Symmetry energy constrained by Nuclear collec:ve excita:ons ( - PowerPoint PPT Presentation

『 Symmetry energy constrained by Nuclear collec:ve excita:ons 』 ( February 16-18, 2017, Iizaka Hot Spa, Japan) H. Sagawa University of Aizu/RIKEN, Japan 1. Introduc:on 2. ISGMR and Incompressibility 3. Symmetry energy and Collec:ve excita:ons and FRDM mass formula 4. Summary Castle of Crane （鶴ヶ城） in Aizu Wakamatsu

Nuclear maXer Theory: roadmap 126 Ξ 82 S=-2 Supernovae protons A 50 ⇒ ∞ Λ Σ 82 S=-1 28 20 50 8 28 n , p neutrons 2 20 S=0 8 Neutron Star 2 Neutron Strangeness maXer

Well-known basics on EDF’s ˆ ˆ [ ] ˆ E H E H ρ = Ψ Ψ = = Φ Φ eff ˆ ρ 1-body density matrix Φ Slater determinant ⇔ Calcula:ng the parameters from a Se_ng the structure by means m o r e f u n d a m e n t a l t h e o r y of symmetries (spin, isospin --) ( Rela:vis:c Bruckner HF or Chiral and fi_ng the parameters field theory and LQCD) Allows calcula:ng nuclear maXer and finite nuclei (even complex states), by disentangling physical parameters. HF/HFB for g.s., RPA/QRPA for excited states. Possible both in non-rela:vis:c and in rela:vis:c covariant form.

Energy Density Func=onals E sym = ρ S ( ρ ) = E ( ρ , δ = 1) − E ( ρ , δ = 0)

Correla:ons are obtained using EDFs ˆ ˆ [ ] ˆ E H E H ρ = Ψ Ψ = = Φ Φ eff ˆ ρ 1-body density matrix Φ Slater determinant ⇔ • H eff = T + V eff . If V eff is well designed, the resulting g.s. (minimum) energy can fit experiment at best. • Within a time-dependent theory, one can describe oscillations around v ≡ δ 2 E the minimum. The restoring force is: δρ 2 • The linearization of the equation of the motion leads to the well known Random Phase Approximation. ✓ ◆ ✓ ◆ ✓ ◆ A B X X = ~ ω − B ∗ − A ∗ Y Y 5

Skyrme vs. rela:vis:c func:onals Skyrme effective force attraction short-range repulsion RMF In the relativistic (that is, covariant) models the nucleons are described as Dirac particles that exchange effective mesons. There are also point coupling versions ! 6

EDF’s for hypernuclei and hypernuclearmaAer E = Ψ (N,Y) ˆ H(NN)+ ˆ H(NY) Ψ (N,Y) = Φ (N,Y) ˆ H eff (NN)+ ˆ H eff (NY) Φ (N,Y) = E ˆ ρ ( N ), ˆ [ ] ρ ( Y ) Slater determ inant ⇔ Φ (N,Y) 1-body density matrix ρ ( N ), ˆ ˆ ρ ( Y ) Se_ng the structure by means Calcula:ng the parameters from of symmetries (spin, isospin --) a m o r e f u n d a m e n t a l and fi_ng the parameters theory(quark models, Quark- Meson coupling model, LQCD) ! # E ρ N , ρ Y " $ Allows calcula:ng nuclear maXer and finite nuclei, neutron stars, by disentangling physical parameters. HF/HFB for g.s., RPA/QRPA for excited states. Possible both in non-rela:vis:c and in rela:vis:c covariant form.

Nuclear MaXer SHF RMF Incompressibility K

イメージを表示できません。メモリ不足のためにイメージを開くことができないか、イメージが破損している可能性があります。コンピューターを再起動して再度ファイルを開いてください。それでも赤い x が表示される場合は、イメージを削除して挿入してください。 Nuclear MaXer EOS Supernova Explosion イメージを表示できません。メモリ不足のためにイメージを開くことができないか、イメージが破損している可能性があります。コンピューターを再起動して再度ファイルを開いてください。それでも赤い x が表示される場合は、イメージを削除して挿入してください。 Isoscalar Giant Monopole Resonances { Isoscalar Compressional Dipole Resonances Incompressibility K Self consistent HF+RPA calcula:ons , ( , ) experimtent α α Self consistent RMF+RPA calcula:ons

The nuclear incompressibility from ISGMR We can give credit to the idea that the link should be provided microscopically through the Energy Functional E[ ρ ]. K ∞ in nuclear matter (analytic) IT PROVIDES AT THE SAME TIME E ISGMR (by means of self- E ISGMR consistent RPA calculations) Skyrme Gogny E exp RPA RMF K ∞ [ MeV] 220 240 260 Extracted value of K ∞

K The incompressibility of nuclear matter ∞ The incompressibility of nuclear matter can not be measured directly, it can be deduced from the response of ISGMR in heavy nuclei, such as 208 Pb. 0.4 E xp. S K I3(258) F raction E 0 E WS R /MeV S L y5(230) 0.3 S K P (201) 208 P b 0.2 0.1 K=217MeV for SkM* K=256MeV for SGI 0.0 K=355MeV for SIII 5 10 15 20 25 E (MeV )

Based on the HFB+QRPA calcula:on, the ISGMR energies in Sn Isotopes are obtained using different Skyrme interac:on, but There is No sa:sfied conclusion according to those calcula:on Because the calcula:ons are not fully self-consistent, such as The two-body spin-orbit interac:on is dropped . J. Li et.al.,PRC78,064304(2008) Or the HF+BCS+QRPA(QTBA). The spin-orbit interac:on is dropped. V. Tselyaev, PRC 79, 034309 (2009) T. Sil, et.al., Phys. Rev. C73, 034316 (2006). The spin-orbit residual interac:on in HF+RPA produces an aXrac:ve effect on the ISGMR strength, the energies are pushed down by about 0.6MeV. No pairing. The strength func:on of QRPA is obtained by fully self-consistent HF+BCS+QRPA model with Residual interaction ：full Skyrme force, two-body spin-orbit, two-body C oulomb , and also the pairing in particle-particle channel

Nuclear MaAer EOS Isoscalar Monopole Giant Resonances in 208 Pb { Isoscalar Compressional Dipole Resonances K=(240 +/-10 +/- 10)MeV K ≈ (240 ± 10) MeV for Skyrme Incompressibility K （ G. Colo ,2004 ） ≈ (230 ± 10) MeV for Gogny ≈ (250 ± 10) MeV for RMF (Lalazissis,2005 ） ≈ (230 ± 10) MeV for Point Coupling （ P. Ring,2007)

Extrac=ng K τ from data Using this formula globally is dangerous and risky (cf. M. Pearson, S. Shlomo and D. Youngblood) but one can use it locally. K Coul can be calculated and ETF calculations give K surf ≈ –K ∞ . What can we learn about neutron EOS from Giant resonances? Isospin dependence of GMR Dipole polarizability in 208 Pb (Tamii)

Results for Sn isotopes Exp at RCNP SLy 5 230 MeV * SKM 217 MeV SKP 202 MeV

Correlation between Isospin GMR and nuclear matter properties 1. Nuclear incompressibility K is determined empirically with the ISGMR in 208 Pb to be K~230MeV(Skyrme,Gogny), K~250MeV(RMF). K=(240 +/-10 +/- 10)MeV K=(225 +/-10)MeV 2. Combining ISGMR data of Sn and Cd isotopes(RCNP) K (500 50)MeV τ = − ± 3. is extracted from isotope dependence of ISGMR.

132 Sn

J=(36+/-2)MeV L=(100+/-20)MeV Ksym= -(0+/-40)MeV To be con:nued

『 FRDM Mass Model and Symmetry Energy 』 ADNDT109-110, p.1-204(May-June, 2016)

FRDM is a nuclear structure model with macro- and microscopic ingredients. To predict not only masses, but also deforma:ons, radii, beta-decay rates, alpha-decay rates and spin-pari:es of odd nuclei with quite reasonable agreements. Macroscopic part: LD model Microscopic part: Holded Yukawa poten:al Symmetry Energy ∂ 2 ( ε / ρ ) S ( ρ ) = 1 where δ =( ρ n − ρ p ) / ρ ∂ δ 2 2 2 " % " % ' + 1 S ( ρ ) = J + L ρ − ρ 0 ρ − ρ 0 2 K sym $ $ ' 3 ρ 0 3 ρ 0 # & # & ∂ 2 S ∂ S , K sym = 9 ρ 2 where J = S ( ρ 0 ), L =3 ρ 0 0 ∂ ρ 2 ∂ ρ ρ 0 ρ 0

J=32.5+/-0.5MeV L=70+/-15MeV (54+/-15MeV) J=32.5+/-0.5MeV L=54+/-15MeV

Summary of Symmetry Energy Studies 1. Micro-macroscopic model (FRDM) is further improved taking into account the op:miza:on of symmetry energy coefficients J and L: J=32.5 +/-0.5 MeV L=55 +/-15 MeV 2. Isospin dependence of GMR gives somewhat larger J and L which should be confirmed further by new experiments in RIKEN/CNS. 3. A controversial value 75<L<122MeV is extracted from AGDR in 208 Pb. 4. K sym can be determined by isotope dependence of ISGMR energies?