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ISTANBUL-06. GCM calculations based on covariant density functional theory. Saclay, April 9, 2008. Peter Ring. Technical University Munich. Colaborators:. E. Lopes (BMW) T. Niksic (Zagreb) R. Rossignoli (La Plata) J. Sheikh (Kashmir) D. Vretenar (Zagreb)
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ISTANBUL-06 GCM calculations based oncovariant density functional theory Saclay, April 9, 2008 Peter Ring Technical University Munich 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) Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
GCM calculations Microscopic description of quantum phase transitions Content Relativistic density functional theory Variation after projection Particle vibrational coupling Conclusions Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Rho-meson: isovector field Omega-meson: short-range repulsive Sigma-meson: attractive scalar field Covariant density functional theory The nuclear fields are obtained by coupling the nucleons through theexchange of effective mesons through an effective Lagrangian. (J,T)=(0+,0) (J,T)=(1-,0) (J,T)=(1-,1) 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, PRL68, 3408 (1992) Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (2005) g(ρ) DD-ME1,DD-ME2 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,…. Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Parameterization of denstiy dependence parameterization saturation density MICROSCOPIC: Dirac-Bruecknercalculations g(r) PHENOMENOLOGICAL: g(r) g(r) 4 parameters for density dependence Typel and Wolter, NPA656, 331 (1999) Niksic, Vretenar, Finelli, Ring, PRC66, 024306 (2002) Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (05) 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 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Point-Coupling Models Point-coupling model σ ω δ ρ J=1, T=1 J=0, T=1 J=1, T=0 J=0, T=0 Manakos and Mannel, Z.Phys.330, 223 (1988) Bürvenich, Madland, Maruhn, Reinhard, PRC 65, 044308 (2002) 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 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
g2 g3 aρ How many parameters ? 7 parameters number of param. symmetric nuclear matter: E/A, ρ0 finite nuclei (N=Z): E/A,radii spinorbit for free Coulomb (N≠Z): a4 K∞ density dependence: T=0 T=1 rn - rp 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) Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Pb: GMR/GDR DD-ME2 G.A. Lalazissis et al, PRC 71, 024312 (2005) 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 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
U. Garg: Monopole-resonance and compressibility c ≈ -1 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Symmetric nuclear matter: point coupling model is fitted to DD-ME2 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) Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
symmetry energy: Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
IVGMR in finite nuclei: Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Conclusions 1 ------- Point coupling is not equivalent to finite range: Point coupling has different surface properties: - smaller surface energy - larger surface thickness - larger surface incompressibility Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
32S:GCM: N+J projection vs. J-projection S-32 surface Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Superdef. Band in 32S: S-32 BE2 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) 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) Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
36Ar:GCM: N+J projection vs. J-projection Ar-36 surface Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Ar-32 wavefunctions GCM-wavefunctions Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Conclusions: Superdef. Band in 36Ar: Ar-36 BE2 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Spectra in 24Mg Mg-24 spectrum Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Spectra in 24Mg Mg-24 spectrum Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
X(5) 152Sm 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) R.F. Casten, V. Zamfir, PRL 85 3584, (2000) 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) Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
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 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Neighboring nuclei: Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Projected Density Functionals and VAP: J.Sheikh and P. R., NPA 665 (2000) 71 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
J.Sheikh et al. PRC 66, 044318 (2002) 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 Cross-fertilization between Shell-Model and Energy Denstiy Functional methods
