)
NL1,NL3,TM1,..
Meson exchange with density dependent coupling constants:
R.Brockmann and H.Toki, PRL 68, 3408 (1992)
Lalazissis, Niksic, Vretenar, Ring, PRC 71, (2005)
DD-ME1,DD-ME2
g(ρ)
8 parameters
Point-coupling models with density dependent coupling constants:
Manakos and Mannel, Z.Phys. 330, 223 (1988)
Buervenich, Madland, Maruhn, Reinhard, PRC 65, (2002
G(ρ)
PC-F1,….
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

7. Parameterization of denstiy dependence
MICROSCOPIC: Dirac-Brueckner calculations
saturation density
g(r)
PHENOMENOLOGICAL:
g(r)
g(r)
4 parameters for density dependence
Typel and Wolter, NPA 656, 331 (1999)
Niksic, Vretenar, Finelli, Ring, PRC 66, (2002)
Lalazissis, Niksic, Vretenar, Ring, PRC 71, (05)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

8. finite range forces → point-coupling models
meson propagator in momentum space:
mσ = 500 MeV
all fits to radii → mσ=800 MeV
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

9. Point-Coupling Modelsσ ω δ ρ
J=0, T=0
J=1, T=0
J=0, T=1
J=1, T=1
Point-coupling model
Manakos and Mannel, Z.Phys. 330, 223 (1988)
Bürvenich, Madland, Maruhn, Reinhard, PRC 65, (2002)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

10. Lagrangian density for point coupling
tree-body and four-body forces
lead to density dependent coupling constants:
PC-F1
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

11. How many parameters ? number of param.
symmetric nuclear matter:
E/A, ρ0
finite nuclei (N=Z):
E/A, radii
spinorbit for free
Coulomb (N≠Z): a4 g2 g3 K∞
density dependence: T=0
T=1
rn - rp aρ
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

12. rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm
Masses: 900 keV
Lalazissis, Niksic, Vretenar, Ring, PRC 71, (2005)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

13. Pb: GMR/GDR DD-ME2 G.A. Lalazissis et al, PRC 71, 024312 (2005)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

14. Isoscalar Giant Monopole in Sn-isotopes
GMR in Sn
Isoscalar GMR in spherical nuclei → nuclear matter compression modulus Knm.
Sn isotopes:
DD-ME2 / Gogny pairing
Theory: Lalazissis et al
Exp: U. Garg, unpublished
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

15. U. Garg: Monopole-resonance and compressibility
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

16. point coupling model is fitted to DD-ME2
Symmetric nuclear matter:
point coupling model is fitted to DD-ME2
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

17. fit to nuclear matter fit to finite nuclei
Dσ[fm4] t [fm] as [MeV] t [fm] as [MeV]
set B
set C
set D
set E
DD-ME
====================
fitted Dσ = set F (Knm=251 MeV)
fitted in addition to GMR set G (Knm=230 MeV)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

18. symmetry energy: April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

19. IVGMR in finite nuclei:
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

20. Point coupling is not equivalent to finite range:
Point coupling has different surface properties:
- smaller surface energy
- larger surface thickness
- larger surface incompressibility
Conclusions
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

21. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

22. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

23. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

24. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

25. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

26. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

27. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

28. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

29. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

30. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

31. 32S: GCM: N+J projection vs. J-projection
S-32 surface
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

32. S-32 BE2 Superdef. Band in 32S: April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

33. 32S: J+N projection: RMF-SLy4-Exp
S-32 BE2
Bender, Flocard, Heenen, PRC 68, (2003)
Niksic, Vretenar, Ring, PRC 74, (2006)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

34. 32S: GCM, J-projection RMF-Gogny
S-32 BE2
Egido et al, PRC 62, (2000)
Niksic, Vretenar, Ring, PRC 74, (2006)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

35. 36Ar: GCM: N+J projection vs. J-projection
Ar-36 surface
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

36. Ar-32 wavefunctions GCM-wave functions April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

37. Ar-36 BE2 Superdef. Band in 36Ar: Conclusions: April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

38. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

39. Mg-24 spectrum Spectra in 24Mg April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

40. Mg-24 spectrum Spectra in 24Mg April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

41. Quantum phase transitions and critical symmetries
Interacting Boson Model
Casten Triangle
E(5): F. Iachello, PRL 85, (2000)
X(5): F. Iachello, PRL 87, (2001)
X(5)
152Sm
R.F. Casten, V. Zamfir, PRL , (2000)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

42. Transition U(5) → SU(3) in Ne-isotopes
R. Krücken et al, PRL 88, (2002)
R = BE2(J→J-2) / BE2(2→0)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

43. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

44. GCM: only one scale parameter: E(21)
R. Krücken et al, PRL 88, (2002)
Niksic et al PRL 99, (2007)
F. Iachello, PRL 87, (2001)
GCM: only one scale parameter: E(21)
X(5): two scale parameters: E(21), BE2(02→21)
Problem in present GCM: restricted to γ=0
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

45. Neighboring nuclei: April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

46. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

47. Projected Density Functionals and VAP:
J.Sheikh and P. R., NPA 665 (2000) 71
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

48. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

49. J.Sheikh et al. PRC 66, 044318 (2002) April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

50. Halo-formation in Ne-isotopes
pairing energies
binding energies
rms-radii
L. Lopes, PhD Thesis, TUM, 2002
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

51. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

52. Particle-vibrational coupling: energy dependent self-energy+
RPA-modes μ
mean field
pole part =
single particle strength:
Density functional theory Landau-Migdal theory
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

53. Distribution of single-particle strength in 209Bi
fragmentation in 209-Bi
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

54. Single particle spectrum
Single particle spectrum in the Pb region
meff
E. Litvinova, P.R., PRC 73, (2006)
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

55. ph-phonon amplitudes(QRPA)
Width of Giant Resonances
The full response contains energy dependent parts
coming from vibrational couplings.
ph-phonon amplitudes(QRPA)
Self energy
induced
interaction
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

56. exp
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

57. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

58. April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

59. Conclusions 1 ------- Conclusions:
Point coupling is not equivalent to finite range
- optimal point coupling set requires K=230 MeV
GCM calculations for spectra in transitional nuclei
- J+N projection is important,
- triaxial calculations so far not possible
- microscopic theory of quantum phase transitions
The admixture of 2p-1h or 2p-2h states is possible by PVC.
- this leads to fragmentation of the single particle states
- enhanced level density at the Fermi surface
- enhanced width of giant resonances
- PVC preserves the collective structure of PDR
Conclusions:
Conclusions
April 9, 2008
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods