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1、Nuclear Collective Excitation in a Femi-Liquid ModelBao-Xi SUNBeijing University of Technology2019.06.15 KITPC, BeijingContentlFermi-liquid Model based on Landau Theory.lRelation between isoscalar giant resonance and isovector giant resonancelCollective excitation in nuclear matterlCollective excita
2、tion in finite nucleilConclusionFermi-liquid Model based on Landau TheorylXiao-Gang Wen, l Quantum field theory of many-body systems,l Oxford University Press, Oxford, 2019.Boltzmann Equation of quasi-nucleonslBoltzmann equation of nucleonslwhereDensity of quasi-nucleonslThe quasi-nucleon density ne
3、ar the Fermi-surface:lwithVibrations of Fermi surface Linearized liquid equation of motion in the momentum spacelwithlandPotential between nucleons in the linear Walecka modelFermi liquid functionFermi liquid functionwithandFermi energy and Fermi velocityC. J. Horowitz and B. D. Serot, Nucl. Phys. A
4、368 (1981) 503The quasi-nucleon density can be expanded in spherical harmonics:Liquid equation of motion in spherical harmonicslThe stability of the Fermi liquid requires the diagonal matrix elements of M must be positive definite, and we can write M as M =W WT. Letting Eigen-energy equation for the
5、 nuclear collective excitation lwith the Hamiltonian andEigenvalues of the HamiltonianlSince the nucleon near Fermi-surface is easier to be excited, in the following calculation, we set the value of nucleon momentum Collective excitation energy El .vs. effective mass M*N . L=0,Dash;L=1,Solid;L=2,Dot
6、.Collective excitationRelation between isoscalar and isovector giant resonanceslThe nuclear isovector giant resonances correspond to the nuclear collective excitation that the collective excitation of protons is creating with the energy ES(l), while the collective excitation of neutrons is annihilat
7、ing with the energy ES(l), and vice versa.Relation between isoscalar and isovector giant resonanceslThe 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 lThe proton and neutron
8、densities can be written approximatelyGiant monopole resonances of finite nucleiL=0M*/ME0(p)E0(n)E0(p) +E0(n)ESEVPb2080.74216.287.0523.3314.17+-0.2826.0+-3.0Sm1440.74215.269.0024.2615.39+-0.28_Sn1160.74215.269.0024.2616.07+-0.12_Zr900.71717.5713.1330.717.89+-0.2028.5+-2.6Ca400.71715.5815.5831.1631.1
9、+-2.2Giant dipole resonances of finite nucleilThe isovector giant dipole resonance of the nucleus is a shift of the center of mass, which l corresponds to the creation of the L=1 collective excitation of protons or neutrons.l Giant dipole resonances of finite nucleilThe isoscalar giant dipole resona
10、nce 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.lB. F. Davis et al., PRL 79, 609 (2019)Giant
11、 dipole resonances of finite nucleil=1M*/ME0(p)E0(n)E0(p) +E0(n)ESEVPb2080.75515.536.5722.122.513.5+-0.2Zr900.74215.5611.3726.93_16.5+-0.2Ca400.719.5819.5839.16_19.8+-0.5Giant quadrupole resonances of finite nucleil=2M*/ME0(p)E0(n)E0(p) +E0(n)ESEVPb2080.74215.025.8420.8610.9+-0.122.0Zr900.74213.168.
12、2721.4314.41+-0.1_Ca400.6918.5418.5437.0817.8+-0.332.5+-1.5O160.6918.5418.5437.0820.7_Mixture of different L state (M*/M=0.742, kF=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. Thanks for your attention!
