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

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

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

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

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

Three relativistic models: Density dependence Meson exchange with non-linear meson couplings: Boguta and Bodmer, NPA. 431, 3408 (1977) Lalazissis, Koenig, Ring, PRC 55. 540 (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, 024312 (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, 44308 (2002 G(ρ) PC-F1,…. April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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, 024306 (2002) Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (05) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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

Point-Coupling Models σ 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, 044308 (2002) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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

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

rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm Masses: 900 keV Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (2005) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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

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

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

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

fit to nuclear matter fit to finite nuclei Dσ[fm4] t [fm] as [MeV] t [fm] as [MeV] -0.76 2.125 15.32 -0.78 2.157 15.57 -0.80 2.189 15.82 set B 2.015 17.925 -0.82 2.221 16.06 set C 2.069 17.856 -0.84 2.254 16.29 set D 2.126 17.780 -0.86 2.286 16.52 set E 2.184 17.717 ----------------------------------- DD-ME2 2.108 17.72 ==================== fitted Dσ = 0.8342 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

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

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

Point coupling is not equivalent to finite range: Point coupling has different surface properties: - smaller surface energy - larger surface thickness - larger surface incompressibility Conclusions 1 ------- April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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

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

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

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

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

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

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

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

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

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

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

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

32S: J+N projection: RMF-SLy4-Exp S-32 BE2 Bender, Flocard, Heenen, PRC 68, 44312 (2003) Niksic, Vretenar, Ring, PRC 74, 064309 (2006) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

32S: GCM, J-projection RMF-Gogny S-32 BE2 Egido et al, PRC 62, 05308 (2000) Niksic, Vretenar, Ring, PRC 74, 064309 (2006) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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

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

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

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

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

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

Quantum phase transitions and critical symmetries Interacting Boson Model Casten Triangle E(5): F. Iachello, PRL 85, 3580 (2000) X(5): F. Iachello, PRL 87, 52502 (2001) X(5) 152Sm R.F. Casten, V. Zamfir, PRL 85 3584, (2000) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

Transition U(5) → SU(3) in Ne-isotopes R. Krücken et al, PRL 88, 232501 (2002) R = BE2(J→J-2) / BE2(2→0) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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

GCM: only one scale parameter: E(21) R. Krücken et al, PRL 88, 232501 (2002) Niksic et al PRL 99, 92502 (2007) F. Iachello, PRL 87, 52502 (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

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

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

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

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

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

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

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

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

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

Single particle spectrum Single particle spectrum in the Pb region meff 0.76 0.92 1.0 0.71 0.85 1.0 E. Litvinova, P.R., PRC 73, 44328 (2006) April 9, 2008 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods

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

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

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

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

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