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Spin-Isospin mode in finite nuclei and EOS in dense nuclear matter

Spin-Isospin mode in finite nuclei and EOS in dense nuclear matter. Theory Workshop “ Nuclear Bulk Properties”, MSU, Nov. 19-22,2008. 1. Skyrme energy density functionals 2. Spin, Spin-Isospin Landau parameters 3. RPA in nuclear matter and neutrino mean free path

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Spin-Isospin mode in finite nuclei and EOS in dense nuclear matter

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  1. Spin-Isospin mode in finite nuclei and EOS in dense nuclear matter Theory Workshop“Nuclear Bulk Properties”, MSU, Nov. 19-22,2008 1. Skyrme energy density functionals 2. Spin, Spin-Isospin Landau parameters 3. RPA in nuclear matter and neutrino mean free path 4. Spin-Isospin mode and tensor correlations 5. Summary and future perspectives J. Margueron, IPN Orsay, France. H. Sagawa, University of Aizu, Japan.

  2. Skyrme interaction T. H. R. Skyrme, Philos. Mag. 1, 1043 (1956)‏ D. Vautherin and D. M. Brink, PRC 5, 626 (1972)‏ Main advantages: simple to use • Widely used and sucessful to describe: • Static properties (Binding energies, Radii, ...)‏ • Dynamical properties (Collective modes, ...)‏ → Could it be applied to astrophysical objects (neutron stars, --) supernovae, ...) ?

  3. Equation of State Symmetric nuclear matter Pure neutron matter

  4. stable unstable Ferromagnetic phase diagramme Symmetric nuclear matter : Spin asymmetry density : Susceptibility : Asymmetric nuclear matter : Diag. or Instability for if : and

  5. Microscopic calculations of the ferromagnetic instabilty S. Fantoni, et al., PRL 87, 018110 (2001)‏ I. Vidana et al., PRC 65, 035804 (2002), 66, 045801 (2002)‏ I. Bombaci et al., PLB 632, 638 (2006), ... Magnetic susceptibility Results: No ferromagnetic instability On the other hand, Skyrme functional is unstable at high density or large asymmetries

  6. Stability under extreme conditions Large asymmetries, high densities, finite T, ... RPA framework: probe the fluctuations around the ground-state → local stability criterium Validity check of residual interaction →Landau parameters Matter is stable if

  7. Landau Parameters (Symm. & Neut. matter)‏ attraction ↓ Instabilities Squares:G-matrix calculation Zuo, Shen, Lombardo, PRC 67 (2003)‏ ↓ repulsion

  8. Ferromagnetic phase diagram: G & G' Symm. matter Neut. matter

  9. Landau parameters and Instabilities Stability requirements: Density : → Spin-density : → → contradiction To extend the domain of application of Skyrme interaction to large asymmetries and high densities (neutron stars, SN), How to cure the desease ?

  10. Extensionof Skyrme EDFalready considered J. W. Negele and D. Vautherin, PRC 5, 1472 (1972)‏ From density matrix expansion : • Separation of neutron and proton densities: → no consequence for spin channels • momentum- and density- dependent term: → → → Collapse of symmetric nuclear matter EoS

  11. We need another kind of correction to Skyrme energy density functionals What is really missing in the interaction ?

  12. New correction terms which may not changre good properties of rms radii and B.E. Mean field: → zero in spin-saturated nuclear systems Contribution to the Landau parameters: In symm. matter: In neutron matter: → dominant contribution at large densities (should bring repulsion)‏

  13. Adjustement of the new parameters Reproduce Landau parameters from G-matrix calculations

  14. Adjustement of the new parameters Reproduce Landau parameters from G-matrix calculations Best Fit:

  15. Adjustement of the new parameters Reproduce Landau parameters from G-matrix calculations Best fit with LNS Still differences !!! Effect of the tensor?

  16. Extension of the Skyrme interaction No influence in double magic nuclei → adjustement of the new parameters on top of existing Skyrme interactions.

  17. Applications to infinite matter and finite nuclei

  18. RPA response functions in symm. Matter (spin channels)‏ T = 1 MeV q = 0.17 fm-1 Large differences

  19.  Z0 n n neutrino mean free path in neutron stars Original Skyrme : Collapse of Extended Skyrme: RPA correlations make matter more transparent to neutrinos

  20. Static properties in spin-non-saturated nuclei: masses, radii, single particle energies , ... Collective spin modes give empirical information of G and G’ Gamow Teller G' → G' + 0.3 applications to nuclei

  21. Multipole Decomposition (MD) Analyses (p,n)/(n,p) data have been analyzed with the same MD technique (p,n) data have been re-analyzed up to 70 MeV Results (p,n) Almost L=0 for GTGR region(No Background) Fairly large L=0 (GT) strength up to 50 MeV excitation (n,p) L=0 strength up to 30MeV Results of MDA for 90Zr(p,n) & (n,p) at 300 MeVK.Yako et al.,PLB 615, 193 (2005) T. Wakasa et al.,PRC55, 2909 (1997)

  22. New empirical sum rule values +strength 20<Ex<50MeV ~30% of Ikeda sum rule was found in this energy region T. Wakasa et al.

  23. Neutron skin thickness Sum rule value ⇒ Neutron thickness e scattering & proton form factor

  24. We propose Simple extension of the Skyrme energy densiy functionals for spin channels: Replace attraction by repulsion in spin channels keeping the good properties of the original Skyrme interactions. Conserve the simplicity of the Skyrme energy density functionals Extend its domain of application for higher density and large isospin Applications to RPA response function and neutrino mean free path in proto-neutron stars (finite T, large asymmetries, high densities)‏ Landau parameter g’0 is positive and close to the empirical ones. Future applications: Gamow-Teller excitations, T=0 T=1 M1 states, Odd nuclei. Summary and Future perspectives

  25. Spin-Isospin mode Diagram Extended Skyrme Interaction+Tensor correlations Pioncondensation (Precursor effect) Gamow-TellerMode Spin-dipole mode Neutron EOS, Neutron Skin Spin-multipole mode

  26. Tensor correlations on Spin-Isospin mode

  27. 1p-1h tensor 1p-1h tensor

  28. Especially to J. Margueron & K. Hagino for fruitful Japanese-French collaboration ! Thank you !!

  29. Stability of Skyrme interaction (varying z)‏ y x J.M., J. Navarro & N. Van Giai PRC 66 014303

  30. z=10 000 Sensivity to empirical values I m*/m K0 S 0.6 16 0.7 18 210 20 0.8 250 230 J.M., J. Navarro & N. Van Giai PRC 66 014303

  31. Sensivity to empirical values II m*/m m*/m 0.6 S K0 0.7 0.8 J.M., J. Navarro & N. Van Giai PRC 66 014303

  32. Skyrme density functional

  33. Symmetry energy at high density Fully asymmetric matter is more stable at high density. Could be cured by fitting the EoS of symm. & neut. matter. Related to the Landau parameter

  34.  G0’   F0n y G0n x The standard Skyrme functionnal is unstable in some domains J. M., J. Navarro & N. Van Giai PRC 66, 014303 (2002)‏ • 10 parameters in the Skyrme interaction • - 1 : spin-orbit is fixed • 6 : empirical quantities (r0, e0, m*, K, as, esurf)‏ → 3 degrees of freedom: x=x1t1, y=x2t2, z=x3t3 • stability constraints : • sound velocity < c → 14 inequalities Result: for reasonable empirical quantities and optimized parameters, Skyrme functional is unstable beyond ~ 3 

  35. GTGR :1963 predicted by Ikeda, Fujii and Fujita • Discovered in 1975（MSU) • Systematic Studies in 1980s at IUCF (C. Gaarde, Goodman,---) • GT strength B(GT) and s(0°) of (p,n) • s(0°) ∝ B(GT) (Proportionality) • GT sum-rule • S-- S + =3(N-Z) C. Gaarde, NP A396, 127c(1983)

  36. Missing GT strength

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