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Constraints on Energy Density Functionals by Giant Resonances Workshop

Explore the relationship between nuclear matter properties and collective excitations through mean field models and self-consistent calculations. Investigate various parameter sets for systematic study of nuclear matter and equation of state (EOS). Understand the impact of isotopic asymmetries on energy density functionals. Study neutron stars and their composition's effect on mass limits. Analyze the neutron skin thickness and its correlations. Discuss future experiments and the significance of multipole decompositions in data analysis.

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Constraints on Energy Density Functionals by Giant Resonances Workshop

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  1. Constraints to Universal Energy Density Functionals by Giant Resonances FIRST FIDIPRO-JSPS WORKSHOP Jyvaskyla、October 25-27, 2007 H. Sagawa, University of Aizu • Introduction • Incompressibility and ISGMR • Isotope Dependence of ISGMR and symmetry term of Incompressibility • Summary

  2. Mean field: Eigenfunctions: Interaction: nuclear energy density functional Density functional theory Slater determinant density matrix Single-particle states p-h interactions Collective Excitations

  3. Theoretical Mean Field Models Skyrme HF model Gogny HF model +tensor correlations （Abe,Satula) RMF model RHF model pion-coupling, rho-tensor coupling (Meng) Many different parameter sets make possible to do systematic study of nuclear matter properties and EOS.

  4. Nuclear Matter SHF RMF

  5. Nuclear Matter EOS Supernova Explosion Isoscalar Giant Monopole Resonances Isoscalar Compressional Dipole Resonances Incompressibility K Self consistent HF+RPA calculations Self consistent RMF+RPA (TD Hatree) calculations

  6. Self-consistent HF+RPA theory with Skyrme Interaction • Direct link between nuclear matter properties and collective • excitations • 2. The coupling to the continuum is taken into account properly • by the Green’s function method. • 3. The sum rule helps to know how much is the collectivenessof obtained states. • 4. Numerical accuracy will be checked also by the sum rules.

  7. RPA Green’s Function Method Unperturbed Green’s function The inverse operator equation can be solved as where and

  8. (355MeV) (217MeV) (256MeV)

  9. Youngblood, Lui et al.,（２００２）、Gogny RPA

  10. Nuclear Matter EOS Isoscalar Monopole Giant Resonances Isoscalar Compressional Dipole Resonances Incompressibility K （G. Colo ,2004） (Lalazissis,2005) What does make this difference ?

  11. Science 298 (2002) 1592-1596

  12. Constraints to Universal Energy Density Functionals by Giant Resonances FIRST FIDIPRO-JSPS WORKSHOP Jyvaskyla、October 25-27, 2007 H. Sagawa, University of Aizu • Introduction • Incompressibility and ISGMR • Isotope Dependence of ISGMR and symmetry term of Incompressibility • Summary

  13. Isovector properties of energy density functional by extended Thomas-Fermi approximation

  14. Parameter sets of SHF and relativistic mean field (RMF) model Notation for the RMF parameter sets Notation for the Skyrme interactions

  15. Correlation among nuclear matter properties

  16. Parameter sets of SHF and relativistic mean field (RMF) model Notation for the RMF parameter sets Notation for the Skyrme interactions

  17. Correlation among nuclear matter properties

  18. Neutron Star Masses The maximum mass and radii of neutron stars largely depend on the composition of the central core. Hyperons, as the strange members of the baryon octet, are likely to exist in high density nuclear matter. The presence of hyperons, as well as of a possible K-condensate, affects the limiting neutron star mass (maximum mass). Independent of the details, Glendenning found a maximum possible mass for neutron stars of only 1.5 solar masses (nucl-th/0009082; astro-ph/0106406). Figure: Neutron stars are complex stellar objects with an interior Figure: Neutron star masses for various binary systems, measured with relativistic timing effects. The upper 5 systems consist of a radio pulsar with a neutron star as companion, the lower systems of a radio pulsar with a White Dwarf as companion. All the masses seem to cluster around the value of 1.4 solar masses. All these results seem to indicate that the presently measured masses are very close to the maximum possible mass. This could indicate that neutron stars are always formed close to the maximum mass. J.M. Lattimer and M. Prakash, Sience 304 (2004)

  19. Summary 1. The pressure and incompressibility of RMF is higher than that of SHF in general. 2. Nuclear incompressibility K is determined empirically to be K~230MeV(Skyrme,Gogny), K~250MeV(RMF). 3. Is extracted from isotope dependence of GMR of Sn 4. Then it turns out to be J=(32+/-2)MeV, L=(５0+/-１０)MeV, Ksym= -(100+/-40)MeV 5.A clear correlation between neutron skin thickness and neutron matter EOS, and volume symmetry energy. 6． Neutron skin thickness can be obtained by the sum rules of charge exchange SD and also spin monopole excitations. 7．The SD strength gives a critical information both on the neutron EOS and mean field models. 90Zr

  20. Model independent observation of neutron skin Electron scattering parity violation experiments Polarized electron beam experiment at Jefferson Lab. ---- scheduled in summer 2008 --- Sum Rule of Charge Exchange Spin Dipole Excitations

  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=1 strength up to 50 MeV excitation at around (4-5)o (n,p) L=1 strength up to 30MeV at around (4-5)o Results of MDA for 90Zr(p,n) & (n,p) at 300 MeV(K.Yako et al.,PLB 615, 193 (2005)) L=0 L=1 L=2

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

  23. Collaborators Theory: Satoshi Yoshida, Guo-Mo Zeng, Jian-Zhong Gu, Xi-Zhen Zhang Publications S. Yoshida and H.S., Phys. Rev. C69, 024318 (2004), C73,024318(2006). H.S., S. Yoshida, G.M.Zeng, J.Z. Gu, X.Z. Zhang, PRC76,024301(2007).

  24. Density Functional Theory self-consistent Mean Field Shell Model Ab Initio Three-body model Nuclear matter Theory: roadmap 126 82 r-process protons 50 rp-process 82 28 20 50 8 28 neutrons 2 20 8 2 Neutron matter

  25. superheavy nuclei proton drip line neutron stars neutron drip line Z=113 RIKEN Nuclear Landscape 126 stable nuclei 82 r-process known nuclei unknown region 50 protons proton halo p-n pairing rp-process 82 28 neutron halo, skin, di-neutrons Clustering, BCS-BEC crossover 20 50 8 28 neutrons 2 20 8 2

  26. J= Volume symmetry energy J=asym as well as the neutron matter pressure acts to increase linearly the neutron surface thickness in finite nuclei.

  27. Pigmy GDR GDR (p,p)

  28. Multipole decomposition analysis MDA 90Zr(n,p) angular dist. ω= 20 MeV 0-, 1-, 2-: inseparable DWIA DWIA inputs • NN interaction: • t-matrix by Franey & Love • optical model parameters: • Global optical potential • (Cooper et al.) • one-body transition density: • pure 1p-1h configurations • n-particle • 1g7/2, 2d5/2, 2d3/2, 1h11/2, 3s1/2 • p-hole • 1g9/2, 2p1/2, 2p3/2, 1f5/2, 1f7/2 • radial wave functions … W.S. / RPA

  29. Neutron Matter AV14+3body

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