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1、Nuclear Collective Excitation in a Femi-Liquid ModelBao-Xi SUNBeijing University of Technology2012.06.15 KITPC,BeijingContentlFermi-liquid Model based on Landau Theory.lRelation between isoscalar giant resonance and isovector giant resonancelCollective excitation in nuclear matterlCollective excitat
2、ion in finite nucleilConclusionFermi-liquid Model based on Landau TheorylXiao-Gang Wen,Quantum field theory of many-body systems,Oxford University Press,Oxford,2004.Boltzmann Equation of quasi-nucleonslBoltzmann equation of nucleonslwhereDensity of quasi-nucleonslThe quasi-nucleon density near the F
3、ermi-surface:lwithVibrations of Fermi surface FkLinearized liquid equation of motion in the momentum spacewithandPotential between nucleons in the linear Walecka modelFermi liquid functionFermi liquid functionwithandFermi energy and Fermi velocityC.J.Horowitz and B.D.Serot,Nucl.Phys.A368(1981)50310.
4、47,13.80,520,783,939.NggmMeVmMeVMMeVThe 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-ener
5、gy equation for the nuclear collective excitation with the Hamiltonian ,iuHu l m q tt,1,1,1,112222*33,(2)(2)Tl llmlllmllFFFFFFHq W KWq aakkvfl lvfl l andTuWEigenvalues of the HamiltonianlSince the nucleon near Fermi-surface is easier to be excited,in the following calculation,we set the value of nuc
6、leon momentum Collective excitation energy El.vs.effective mass M*N.L=0,Dash;L=1,Solid;L=2,Dot.Collective excitation*0.742NNMMRelation between isoscalar and isovector giant resonanceslThe nuclear isovector giant resonances correspond to the nuclear collective excitation that the collective excitatio
7、n of protons is creating with the energy ES(l),while the collective excitation of neutrons is annihilating 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
8、giant resonance in the nuclear matter,i.e.,Giant resonances of finite nuclei lThe proton and neutron 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.
9、74215.269.0024.2616.07+-0.12_Zr900.71717.5713.1330.717.89+-0.2028.5+-2.6Ca400.71715.5815.5831.1631.1+-2.2Giant dipole resonances of finite nucleilThe 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
10、 protons or neutrons.Giant dipole resonances of finite nucleilThe 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
11、 excitation of neutrons or protons simultaneously.lB.F.Davis et al.,PRL 79,609(1997)Giant 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 nucl
12、eil=2M*/ME0(p)E0(n)E0(p)+E0(n)ESEVPb2080.74215.025.8420.8610.9+-0.122.0Zr900.74213.168.2721.4314.41+-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!
原子核集体激发的费米液体模型研究
