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

Feb 13, 2024 434 likes •737 views

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

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Castle of Crane（鶴ヶ城） in Aizu Wakamatsu

『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
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protons neutrons

82 50 28 28 50 82 20 8 2 2 8 20 126

Theory: roadmap

Nuclear maXer Neutron maXer

A ⇒ ∞

Supernovae Neutron Star Strangeness S=0 S=-1 S=-2

Ξ

Λ Σ

n, p

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SLIDE 3

[ ]

E E = = Ψ Ψ =

eff

H ˆ

H ˆ Φ Φ ρ ˆ

Φ

Slater determinant

⇔

1-body density matrix

ρ ˆ

Calcula:ng the parameters from a m o r e f u n d a m e n t a l t h e o r y ( Rela:vis:c Bruckner HF or Chiral field theory and LQCD)

Se_ng the structure by means

  • f symmetries (spin, isospin --)

and fi_ng the parameters 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.

Well-known basics on EDF’s

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Energy Density Func=onals

Esym = ρS(ρ) = E(ρ,δ =1)− E(ρ,δ = 0)

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Correla:ons are obtained using EDFs

5

[ ]

E E = = Ψ Ψ =

eff

H ˆ

H ˆ Φ Φ ρ ˆ

Φ

Slater determinant

⇔

1-body density matrix

ρ ˆ

  • Heff = T + Veff. If Veff is well

designed, the resulting g.s. (minimum) energy can fit experiment at best.

  • Within a time-dependent theory, one can describe oscillations around

the minimum. The restoring force is:

  • The linearization of the equation of the motion leads to the well known

Random Phase Approximation. v ≡ δ2E δρ2

✓ A B −B∗ −A∗ ◆ ✓ X Y ◆ = ~ω ✓ X Y ◆

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Skyrme vs. rela:vis:c func:onals

6

attraction short-range repulsion

Skyrme effective force In the relativistic (that is, covariant) models the nucleons are described as Dirac particles that exchange effective mesons. There are also point coupling versions ! RMF

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Slater determinant ⇔ 1-body density matrix

Calcula:ng the parameters from a m o r e f u n d a m e n t a l theory(quark models, Quark- Meson coupling model, LQCD) Se_ng the structure by means

  • f symmetries (spin, isospin --)

and fi_ng the parameters 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.

EDF’s for hypernuclei and hypernuclearmaAer

E ρ N,ρY ! " # $

Φ(N,Y)

ˆ ρ(N), ˆ ρ(Y)

E = Ψ(N,Y) ˆ H(NN)+ ˆ H(NY) Ψ(N,Y) = Φ(N,Y) ˆ Heff (NN)+ ˆ Heff (NY) Φ(N,Y) = E ˆ ρ(N), ˆ ρ(Y)

[ ]

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SHF RMF

Nuclear MaXer Incompressibility K

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Nuclear MaXer EOS Incompressibility K Isoscalar Giant Monopole Resonances Isoscalar Compressional Dipole Resonances

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{

Self consistent HF+RPA calcula:ons Self consistent RMF+RPA calcula:ons

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,

( , ) experimtent α α

Supernova Explosion

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We can give credit to the idea that the link should be provided microscopically through the Energy Functional E[ρ].

IT PROVIDES AT THE SAME TIME K∞ in nuclear matter (analytic) EISGMR (by means of self- consistent RPA calculations) K∞ [MeV] 220 240 260 Eexp Extracted value of K∞ RPA EISGMR

Skyrme Gogny RMF

The nuclear incompressibility from ISGMR

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The incompressibility of nuclear matter

∞

K

The incompressibility of nuclear matter can not be measured directly, it can be deduced from the response of ISGMR in heavy nuclei, such as 208Pb.

5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 F raction E 0 E WS R /MeV E (MeV ) E xp. S K I3(258) S L y5(230) S K P (201)

208P b

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

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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. Residual interaction ：full Skyrme force, two-body spin-orbit, two-body Coulomb, and also the pairing in particle-particle channel The strength func:on of QRPA is obtained by fully self-consistent HF+BCS+QRPA model with

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Nuclear MaAer EOS

Incompressibility K Isoscalar Monopole Giant Resonances in 208Pb Isoscalar Compressional Dipole Resonances

{

（G. Colo ,2004） (Lalazissis,2005） （P. Ring,2007) K=(240 +/-10 +/- 10)MeV

K ≈ (240±10) MeV for Skyrme ≈ (230±10) MeV for Gogny ≈ (250 ±10) MeV for RMF ≈ (230±10) MeV for Point Coupling

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Extrac=ng Kτ from data

Using this formula globally is dangerous and risky (cf. M. Pearson, S. Shlomo and D. Youngblood) but one can use it locally. KCoul can be calculated and ETF calculations give Ksurf ≈ –K∞.

What can we learn about neutron EOS from Giant resonances? Isospin dependence of GMR Dipole polarizability in 208Pb (Tamii)

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Results for Sn isotopes Exp at RCNP

MeV SKP MeV SKM MeV SLy 202 217 230 5

*

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Correlation between Isospin GMR and nuclear matter properties

  • 1. Nuclear incompressibility K is determined empirically with the ISGMR in 208Pb to be

K~230MeV(Skyrme,Gogny), K~250MeV(RMF).

  • 2. Combining ISGMR data of Sn and Cd isotopes(RCNP)
  • 3. is extracted from isotope dependence of ISGMR.

K (500 50)MeV

τ = −

±

K=(240 +/-10 +/- 10)MeV K=(225 +/-10)MeV

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132Sn

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

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『 FRDM Mass Model and Symmetry Energy 』

ADNDT109-110, p.1-204(May-June, 2016)

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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

S(ρ) = 1 2 ∂2(ε / ρ) ∂δ 2 where δ=(ρn − ρp) / ρ

S(ρ) = J + L ρ − ρ0 3ρ0 " # $ % & '+ 1 2 Ksym ρ − ρ0 3ρ0 " # $ % & '

2

where J=S(ρ0), L=3ρ0 ∂S ∂ρ ρ0 ,Ksym = 9ρ2 ∂2S ∂ρ2

ρ0

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SLIDE 26

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

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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 208Pb.

  • 4. Ksym can be determined by isotope dependence of ISGMR

energies?