1. Nuclear Collective Excitation in a Femi-Liquid Model Bao-Xi SUN Beijing University of Technology 2012.06.15 KITPC, Beijing

2. Content Fermi-liquid Model based on Landau Theory. Relation between isoscalar giant resonance and isovector giant resonance Collective excitation in nuclear matter Collective excitation in finite nuclei Conclusion

3. Fermi-liquid Model based on Landau Theory Xiao-Gang Wen, Quantum field theory of many-body systems, Oxford University Press, Oxford, 2004.

4. Boltzmann Equation of quasi-nucleons Boltzmann equation of nucleons where

5. Density of quasi-nucleons The quasi-nucleon density near the Fermi- surface: with

6. Vibrations of Fermi surface

7. Linearized liquid equation of motion in the momentum space with and

8. Potential between nucleons in the linear Walecka model

9. Fermi liquid function

10. with and

11. Fermi energy and Fermi velocity

12. C. J. Horowitz and B. D. Serot, Nucl. Phys. A368 (1981) 503

13. The quasi-nucleon density can be expanded in spherical harmonics:

14. Liquid equation of motion in spherical harmonics

15. The stability of the Fermi liquid requires the diagonal matrix elements of M must be positive definite, and we can write M as M =W W T. Letting

16. Eigen-energy equation for the nuclear collective excitation with the Hamiltonian

17. and

18. Eigenvalues of the Hamiltonian

19. Since the nucleon near Fermi-surface is easier to be excited, in the following calculation, we set the value of nucleon momentum

20. Collective excitation energy E l.vs. effective mass M* N. L=0,Dash;L=1,Solid;L=2,Dot.

21. Collective excitation

22. Relation between isoscalar and isovector giant resonances The nuclear isovector giant resonances correspond to the nuclear collective excitation that the collective excitation of protons is creating with the energy E S (l), while the collective excitation of neutrons is annihilating with the energy E S (l), and vice versa.

23. Relation between isoscalar and isovector giant resonances The energy of the nuclear isovector giant resonance is about twice of the corresponding isoscalar giant resonance in the nuclear matter, i.e.,

24. Giant resonances of finite nuclei The proton and neutron densities can be written approximately

25. Giant monopole resonances of finite nuclei L=0M * /ME 0 (p)E 0 (n)E 0 (p) +E 0 (n) ESES EVEV Pb2080.74216.287.0523.3314.17 +-0.28 26.0+-3.0 Sm1440.74215.269.0024.2615.39 +-0.28 _ Sn1160.74215.269.0024.2616.07 +-0.12 _ Zr900.71717.5713.1330.717.89 +-0.20 28.5+-2.6 Ca400.71715.58 31.1631.1+-2.2

26. Giant dipole resonances of finite nuclei The isovector giant dipole resonance of the nucleus is a shift of the center of mass, which corresponds to the creation of the L=1 collective excitation of protons or neutrons.

27. Giant dipole resonances of finite nuclei The isoscalar giant dipole resonance in Pb- 208 with a centroid energy E=22.5MeV should be a compression mode, which corresponds to a creation of the L=1 collective excitation of protons or neutrons and an annihilation of the L=1 collective excitation of neutrons or protons simultaneously. B. F. Davis et al., PRL 79, 609 (1997)

28. Giant dipole resonances of finite nuclei l=1M * /ME 0 (p)E 0 (n)E 0 (p) +E 0 (n) ESES EVEV Pb2080.75515.536.5722.122.513.5+-0.2 Zr900.74215.5611.3726.93_16.5+-0.2 Ca400.719.58 39.16_19.8+-0.5

29. Giant quadrupole resonances of finite nuclei l=2M * /ME 0 (p)E 0 (n)E 0 (p) +E 0 (n) ESES EVEV Pb2080.74215.025.8420.8610.9+-0.122.0 Zr900.74213.168.2721.4314.41+-0.1_ Ca400.6918.54 37.0817.8+-0.332.5+-1.5 O160.6918.54 37.0820.7_

30. Mixture of different L state (M*/M=0.742, k F =1.36fm -1 )

31. Conclusion In the Fermi-liquid model, the exchange interaction between nucleons causes the nuclear collective excitation. It is different from RMF+RPA. Of course, we need not take into account the contribution from Dirac sea.

32. Thanks for your attention!