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Constraining the slope parameter of symmetry energy from nuclear structure International Symposium on Neutron Star Matter (NSMAT2016) - Recent Progress in Observations, Experiments and Theories - November 21 st 24 th , 2016 Tohoku

SLIDE 1

Constraining the slope parameter of symmetry energy from nuclear structure

International Symposium on Neutron Star Matter (NSMAT2016)

Recent Progress in Observations, Experiments and Theories -

November 21st – 24th, 2016 Tohoku University

INAKURA Tsunenori (Niigata Univ.)

NAKADA Hitoshi (Chiba Univ.)

SLIDE 2

EoS calculated by effective interactions Symmetric Nuclear Matter (SNM) EoS is known rather well. Pure Neutron Matter (PNM) EoS has large uncertainty.

Nuclear Matter Equation of State (EoS)

PNM SNM

SLIDE 3

Quantities characterizing EoS

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Low-Energy Dipole (LED) mode

Pygmy Dipole Resonance (PDR)

Emerge around (neutron) threshold. Observed in many nuclei. develop well in neutron-rich nuclei. connected with neutron skin which is approximately neutron matter.

LED ≈ neutron skin dynamics.
LED may provide some information on EoS in ≤ region.

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L from LED

Carbone+, PRC81, 041301 Reinhard+, PRC81, 051303 Roca-Maza+, PRC88, 024316

Which is best?

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L from LED

Carbone+, PRC81, 041301 Reinhard+, PRC81, 051303 Roca-Maza+, PRC88, 024316

Correlation is analyzed within single interaction. Correlation is calculated using many interactions.

Same correlation?

SLIDE 7

L from LED

Carbone+, PRC81, 041301 Reinhard+, PRC81, 051303 Roca-Maza+, PRC88, 024316

Which is best? Same correlation?

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Selfconsistent mean-field calc. (density functional theory)

Hartree-Fock + Random Phase Approximation.
Fully self-consistent calculation.

16 interactions

3 Skyrme which are widely used: SkM*, SLy4, SGII 2 Skyrme which are less used: SkT4, Ska 2 Skyrme which are recently made: UNEDF0, UNEDF1 4 Skyrme to cover wide range of L: SkI2, SkI3, SkI4, SkI5 3 Gogny and 2 M3Y to check model dependence: D1, D1S, D1M, M3Y-P6, M3Y-P7

SLIDE 9

Ono+, PRC68, 051601

Introduction of L-dependence

The additional term does not affect SNM EoS nor S0. changes L. VL is a parameter to control L.

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Correlations in 132Sn

Correlation coefficient = 0.953. Uncertainty for L : 12 MeV.

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Comparison with experimental data

Assuming = 30 – 32 MeV.

68Ni experimental data: Rossi+, PRL111, 242503. 208Pb experimental data: Tamii+, PRL107, 062502.

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Summary

We calculate correlations between and observables using many interactions and their variants.

LED provides constraint on PNM EoS.
αDS0 correlates well with slope parameter L.
Theoretical uncertainty (standard deviation) is

10-20 MeV.

Inakura and Nakada, Phys. Rev. C 92, 064302.