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

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

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

Boltzmann Equation of quasi-nucleons Boltzmann equation of nucleons where

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

Vibrations of Fermi surface

Linearized liquid equation of motion in the momentum space with and

Potential between nucleons in the linear Walecka model

Fermi liquid function

with and

Fermi energy and Fermi velocity

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

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

Liquid equation of motion in spherical harmonics

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

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

and

Eigenvalues of the Hamiltonian

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

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

Collective excitation

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.

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.,

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

Giant monopole resonances of finite nuclei L=0M * /ME 0 (p)E 0 (n)E 0 (p) +E 0 (n) ESES EVEV Pb Sm _ Sn _ Zr Ca

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.

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)

Giant dipole resonances of finite nuclei l=1M * /ME 0 (p)E 0 (n)E 0 (p) +E 0 (n) ESES EVEV Pb Zr _ Ca _

Giant quadrupole resonances of finite nuclei l=2M * /ME 0 (p)E 0 (n)E 0 (p) +E 0 (n) ESES EVEV Pb Zr _ Ca O _

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

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.

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