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Li Gang Cao IMP-CAS, Lanzhou Collaborators: H. Sagawa (Aizu University)

Microscopic study of ISGMR in Cd, Sn and Pb isotopes. Li Gang Cao IMP-CAS, Lanzhou Collaborators: H. Sagawa (Aizu University) G. Colo (Milano University).

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Li Gang Cao IMP-CAS, Lanzhou Collaborators: H. Sagawa (Aizu University)

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  1. Microscopic study of ISGMR in Cd, Sn and Pb isotopes • Li Gang Cao • IMP-CAS, Lanzhou • Collaborators: • H. Sagawa(Aizu University) • G. Colo(Milano University) From nucleon structure to nuclear structure and compact astrophysical objects , Beijing, Kavli,2012.6.11-29

  2. The Nuclear equation of state Nuclear structure Heavy ion collision Physics of neutron star

  3. The incompressibility of nuclear matter 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.

  4. The incompressibility of nuclear matter 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 250 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. Some groups try to solve this problem by introducing a isospin dependent Incompressibility, they can get better description in Sn isotopes, but fails in Pb208. J. Piekarewicz, PRC79, 054311 (2009)

  8. 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, 011307(R)(2008).

  9. 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.,PRC78,064304(2008) Or the HF+BCS+QRPA(QTBA). The spin-orbit interaction is dropped. V. Tselyaev, PRC 79, 034309 (2009) T. Sil, et.al., Phys. Rev. C73, 034316 (2006). The spin-orbit residual interaction produces an attractive effect on the ISGMR strength, the energies are pushed down by about 0.6MeV.

  10. 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 pairing in pp channel

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

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

  13. Results for Pb isotopes E. Khan, Phys. Rev. C80, 057302 (2009). The so-called mutually-enhanced-magicity effect, which is proposed by Lunney and Zeldes.

  14. Results for Pb isotopes

  15. Results for Sn isotopes

  16. Results for Cd isotopes

  17. Summary • 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 calculations. • We found that the pairing plays 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 surface effect…….

  18. Thank You!

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