Equazione di Stato ed energia di simmetria

Transcription

1 Equazione di Stato ed energia di simmetria Xavier Roca-Maza Università degli Studi di Milano e INFN, sezione di Milano Workshop Strength, Napoli. Aprile 16th 17th, 215 1

2 Table of contents: Introduction The Nuclear Many-Body Problem Nuclear Energy Density Functionals EoS: Symmetry energy The impact of the symmetry energy on nuclear and astrophyiscs observables Some examples: Neutron stars outer crust, neutron skin thickness, parity violating asymmetry, pygmy states (?), GDR, dipole polarizability,... New EDF for a better description of spin-isospin properties: SAMi (Skyrme Aizu Milano) Gamow Teller and Spin Dipole Resonaces SAMi family of systematically varied interactions Antianalog Giant Dipole Resonances Giant Quadrupole Resonances Conclusions 2

3 INTRODUCTION 3

4 The Nuclear Many-Body Problem: Nucleus: from few to more than 2 strongly interacting and self-bound fermions. Underlying interaction is not perturbative at the (low)energies of interest for the study of masses, radii, deformation, giant resonances,... Complex systems: spin, isospin, pairing, deformation,... Many-body calculations based on NN scattering data in the vacuum are not conclusive yet: different nuclear interactions in the medium are found depending on the approach EoS and (recently) few groups in the world are able to perform extensive calculations for light and medum mass nuclei Based on effective interactions, Nuclear Energy Density Functionals are successful in the description of masses, nuclear sizes, deformations, Giant Resonances,... 4

5 Nuclear Energy Density Functionals: Main types of successful EDFs for the description of masses, deformations, nuclear distributions, Giant Resonances,... Relativistic mean-field models, based on Lagrangians where effective mesons carry the interaction: L int = ΨΓ σ ( Ψ,Ψ)ΨΦ σ + ΨΓ δ ( Ψ,Ψ)τΨΦ δ ΨΓ ω ( Ψ,Ψ)γ µ ΨA (ω)µ ΨΓ ρ ( Ψ,Ψ)γ µ τψa (ρ)µ e Ψ ˆQγ µ ΨA (γ)µ Non-relativistic mean-field models, based on Hamiltonians where effective interactions are proposed and tested: VNucl eff = Vlong range attractive +V short range repulsive +V SO +V pair Fitted parameters contain (important) correlations beyond the mean-field Nuclear energy functionals are phenomenological not directly connected to any NN (or NNN) interaction 5

6 The Nuclear Equation of State: Infinite System 3 2 neutron matter e(ρ,δ=1) e ( MeV ) 1 Saturation (.16 fm 3, 16. MeV) S(ρ)~ -1 e(ρ,δ=) symmetric matter ρ ( fm 3 ) E A (ρ,β) = E A (ρ,β = ) + S(ρ)β2 +O(β 4 ) Nuclear Matter [ β = ρ ] n ρ p ρ 6

7 The Nuclear Equation of State: Infinite System 3 2 neutron matter e(ρ,δ=1) e ( MeV ) 1 Saturation (.16 fm 3, 16. MeV) S(ρ)~ -1 e(ρ,δ=) symmetric matter ρ ( fm 3 ) E A (ρ,β) = E A (ρ,β = ) + S(ρ)β2 +O(β 4 ) Nuclear Matter Symmetric Matter [ β = ρ ] n ρ p ρ 7

8 The Nuclear Equation of State: Infinite System 3 2 neutron matter e(ρ,δ=1) e ( MeV ) 1 Saturation (.16 fm 3, 16. MeV) S(ρ)~ -1 e(ρ,δ=) symmetric matter ρ ( fm 3 ) E A (ρ,β) = E A (ρ,β = ) + S(ρ)β2 +O(β 4 ) Nuclear Matter Symmetric Matter Symmetry energy [ β = ρ ] n ρ p ρ 8

9 The Nuclear Equation of State: Infinite System 3 2 neutron matter e(ρ,δ=1) e ( MeV ) 1 Saturation (.16 fm 3, 16. MeV) S(ρ)~ -1 e(ρ,δ=) symmetric matter ρ ( fm 3 ) E A (ρ,β) = E A (ρ,β = ) + S(ρ)β2 +O(β 4 ) = E (J+Lx+ A (ρ,β = 1 ) )+β2 2 K symx 2 +O(x 3 ) [ β = ρ n ρ p ρ ; x = ρ ρ ] 3ρ 9

10 The Nuclear Equation of State: Infinite System 3 2 neutron matter e(ρ,δ=1) e ( MeV ) 1 Saturation (.16 fm 3, 16. MeV) S(ρ)~ -1 e(ρ,δ=) symmetric matter ρ ( fm 3 ) E A (ρ,β) = E (ρ,β = )+β2 A ( J + L x+ 1 ) 2 K sym x 2 +O(x 3 ) S(ρ ) = J d dρ S(ρ) = L = P ρ 3ρ [ ρ 2 β = ρ n ρ p ρ d 2 dρ 2S(ρ) = K sym ρ 9ρ 2 ; x = ρ ρ ] 3ρ 1

11 The Nuclear Equation of State: Infinite System 3 2 neutron matter e(ρ,δ=1) e ( MeV ) 1 Saturation (.16 fm 3, 16. MeV) S(ρ)~ -1 e(ρ,δ=) symmetric matter ρ ( fm 3 ) E A (ρ,β) = E (ρ,β = )+β2 A ( J + L x+ 1 ) 2 K sym x 2 +O(x 3 ) The uncertainties on S(ρ) impacts on many nuclear d S(ρ ) = J dρ S(ρ) = L = P d 2 physics and astrophysics observables. ρ 3ρ ρ 2 dρ 2S(ρ) = K sym ρ 9ρ 2 [ ρ n ρ p ρ ρ ] 11

12 The impact of the symmetry energy on nuclear and astrophyiscs observables 12

13 Relevance of the neutron star crust on the star evolution and dynamics (brief motivation) The crust separates neutron star interior from the photosphere (X-ray radiation). The thermal conductivity of the crust is relevant for determining the relation between observed X-ray flux and the temperature of the core. Electrical resistivity of the crust might be important for the evolution of neutron star magnetic field. Conductivity and resistivity depend on the structure and composition of the crust Neutrino emission from the crust may significantly contribute to total neutrino losses from stellar interior (in some cooling stages). A crystal lattice (solid crust) is needed for modelling pulsar glitches, enables the excitation of toroidal modes of oscillations, can suffer elastic stresses... Mergers (binary systems that merge) may enrich the interstellar medium with heavy elements, created by a rapid neutron-capture process. In accreting neutron stars, instabilities in the fusion light elements might be responsible for the phenomenon of X-ray bursts Source: Pawel Haensel 21 13

14 The symmetry energy and the structure and composition of a neutron star outer crust span 7 orders of magnitude in denisty (from ionization 1 4 g/cm to the neutron drip 1 11 g/cm) it is organized into a Coulomb lattice of neutron-rich nuclei (ions) embedded in a relativistic uniform electron gas T 1 6 K.1 kev one can treat nuclei and electrons at T = K At the lowest densities, the electronic contribution is negligible so the Coulomb lattice is populated by 56 Fe nuclei. As the density increases, the electronic contribution becomes important, it is energetically advantageous to lower its electron fraction by e +(N,Z) (N+1,Z 1)+ν e and therefore Z with constant (approx) number of N As the density continues to increase, penalty energy from the symmetry energy due to the neutron excess changes the composition to a different N plateau Z A Z A p Fe 8a sym where(a,z ) = 56 Fe 26 The Coulomb lattice is made of more and more neutron-rich nuclei until the critical neutron-drip density is reached (µ drip = m n). [M(N,Z)+m n < M(N+1,Z)] Composition Composition FSUGold Protons Neutrons Ni NL3 N=82 N=32 Fe Sr Sr Kr Kr N=5 N= Se Se ρ(1 11 g/cm 3 ) Sn N=82 Ge Zn Ni Cd Pd Ru Mo Zr Sr Mo Kr Zr SrKr Physical Review C 78, 2587 (28) The faster the symmetry energy increases with density (L ), the more exotic the composition of the outer crust. 14

15 The symmetry energy and the neutron skin in nuclei r np (fm) Linear Fit, r =.979 Mean Field SkM* DD-ME1 DD-ME2 FSUGold Ska DD-PC1 G2 Sk-T4 NL3.s25 PK1.s24 Sk-Rs RHF-PKO3 SkI2 RHF-PKA1 SV Sk-Gs NL3* NL3 PK1 NL-SV2 TM1 SkI5 G1 NL-RA1 PC-F1 NL-SH PC-PK1 NL2 NL1.15 HFB-8 MSk7 v9 SkP SkX Sk-T6 HFB-17 SGII D1N SLy5 SLy4 SkMP SkSM* SIV MSL MSkA BCP D1S L (MeV) Physical Review Letters 16, (211) The faster the symmetry energy increases with density, the largest the size of the neutron skin in (heavy) nuclei. r np 1 IR 12 J L [Exp. from strongly interacting probes:.18±.3 fm (Physical Review C (212))]. 15

16 The symmetry energy and parity violating electron scattering (A pv: relative difference between the elastic cross sections of right- and left-handed electrons) 1 7 A pv 7,4 7,2 7, 6,8 MSk7 D1S D1N SGII Sk-T6 SkP HFB-17 SkX SLy4 SLy5 SkM* BCP MSkA MSL DD-ME2 SIV SkMP SkSM* DD-ME1 DD-PC1 RHF-PKO3 FSUGold Zenihiro Ska Sk-Rs RHF-PKA1 Sk-Gs SV PK1.s24 SkI2 HFB-8 v9 Tarbert Hoffmann Klos Linear Fit, r =.995 Mean Field From strong probes Sk-T4 NL3.s25 PC-PK1 G2 NL-SH NL-SV2 TM1, NL-RA1 NL3 SkI5 PC-F1 PK1 G1 NL3*,1,15,2,25,3 r np (fm) Physical Review Letters 16, (211) NL2 NL1 Electrons interact by exchanging a γ (couples to p) or a Z boson (couples to n) Ultra-relativistic electrons, depending on their helicity (±), will interact with the nucleus seeing a slightly different potential: Coulomb ± Weak Apv dσ+/dω dσ /dω dσ Weak +/dω+dσ /dω Coulomb Input for the calculation are the ρp and ρ n (main uncertainty) and nucleon form factors for the e-m and the weak neutral current. In PWBA for small momentum transfer: A pv G Fq 2 4 2πα ( 1 q2 r 2 p 1/2 ) r np 3F p(q) (Calculation at a fixed q equal to PREx) The largest the size of the neutron distribution in nuclei, the smaller the elastic electron parity violating asymmetry. [Exp. from ew probes:.32±.175 fm (Physical Review C 85, 3251 (212))]. 16

17 Isovector Giant Resonances In isovector giant resonances neutrons and protons oscillate out of phase Isovector resonances will depend on oscillations of the density ρ iv ρ n ρ p S(ρ) will drive such oscillations The excitation energy (E x ) within a Harmonic Oscillator approach is expected to depend on the symmetry energy: 1 d ω = 2 U m dx 2 δ k E x 2 e δβ 2 S(ρ) where β = (ρ n ρ p )/(ρ n +ρ p ) σγ abs The dipole polarizability (α Energy 2 IEWSR) measures the tendency of the nuclear charge distribution to be distorted, that is, from a macroscopic point of view α electric dipole moment external electric field 17

18 The symmetry energy and the Giant Dipole Resonance (E x f(.1) S(.1fm 3 ) ) 6.4 f(.1)={s(.1)(1+k}} 1/2 [MeV 1/2 ] E -1 [MeV] Physical Review C 77, 6134 (28) The larger the symmetry energy at an average density of a finite heavy nucleus, the larger the excitation energy of the Giant Dipole Resonance (GDR). 18

19 The symmetry energy and the Pygmy Dipole Resonance (Pygmy: low-energy excited state appearing in the dipole response of N Znuclei) Physical Review C 81, 4131 (21) The faster the symmetry energy increases with density, the larger is the energy (E) times the probability (P) of exciting the Pygmy state larger the Energy Weighted Sum Rule (EWSR) E P. WARNING: we lack of a clear understanding of the physical reason for this correlation 19

20 Dipole polarizability and the symmetry energy 1 2 α D J (MeV fm 3 ) r=.97 FSU NL3 DD-ME Skyrme SV SAMi TF (fm) r np Physical Review C (213) Macroscopic model: Using the dielectric theorem: m 1 moment can be computed from the expectation value of the Hamiltonian in the constrained (D dipole operator) ground state H = H+λD Assuming the Droplet Model (heavy nucleus): α D α bulk D α bulk D πe2 54 [ A r 2 J L J α exp L D αbulk D α bulk 5J D ] where (Migdal first derived) By using the Droplet Model [ one can also find: ] α D J πe2 54 A r r np r coul np r surf np 2 r 2 1/2 (I I C ) For a fixed value of the symmetry energy at saturation, the faster the symmetry energy increases with density, the larger the dipole polarizability. 2

21 The symmetry energy and the Gamow-Teller Resonance (GT transitions change spin and isospin of the initial quantum state and favors n ) Spin orbit splittings around the Fermi surface Proton and neutron single particle potentials V sym 1g 7/2 1g 9/2 9 Zr 1g 9/2 Gamow-Teller transitions determine: weak interaction rates essential in core-collapse dynamics of massive stars in neutron-rich environment, neutrino-induced nucleosynthesis studies of double-β decay useful in the calibration of detectors used to measure neutrinos protons neutrons Physical Review C (212) 21

22 New EDF for a better description of spin-isospin properties: SAMi 22

23 Motivation: Gamow Teller Resonance I Neither the strength nor the E x properly described in HF+RPA SGII a earliest attempt to give a quantitative description of the GTR SkO b accurate in ground state finite nuclear properties and improves the GTR Relativistic MF and Relativistic HF (PKO1 c ) calculations are also available R GT [MeV 1 ] R GT [MeV 1 ] R GT [MeV 1 ] Zr Exp. x 3 PRC 55, 299 (1997) PRC 64, 6732 (21) 28 Pb RHF-PKO1 Exp. PRC 85, 6466 (212) SkO SGII 48 Ca Exp. x 3 PRL 13, 1253 (29) SLy E x [MeV] a N. Giai and H. Sagawa, Phys. Lett. B 16, 379 (1981), b P.-G. Reinhard et al., Phys. Rev. C 6, (1999), c H. Liang, N. Van Giai, and J. Meng, Phys. Rev. Lett. 11, (28), SLy5 E. Chabanat et al., Nucl. Phys. A 635, 231 (1998); E. Chabanat et al., ibid. 643, 441 (1998) 23

24 Motivation: Which gs properties are important for describing the E GTR x? A recent study a on the GTR and the spin-isospin Landau-Migdal parameter G using several Skyrme sets, concluded that G is not the only important quantity in determining the excitation energy of the GTR in nuclei spin-orbit splittings also influences the GTR Empirical indications b suggest that G > G > Not a very common feature within available Skyrme forces c a M. Bender, J. Dobaczewski, J. Engel, and W. Nazarewicz, Phys. Rev. C 65, (22); b T. Wakasa, M. Ichimura, and H. Sakai, Phys. Rev. C 72, 6733 (25); T. Suzuki and H. Sakai, Phys. Lett. B 455, 25 (1999), c Li-Gang Cao, G. Colo, and H. Sagawa, Phys. Rev. C 81, 4432 (21) 24

25 Why spin-orbit splittings are important? E 1 x ǫ π1g7/2 ǫ ν1g9/2 +ǫ 1 ph E 2 x ǫ π1g9/2 ǫ ν1g9/2 +ǫ 2 ph E x ǫ π1g + ǫ ph 1g 7/2 1g 9/2 9 Zr 1g 9/2 protons neutrons Schematic picture of single-particle transitions involved in the Gamow Teller Resonance of 9 Zr. Transitions excited by στ operator. 25

26 Skyrme Model Hamiltonian a Includes central tensor terms (J 2 terms) due to the coupling of tensor and spin and gradients terms and two spin-orbit parameters (same as SkO and some SkI forces) H = K+H +H 3 +H eff +H fin +H SO +H sg +H Coul K = h 2 τ/2m H = (1/4)t [(2+x )ρ 2 (2x +1)(ρ 2 n +ρ 2 p)] H 3 = (1/24)t 3 ρ α [(2+x 3 )ρ 2 (2x 3 +1)(ρ 2 n +ρ 2 p)] H eff = (1/8)[t 1 (2+x 1 )+t 2 (2+x 2 )]τρ +(1/8)[t 2 (2x 2 +1) t 1 (2x 1 +1)](τ n ρ n +τ p ρ p ) H fin = (1/32)[3t 1 (2+x 1 ) t 2 (2+x 2 )]( ρ) 2 (1/32)[3t 1 (2x 1 +1)+t 2 (2x 2 +1)][( ρ n ) 2 +( ρ p ) 2 ] H SO = (1/2)W J ρ+(1/2)w (J n ρ n + J p ρ p ) H sg = (1/16)(t 1 x 1 +t 2 x 2 )J 2 +(1/16)(t 1 t 2 )(J n 2 + J p 2 ) a E. Chabanat et al., Nucl. Phys. A 635, 231 (1998); E. Chabanat et al., ibid. 643, 441 (1998) 26

27 Fitting Protocol χ 2 definition: χ 2 = 1 N data (O theo. i N data i O data i ) 2 ( O data i ) 2 Landau-Migdal parameters in infinite nuclear matter G and G fixed to.15 and.35, respectively, at ρ. Table: Data and pseudo-data O i, adopted errors for the fit O i and selected finite nuclei and EoS. O i O i B 1. MeV 4,48 Ca, 9 Zr, 132 Sn and 28 Pb r c.1 fm 4,48 Ca, 9 Zr and 28 Pb E SO.4 O i π1g in 9 Zr and π2f in 28 Pb e n (ρ).2 O i R. B. Wiringa et al., PRC 38, 11 (1988) 27

28 Skyrme Aizu Milano interaction: SAMi Parameter set and nuclear matter properties: Table: SAMi parameter set and saturation properties with the estimated standard deviations inside parenthesis value(σ) value(σ) t (75) MeV fm 3 ρ.159(1) fm 3 t (1.4) MeV fm 5 e 15.93(9) MeV t (1.) MeV fm 5 m IS.6752(3) t (7.6) MeV fm 3+3α m IV.664(13) x.32(16) J 28(1) MeV x 1.532(7) L 44(7) MeV x 2.14(15) K 245(1) MeV x 3.688(3) G.15 (fixed) W 137(11) G.35 (fixed) W 42(22) α.25614(37) 28

29 Results Equation of State: SAMi vs ab initio calculations e(ρ) ( MeV ) Variational-Wiringa 1988 BHF--Vidana 212 BHF--Li 28 BHF--Baldo 24 SLy5 SAMi ρ =.152 fm 3 E / A = MeV K = MeV J = MeV L = MeV K τ = MeV ρ ( fm 3 ) Figure: Neutron and symmetric matter EoS as predicted by the HF SAMi (dashed line) and SLy5 (solid line) interactions and by the benchmark microscopic calculations of R. B. Wiringa et al., PRC 38, 11 (1988) (circles). State-of-the-art BHF calculations are shown by diamonds I. Vidaña, private communication, triangles Z. H. Li et al., Phys. Rev. C 77, (28) and squares M. Baldo et al., Nucl. Phys. A 736, 241 (24). 29

30 Results Finite Nulcei: spherical double-magic nuclei 1x(O theo. O exp. ) / O exp Mass Number O 4Ca Ca Ni Ca 9 Zr Sn Pb 16 O 4 Ca 1 Sn 56 Ni 48 Ca 48 1g 16 4 O Ca Ca Sn Ni 1 1p 1d 1d Sn 1h 1f 1g 9 Zr 28 Pb 9 Zr 28 Pb Mass Number 2f N=Z Fitted data Prediction Binding Energies Charge Radii Spin Orbit Splittings Figure: Finite nuclei properties as predicted by the HF SAMi (black circles) and some predictions (blue circles) for spherical double-magic nuclei. Experimental data taken from Refs. G. Audi et al., NPA 729, 337 (23), I. Angeli, ADNDT 87, 185 (24), M. Zalewski et al., PRC 77, (28) 3

31 Results Giant Monopole and Dipole Resonances in 28 Pb 1 2 R ISGMR [fm 4 MeV 1 ] SLy5 SAMi Exp. 28 Pb SLy5 SAMi Exp. 28 Pb R IVGDR [fm 2 MeV 1 ] E x [MeV] E x [MeV] Figure: Strength function at the relevant excitation energies in 28 Pb as predicted by SLy5 and the SAMi interaction for GMR and GDR. A Lorentzian smearing parameter equal to 1 MeV is used. Experimental data for the centroid energies are also shown: E c(gmr) = 14.24±.11 MeV [D. H. Youngblood, et al., Phys. Rev. Lett. 82, 691 (1999)] and E c(gdr) = 13.25±.1 MeV [N. Ryezayeva et al., Phys. Rev. Lett. 89, (22)]. 31

32 Results Gamow Teller Resonance in 48 Ca, 9 Zr and 28 Pb Operator: A σ(i)τ ± (i) i=1 R GT [MeV 1 ] SkO SGII SAMi 48 Ca Exp. x 3 PRL 13, 1253 (29) Figure:Gamow Teller strength distributions in 48 Ca (upper panel), 9 Zr (middle panel) and 28 Pb (lower panel) as measured in the experiment [T. Wakasa et al., Phys. Rev. C 55, 299 (1997), K. Yako et al., Phys. Rev. R GT [MeV 1 ] Zr Exp. x 3 PRC 55, 299 (1997) PRC 64, 6732 (21) SLy5 Lett. 13, 1253 (29), A. Krasznaborkay et al., Phys. Rev. C 64, 6732 (21), H. Akimune et al., Phys. Rev. C 52, 64 (1995) and T. Wakasa et al., Phys. Rev. C 85, 6466 (212)] and predicted by SLy5, SkO, SGII and R GT [MeV 1 ] Pb RHF-PKO1 Exp. PRC 85, 6466 (212) SAMi forces E x [MeV] 32

33 Results Spin Dipole Resonance: M τ ± r L [Y L (ˆr) σ] JM R SD - [fm 2 MeV 1 ] R SD SAMi 9 Zr J π = J π = 1 J π = 2 Total Exp E x [MeV] 5 6 Figure: Spin Dipole strength distributions in 9 Zr as a function of the excitation energy E x in the τ channel (upper panel) and τ + channel (lower panel) measured in the experiment [K. Yako et al., Phys. Rev. C 74, 5133(R) (26)] and predicted by SAMi. Multipole decomposition is also shown. A Lorentzian smearing parameter equal to 2 MeV is used. R SD - [fm 2 MeV 1 ] SAMi Total 28 Pb Exp J π = J π = 1 J π = E x [MeV] Figure: SDR strength distributions for 28 Pb in the τ channel from experiment [T. Wakasa et al., Phys. Rev. C 85, 6466 (212)] and SAMi calculations. Total and multipole decomposition of the SDR strength are shown: total (upper panel), J π = (middle-upper panel), J π = 1 (middle-lower panel) and J π = 2 (lower panel). A Lorentzian smearing parameter equal to 2 MeV is used. 33

34 SAMi family of systematically varied interactions 34

35 SAMi family of systematically varied interactions After an optimal model is found. The systematic variation of a quantity, fixing it to a non-optimal value (but close) and re-fitting the model for preserving its accuracy, is a technique to isolate (or better understand) the correlations predicted by the choosen model. We have produced three SAMi families using the fitting protocol previously described... SAMi-J: we fix the values of the K, m to the SAMi values, change J in steps of 1 MeV around the optimal SAMi value refitting at each step. SAMi-m: we fix the values of the K, J and L to the SAMi values, change m in steps of.5m around the optimal SAMi value refitting at each step. SAMi-K: we fix the values of the m, J and L to the SAMi values, change K in steps of 5 MeV around the optimal SAMi value refitting at each step. 35

36 Results: IVGQR Within the Quantum Harmonic Oscillator approach E IV x = 2 hω 1+ 5 h 2 V sym r 2 4 2m ( hω ) 2 r 4 and EDF calculations, one can deduce V sym 8(S(ρ A ) S kin (ρ )) S kin (ρ ) ε F /3 and the expression one finds depend on well known quantities from the theory and observable GQR energies. S(ρ A ) = ε F 3 { A 2/3 8ε 2 F B(E2;IV) (1 3 fm 4 MeV -1 ) E (MeV) [ ( ) 2 ( E IV x 2 E IS x ) ] } 2 +1 S(ρ =.1 fm 3 for 28 Pb) = 23.3±.6 MeV 36

37 Results: IGQR IS E x (MeV) m*/m Weighted Average r =.9998 SAMi-m85 SAMi-m8 SAMi-m75 SAMi-J27 SAMi-m65 SAMi-J28 SAMi-J29 SAMi-J3 SAMi-J31 SAMi-m (m/m*) 1/2 r np r surf np r 2 1/2 = 2 3 (I I C) { r np (fm).3.25 DDMEe.2 SAMi-J31.15 DDMEd DDMEc SAMi-J3 SAMi-J29 DDMEb Exp. DDMEa SAMi-J28 SAMi-J IV 2 IS 2 [(E x ) 2(Ex ) ] / J (MeV) I C 1 ε F 3J 3 A2/3 7I I C 24ε F r np.14±.3 fm [( E IV x ) 2 2 ( E IS x ) 2 J ]} 37

38 Results: AGDR 1 -,T -1 -,1 -,2 - IVSGDR,T ,T -1 +,T AGDR GT IAS T Z =T -1 Daughter nucleus L=1 L=1, S=1 S=1 strong (p,n) E1 M1 Target nucleus 1 -,T 1 +,T T Z =T +,T E AGDR -E IAS (MeV) Exp. Data from Ref. [56] Exp. Data from Ref. [53] R n -R p (fm) AGDR ( J π = 1 with L = 1 and S = ) is the T 1 component of the charge-exchange of the GDR. 5 J E AGDR E IAS 5 3 I 1+γ α H Z hc m r 2 1/2 [ ( 1 ε F 3J ) I 3 2 ( Rnp R surf ) ] np r 2 1/2 3 7 I C E AGDR E IAS ε (E E IVGDR ε) magdr C m IVGDR r np.21±.1 fm 38

39 CONCLUSIONS 39

40 Conclusions: EoS around saturation The isovector channel of the nuclear effective interaction is not well constrained by current fits of modern EDFs. Many observables available in current laboratories are sensitive to the symmetry energy. Problems: accuracy and model dependent analysis. Systsematic experiments may help. Exotic nuclei more sensitive to the isovector properties (due to larger neutron excess). Problems: more difficult to measure, accuracy and model dependent analysis. Systematic experiments may help. 4

41 Conclusions: SAMi we have successfully determined a new Skyrme energy density functional which accounts for the most relevant quantities in order to improve the description of charge-exchange nuclear resonances: the hierarchy and positive values of the spin and spin-isospin Landau-Migdal parameters G and G the proton spin-orbit splittings of different high angular momenta single-particle levels the GTR in 48 Ca and the GTR, IAR, and SDR in 9 Zr and 28 Pb are predicted with good accuracy by SAMi SAMi does not deteriorate the description of other nuclear observables applicability in nuclear physics and astrophysics Varied interactions may help in understanding underlying correlations. Problem: the fitting protocol may influence conclusions. Macroscopic models may guide and systematics on teoretical microscopic calculations help. 41

42 Co-workers: G. Colò, P. F. Bortignon and M. Brenna (U. Milan, Italy) M. Centelles and X. Viñas (U. Barcelona, Spain) N. Paar and D. Vretenar (U. Zagreb, Croatia) B. K. Agrawal (SINP, Kolkata, India) W. Nazarewicz (U. Tennessee & ORNL, USA) J. Piekarewicz (Florida State University, USA) P.-G. Reinhard (Universität Erlangen-Nürnberg, Germany) L. Cao (Electric Power U., ITP-CAS and NLHIA, China) H. Sagawa (Aizu U. and RIKEN, Japan) 42

43 Thank you for your attention! 43

44 Available constraints on L Chiral Lagrangian and Quantum Montecarlo Neutron-Star Observations p & α scattering ch-exch excitations Antiprotonic Atoms Nuclear Model Fit Heavy Ion Collisions Giant Resonancies N A scattering Charge Ex. Reac. Energy Levels BHF PVES Neutron Skins Sn Neutron Skins PDR Masses Neutron Skins Masses Masses n p Emission Ratios Isospin Diffusion GDR PDR Optical Potentials 1% acc. Neutron Matter Mass-Radius Bare N N Potential (arb. cent.) PREX L (MeV) AIP Conference Proceedings 1491, 11 (212) H. Kebeler et al. PRL15 (21) and s. Gandolfi et al. PRC85 (212) 3281 (R) A. W. Steiner et al. Astrophys. J. 722 (21) 33 Lie-Wen Chen et al. PRC 82 (21) Centelles et al. PRL 12 (29) Warda et al. PRC 8 (29) Kortelainen et al. PRC 82 (21) Danielewicz NPA 727 (23) 233 Myers et al. PRC 57 (1998) 32 Famiano et al. PRL 97 (26) 5271 B. Tsang et al. PRL 13 (29) Trippa et al. PRC 77 (28) 6134(R) Klimkiewicz et al. PRC 76 (27) 5163(R) Carbone et al. PRC 81 (21) 4131(R) Xu et al. PRC 82 (21) Vidaña et al. PRC 8 (29) 4586 X. Roca-Maza et. al. PRL (211) PREx Collab. et. al. PRL (212) 44

45 Motivation: Gamow Teller Resonance II: quenching of the strength Experimentally, the GTR exhausts 6 7% of the Ikeda sum rule: [R GT (E) R GT +(E)]dE = 3(N Z) To explain the problem, two possibilities that go beyond RPA correlations have been drawn: the effects of the second-order configuration mixing: 2p-2h correlations within the quark model, a n(p) can become a p(n) or a + ( ++ ) under the action of the GT operator and since there is no Pauli blocking for h excitations it may contribute to the GTR. The experimental analysis of 9 Zr quenching ( 2/3) has to be mainly attributed to 2p-2h coupling and not to isobar effects much smaller [T. Wakasa et. al., Phys. Rev. C 55, 299 (1997)]. E x GTR in nuclei mainly in the region of several tens of MeV and the h states are hundreds of MeV above the GT hard to excite the in the nuclear medium. 45