1. Lectures in Milano University Hiroyuki Sagawa, Univeristy of Aizu March 6,12,13, 2008 1. Pairing correlations in Nuclei 2. Giant Resonances and Nuclear Equation of States 3. Exotic nuclei

2. Giant Resonances and Nuclear Equation of States Milano ， Italy, March 12, 2008 H. Sagawa, University of Aizu 1.Introduction 2.Incompressibility and ISGMR 3.Neutron Matter EOS and Neutron Skin Thickness 4.Isotope Dependence of ISGMR and symmetry term of Incompressibility 5.Summary ---nuclear structure from laboratory to stars----

3. IS mode IV(Isospin) mode np Spin mode Spin-Isospin mode p n Various excitation mode of finite nucleus (spin ｘ isospin x multipolarity)

4. IS monopole mode (compression mode)

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

6. Theoretical Mean Field Models Skyrme HF model Gogny HF model +tensor correlations RMF model RHF model Many different parameter sets make possible to do systematic study of nuclear matter properties. +pion-coupling, rho-tensor coupling

7. Skyrme Hartree Fock (SHF) model

9. Physical properties of the infinite nuclear matter by the parameters of Skyrme interaction

10. Lagrangian of RMF

13. 1SI2SIII3SIV 4SVI5Skya6SkM 7SkM*8SLy49MSkA 10SkI311SkI412SkX 13SGII Notation for the Skyrme interactions 14NL315NLC 16NLSH17TM1 18TM219DD-ME1 20DD-ME2 Notation for the RMF parameter sets Parameter sets of SHF and relativistic mean field (RMF) model

14. SHF RMF Nuclear Matter

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

16. Self-consistent HF+RPA theory with Skyrme Interaction 1.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 collectiveness of obtained states. 4. Numerical accuracy will be checked also by the sum rules.

17. Tamm-Dancoff Approximation(TDA) Random Phase Approximation(RPA) p-h phonon operator RPA equation Fermi Energy

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

19. IS monopole

20. (355MeV) (217MeV) (256MeV)

21. K=217MeV for SkM* K=256MeV for SGI K=355MeV for SIII

22. (RPA)

23. Youngblood, Lui et al., （２００２） ( Gogny interaction)

24. What can we learn about neutron EOS from nuclear physics? Nuclear Matter EOS Incompressibility K Isoscalar Monopole Giant Resonances Isoscalar Compressional Dipole Resonances Neutron surface thicknessPressure of neutron EOS Size ~10fm Neutron star ~10km size difference ~ （ G. Colo,2004 ） (Lalazissis,2005)

25. H. Sagawa, University of Aizu 1.Introduction 2.Incompressibility and ISGMR 3.Neutron Matter EOS and Neutron Skin Thickness 4.Isotope Dependence of ISGMR and symmetry term of Incompressibility 5.Summary ---nuclear structure from laboratory to stars---- Giant Resonances and Nuclear Equation of States Milano ， Italy, March 12, 2008

26. Lake Inawashiro Mt. Bandai UoA

27. 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)

28. AV14+3body Neutron Matter

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

32. 208 Pb analysis R n – R p = 0.18 ± 0.035 fm ∑B pdr (E1)=1.98 e 2 fm 2 from N.Ryezayeva et al., PRL 89(2002)272501 ∑B gdr (E1)=60.8 e 2 fm 2 from A.Veyssiere et al.,NPA 159(1970)561 RQRPA- N.Paar LAND C.Satlos et al. NPA 719(2003)304 A.Krasznahorkay et al. NPA 567(1994)521 C.J.Batty et al. Adv.Nucl.Phys. (1989)1 B.C. Clark et al. PRC 67(2003)044306

33. GDR (p,p) Pigmy GDR

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

35. Polarized electron scattering (Jafferson laboratory) More precise (p,p’) experiments (RCNP) Future experiments

37. Multipole decomposition analysis 0 -, 1 -, 2 - : inseparable 90 Zr(n,p) angular dist. ω= 20 MeV 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 1g 7/2, 2d 5/2, 2d 3/2, 1h 11/2, 3s 1/2 p-hole 1g 9/2, 2p 1/2, 2p 3/2, 1f 5/2, 1f 7/2 radial wave functions … W.S. / RPA MDA DWIA DWIA inputs

38. Results of MDA for 90 Zr(p,n) & (n,p) at 300 MeV (K.Yako et al.,PLB 615, 193 (2005)) 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 L=0 L=1 L=2

43. Neutron skin thickness e scattering & proton form factor Neutron thickness Sum rule value ⇒ methodnucleus(fm)Ref. p elastic scatt. 90 Zr0.09±0.07Ray, PRC18(1978)1756 IVGDR by α scatt. 116,124 Sn … ±0.12Krasznahorkay, PRL66(1991)1287 SDR by ( 3 He,t) 114--124 Sn … ±0.07Krasznahorkay, PRL82(1999)3216 Yako(2006) 90 Zr0.07±0.04

45. Isoscalar and Isovector nuclear matter properties and Giant Resonances H. Sagawa, University of Aizu 1.Introduction 2.Incompressibility and ISGMR 3.Neutron Matter EOS and Neutron Skin Thickness 4.Isotope Dependence of ISGMR and symmetry term of Incompressibility 5.Summary ---nuclear structure from laboratory to stars---- Trento ， Italy, October 8, 2007

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

47. 1SI2SIII3SIV 4SVI5Skya6SkM 7SkM*8SLy49MSkA 10SkI311SkI412SkX 13SGII Notation for the Skyrme interactions 14NL315NLC 16NLSH17TM1 18TM219DD-ME1 20DD-ME2 Notation for the RMF parameter sets Parameter sets of SHF and relativistic mean field (RMF) model

48. Correlation among nuclear matter properties

50. 1SI2SIII3SIV 4SVI5Skya6SkM 7SkM*8SLy49MSkA 10SkI311SkI412SkX 13 SGII 14 SGI Notation for the Skyrme interactions 15NLSH16NL3 17NLC18TM1 19TM220DD-ME1 21DD-ME2 Notation for the RMF parameter sets Parameter sets of SHF and relativistic mean field (RMF) model

56. Correlation among nuclear matter properties

58. 1.Nuclear incompressibility K is determined empirically to be K~230MeV(Skyrme,Gogny), K~250MeV(RMF). 2.A clear correlation between neutron skin thickness and neutron matter EOS, and volume symmetry energy. 3. The pressure of RMF is higher than that of SHF in general. 4. Neutron skin thickness can be obtained by the sum rules of charge exchange SD and also spin monopole excitations. 5. The SD strength gives a critical information both on the neutron EOS and mean field models. 90 Zr 6. is extracted from isotope dependence of ISGMR 7.J=(32+/-1)MeV, L=(60+/-5)MeV, Ksym= -(100+/-40)MeV Summary

59. S. Yoshida and H.S., Phys. Rev. C69, 024318 (2004), C73,024318(2006). K. Yako, H.S. and H. Sakai, PRC74,051303(R) (2007). H.S., S. Yoshida, G.M.Zeng, J.Z. Gu, X.Z. Zhang, PRC76,024301(2007). Collaborators Theory: Satoshi Yoshida, Guo-Mo Zeng, Jian-Zhong Gu, Xi-Zhen Zhang Experiment: Kentaro Yako, Hideyuki Sakai Publications