1. Constraining the Nuclear Equation of State via Nuclear Structure observables
曹李刚
中科院近物所
第十四届全国核结构大会，湖州，

2. IS Monopole giant resonance
The Nuclear equation of state
IS Monopole giant resonance

3. The Nuclear equation of state IV dipole giant resonance

4. The incompressibility of nuclear matter
Nuclear structure, Heavy ion collision, Physics of neutron star
The incompressibility of nuclear matter can not be measured directly, it can be deduced from the distribution Of ISGMR in heavy nuclei, such as 208Pb.

5. is found around 230 MeV by using non relativistic interaction, such as Skyrme and Gogny
In the case of relativistic interaction, It is around 260 MeV.
Both of them can produce very well the ISGMR energy in Pb208
Using different density dependent Skyrme force, Colo point out that it is possible to reproducing the ISGMR energy in Pb208 for some Skyrme interaction Which have 250 MeV of incompressibility.
Piekarewicz built non-linear relativistic Lagrangian with 230 MeV incompressibility, which can produce
the ISGMR energy in Pb208.
both non relativistic and relativistic.

6. New problem is appeared.
Why Tin is so soft? Or
Why pb is so hard?

7. How to understand this discrepancy in Sn isotopes and Pb208,
Several theoretical works have been done to try to explain it.
Since the Sn isotopes are open shell nuclei, the pairing shall play
A role both in ground states and excited states. Using the
Constraint HF(HFB) and energy-weighted sum rule approach, one
can get the constrained energy of ISGMR, it is found that pairing
Has an important effect in producing the ISGMR energies in Sn
Isotopes. E. Khan PRC80, (R)(2008).
Based on the HFB+QRPA calculation, the ISGMR energies in Sn
Isotopes are obtained using different Skyrme interaction, but
There is No satisfied conclusion according to those calculation
Because the calculations are not fully self-consistent, such as
The spin-orbit interaction is dropped . J. Li et.al.,78,064304(2008)
Some groups try to solve this problem by introducing a isospin dependent Incompressibility, they can get better description in Sn isotopes, but fails in Pb J. Piekarewicz, PRC79, (2009)
The problem is still open.

8. In this talk, I will present our recent work on ISGMR in Cd, Sn and Pb isotopes. It is based on the HF+BCS+QRPA.
Vmjin includes：full Skyrme force, spin-orbit, coulomb, and also the pp channel

9. The strength function is
The various moments are defined as
And various energies are defined as

10. equals to 1, 0.5,0 corresponding to surface, mixed, and volume
Pairing.

16. Summary I
We have studied the ISGMR in Cd, Sn and Pb isotopes based on the fully self-consistent HF+BCS plus QRPA calculations. The SLy5, SKM*, and SKP and different pairing interactions are used in our work.
We found that the pairing does play a role in producing the ISGMR properties.
The SLy5 interaction together with the effect of pairing can give better description on ISGMR both in Cd and Pb isotopes, but it still can not get better results in Sn isotopes, while SKM* can produce the experimental data in Cd and Sn isotopes, but fails in Pb isotopes, for SKP, it fails for all isotopes because the incompressibility is too low.
For future work, the calculations based on fully self-consistent HFB+QRPA may give more satisfied description, or other effect will be investigated, such as isospin-dependent incompressibility, surface effect, isospin-dependent pairing interaction.

17. Ni68
Sn132

19. Summary II
We have constrained the slope of symmetry energy at saturation density using the recent experimental results on pygmy dipole resonance.

20. Thank You!