Peter Ring. ISTANBUL-06 New developments in covariant density functional theory. Saariselkä April 20, 2009

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1 ISTANBUL-06 New developments in covariant density functional theory Saariselkä April 20, 2009 Peter Ring Technical University Munich Universidad Autónoma de Madrid 1

2 Content Covariant density functionals Collective excitations in deformed nuclei - Magnetic dipole bands (tilted axis cranking) - E1-strength in relativistic QRPA - M1-strength and scissor modes Methods beyond mean field - particle vibrational coupling PVC widths of giant resonances Tensor force? Conclusions 2

3 Walecka model Nucleons are coupled by exchange of mesons through an effective Lagrangian. (J π,t)=(0 +,0) S ( r) = g σ σ( r) (J π,t)=(1 -,0) (J π,t)=(1 -,1) rr V ( r) = gωω( r) + gρτρ( r) + ea( r) Sigma-meson: attractive scalar field Omega-meson: short-range repulsive Rho-meson: isovector field 3

4 Effective density dependence: Typel, Wolter, NPA 656, 331 (1999) Niksic, Vretenar, Finelli, P.R., PRC 66, (2002): DD-ME Lalazissis, Niksic, Vretenar, Arctic FIDIPRO-EFES P.R., PRC Workshop, 78, April (2008): 20-24, 2009 DD-ME2 4

5 Point-Coupling Models σ ω δ ρ J=1, T=0 J=1, T=0 J=0, T=1 J=1, T=1 + derivative terms + density dependence: G(ρ) Manakos and Mannel, Z.Phys. 330, 223 (1988) Bürvenich, Madland, Maruhn, Reinhard, PRC 65, (2002): PC-F Niksic, Vretenar, Arctic P.R., FIDIPRO-EFES PRC 78, Workshop, (2008): April 20-24, 2009 DD-PC1 5

6 Effective pairing forces: seniority force: constant G zero range; δ-force pairing part of Gogny D1S Gonzales-Llarena et al, PLB 379, 13 (1996) Gogny equivalent separable force: Tian, Ma, P.R. PLB (2009) in print 6

7 Influence of pairing on the fission barriers: - fission barriers depend senitively on the strength of the pairing force -for δ-pairing with identical ground state gap the barrier height depends on the cut-off energy (Karatzikos et al to be published) 7

8 comparison with ab initio calculations: ab initio (Baldo et al) neutron matter DD-ME2 (Lalazissis et al) nuclear matter see talk of X. Vinas 8

9 rms-deviations: masses: Δm = 915 kev radii: Δr = fm G.A.Lalazissis et al, Phys.Rev. C71, (2005) S. Karatzikos et al. (2008) 9

10 U. Garg: Monopole-resonance and compressibility U. Garg et al, Proceedings INPC2007), Tokyo, June 3-8, FSUGold K τ (MeV) SG2 SkM* SLy4 SkM NLC SkI4 SG1 SkI3 MSkA Sa TM1 DDME2 S4 DDME1 SkX S3 S1 S6-700 NL3 TM K OO (MeV) 10

11 Content Covariant density functionals Collective excitations in deformed nuclei - Magnetic dipole bands (tilted axis cranking) - Relativistic QRPA - E1-strength for Pygmy modes - M1-strength and scissor modes Methods beyond mean field Tensor force? Conclusions 11

12 Magnetic dipole bands (vh 11/2 ) -2 (πh 11/2 ) 2 CDFT: Jing Peng et al, PRC 78, (2008) Skyrme: P. Olbratowski et al, PRL. 93, (2004) 12

13 Tilted Axis Cranking (TAC) S. Frauendorf, NPA 557, 259c (1993) (vh 11/2 ) -2 Ω (πh 11/2 ) 2 13

14 Cranked RMF-theory Jing Peng et al, PRC 78, (2008) no nuclear magnetism A. A. Pasternak, EPJA 23, 191 ('05). nuclear magnetism Coriolis-field 14

15 Comparison of full continuum RPA (non spectral) and discrete RPA in a basis (spectral) FC-F1 J.Daoutidis, P.R. (see poster) 15

16 Vibrations in deformed nuclei J T=0 T=1 K Goldstone modes Translations: Giant dipole modes: K=0 - K=1 - Rotations: K=1 + K=0 - Scissor modes: K=1 - Gauge rotations: K=0 + K=1 + 16

17 isovector-dipole response in 100 Mo Exp: Rossendorf 17

18 IV-GDR in 100 Mo IV-GDR ρ 0 + δρ(t) K=0 - K=1-18

19 pygmy modes in 100 Mo 19

20 scissor mode in 156 Gd A. Richter et al 20

21 magnetic dipole response in 154 Sm 21

22 E = 2.5 MeV E = 3.2 MeV skin core 22

23 E1-strength for very neutron-rich Sn-isotopes: PDR GDR deformation centroid energy splitting ΔE K Peña Arteaga, Arctic FIDIPRO-EFES Khan, P.R. Workshop, PRC 79, April , (2009) 23

24 Strength of the PDR in Sn isotopes: Transition densities: intrinsic densities: K=1 - K=0 - projected densities: 150 Sn 150 Sn Peña Arteaga, Khan, P.R. PRC 79, Arctic (2009) FIDIPRO-EFES Workshop, April 20-24,

25 Content Covariant density functionals Collective excitations in deformed nuclei Methods beyond mean field - particle vibrational coupling PVC widths of giant resonances Tensor force? Conclusions 25

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28 Particle-vibrational coupling: energy dependent self-energy mean field pole part μ RPA-modes = + single particle strength: + μ Density functional theory - Landau-Migdal theory 28

29 1,0 Distribution of single-particle strength in 209 Bi fragmentation in 209-Bi 1,0 0,8 209 Bi 1h9/2 0,8 209 Bi 1i13/2 Spectroscopic factor 0,6 0,4 0,2 Spectroscopic factor 0,6 0,4 0,2 0, ,0 E, MeV 0, ,0 E, MeV Spectroscopic factor 0,8 0,6 0,4 0,2 209 Bi 2f5/2 Spectroscopic factor 0,8 0,6 0,4 0,2 209 Bi 2h11/2 0, , E, MeV E, MeV 29

30 Single Single particle particle spectrum spectrum in the Pb region m eff E. Litvinova, P.R., PRC 73, (2006) 30

31 Width of Giant Resonances The full response contains energy dependent parts coming from vibrational couplings. Self energy V ( ω) = δσ( ω) δρ ph-phonon amplitudes(qrpa) induced interaction Arctic Litvinova, FIDIPRO-EFES P.R. Tselyaev, Workshop, PRC April 75, 20-24, (2007) 31

32 exp centroid energies for GDR and PDR Litvinova, P.R. Tselyaev, PRC 78, (2008) Litvinova, P.R. Tselyaev, Langanke, v[nucl-th] 32

33 S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] Dipole strength in Sn isotopes Sn RQRPA RQTBA Sn RQRPA RQTBA 130 Sn RQRPA RQTBA E [MeV] RQRPA RQTBA 116 Sn RQRPA RQTBA 120 Sn E [MeV] RQRPA RQTBA 130 Sn cross section [mb] cross section [mb] cross section [mb] Litvinova, P.R. Tselyaev, PRC 78, (2008) 33

34 Dipole strength in Sn isotopes S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] Exp Th B n B n RQRPA RQTBA 134 Sn RQRPA RQTBA 132 Sn RQRPA RQTBA 130 Sn B n Exp B n Th Exp Th E [MeV] B n B n RQRPA RQTBA 134 Sn RQRPA RQTBA 132 Sn E [MeV] RQRPA RQTBA 130 Sn cross section [mb] cross section [mb] cross section [mb] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] B n Th RQRPA RQTBA 140 Sn B n Th RQRPA RQTBA 138 Sn B n Th RQRPA RQTBA 136 Sn E [MeV] RQRPA RQTBA 140 Sn RQRPA RQTBA 138 Sn Sn E [MeV] RQRPA RQTBA cross section [mb] cross section [mb] cross section [mb] Litvinova, P.R. Tselyaev, Langanke, v[nucl-th] 34

35 Litvinova, P.R., Vretenar, PLB 647, 111 (2007) 35

36 36

37 Content Covariant density functionals Collective excitations in deformed nuclei Methods beyond mean field Tensor force? Conclusions 37

38 Facts to the tensor force: - The bare nuclear force has a strong tensor component (pion exchange) - Brueckner calculations show a reduced, but not vanisching tensor force in the nuclear medium - second order tensor is responsible for intermediate nuclear attraction (σ-meson) - all present successful mean field calculations do not need tensor explicitly for bulk properties - Usual fits to masses and radii do not like tensor - relativistic Hartree-Fock calculations with pion have tensor strength has to be reduced (density dependent) (V. Giai) 38

39 Fit to masses and radii (as DD-ME2) + c L πn no pion full pion G.A. Lalazissis, M. Serra, P.R., T. Otsuka 39

40 Further observations : - effective single particle energies in shell-model calculations show specific trends due to the tensor force, which agrees with many data (Otsuka, Schiffer, Greavy) - the same trend can be found qualitatively if one adds a the pion with an effective coupling constant in fully selfconsistent RHF calculations (Long+Giai) - particle-vibrational coupling is also important Much work is left! 40

41 G. A. Lalazissis, M. Serra, P. R., T. Otsuka: Experiment: J. P. Schiffer et al., Phys. Rev. Lett, , (2004) 41

42 Conclusions: Relativistic DFT allows to calculate excited configurations - with the same energy functional (no new parameters) - in a fully selfconsistent way (current conservation, sum rules, Goldstone modes) Conclusions cranking for rotional excitations -> magnetic rotation - QPRA for vibrations -> deformed QRPA The admixture of 2p-1h or 2p-2h states is possible by particle vibrational coupling (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 GCM calculations for spectra in transitional nuclei - J+N projection is important, - triaxial calc. in the GOA (see talk of Tamara Niksic on - microscopic theory of quantum phase transitions 42

43 Colaborators: S. Karatzikos (Thessaloniki) G. A. Lalazissis (Thessaloniki) E. Litvinova (GSI) V. Tselyaev (St. Petersburg) J. Peng (Beijing) JM. Yao (Beijing) J. Meng (Beijing) Y. Tian (Beijing) ZY. Ma (Beijing) T. Niksic (Zagreb) N. Paar (Zagreb) D. Vretenar (Zagreb) D. Peña Arteaga (Orsay) E. Khan (Orsay( Orsay) T. Otsuka (Tokyo) J. Daoutidis (Munich) 43