Lectures in Milano University Hiroyuki Sagawa, Univeristy of Aizu March 6,12,13, 2008

1. Lectures in Milano UniversityHiroyuki Sagawa, Univeristy of AizuMarch6,12,13, 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 ---nuclear structure from laboratory to stars---- H. Sagawa, University of Aizu • Introduction • Incompressibility and ISGMR • Neutron Matter EOS and Neutron Skin Thickness • Isotope Dependence of ISGMR and symmetry term of Incompressibility • Summary

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

4. IS monopole mode (compression mode)

5. 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

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

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

14. Nuclear Matter SHF RMF

15. 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

16. 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.

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

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

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

26. Mt. Bandai UoA Lake Inawashiro

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. Neutron Matter AV14+3body

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

32. RQRPA-N.Paar RQRPA-N.Paar A.Krasznahorkay et al. NPA 567(1994)521 C.J.Batty et al. Adv.Nucl.Phys. (1989)1 C.Satlos et al. NPA 719(2003)304 RQRPA-N.Paar B.C. Clark et al. PRC 67(2003)044306 LAND 208Pb analysis ∑Bpdr(E1)=1.98 e2 fm2 from N.Ryezayeva et al., PRL 89(2002)272501 ∑Bgdr(E1)=60.8 e2 fm2 from A.Veyssiere et al.,NPA 159(1970)561 Rn – Rp= 0.18 ± 0.035 fm

33. Pigmy GDR GDR (p,p)

34. 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

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

37. 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

38. 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

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

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

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

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

48. Correlation among nuclear matter properties

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