nuclear collective excitation in a femi-liquid model bao-xi sun beijing university of technology...
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Nuclear Collective Excitation in a Femi-Liquid Model
Bao-Xi SUN
Beijing University of Technology
2012.06.15 KITPC, Beijing
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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
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Fermi-liquid Model based on Landau Theory
Xiao-Gang Wen,
Quantum field theory of many-body systems,
Oxford University Press, Oxford, 2004.
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Boltzmann Equation of quasi-nucleons
Boltzmann equation of nucleons
where
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Density of quasi-nucleons
The quasi-nucleon density near the Fermi-surface:
with
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Vibrations of Fermi surface
Fk
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Linearized liquid equation of motion in the momentum space
with
and
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Potential between nucleons in the linear Walecka model
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Fermi liquid function
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Fermi liquid function
with
and
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Fermi energy and Fermi velocity
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C. J. Horowitz and B. D. Serot, Nucl. Phys. A368 (1981) 503
10.47, 13.80,
520 , 783 ,
939 .N
g g
m MeV m MeV
M MeV
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The quasi-nucleon density can be expanded in spherical harmonics:
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Liquid equation of motion in spherical harmonics
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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 WT. Letting
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Eigen-energy equation for the nuclear collective excitation
with the Hamiltonian
, , ,i u Hu l m q tt
,
1, 1, 1,
1 12 22 2
* *3 3
, ,(2 ) (2 )
Tl l
lm l l l m l l
F FF F F F
H q W KW
q a a
k kv f l l v f l l
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and
Tu W
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Eigenvalues of the Hamiltonian
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Since the nucleon near Fermi-surface is easier to be excited, in the following calculation, we set the value of nucleon momentum
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Collective excitation energy El .vs. effective mass M*N .
L=0,Dash;L=1,Solid;L=2,Dot.
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Collective excitation
* 0.742N NM M
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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 ES(l), while the collective excitation of neutrons is annihilating with the energy ES(l), and vice versa.
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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.,
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Giant resonances of finite nuclei
The proton and neutron densities can be written approximately
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Giant monopole resonances of finite nuclei
L=0 M*/M E0(p) E0(n) E0(p) +E0(n)
ES EV
Pb208 0.742 16.28 7.05 23.33 14.17
+-0.28
26.0+-3.0
Sm144 0.742 15.26 9.00 24.26 15.39
+-0.28
_
Sn116 0.742 15.26 9.00 24.26 16.07
+-0.12
_
Zr90 0.717 17.57 13.13 30.7 17.89
+-0.20
28.5+-2.6
Ca40 0.717 15.58 15.58 31.16 31.1+-2.2
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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.
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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)
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Giant dipole resonances of finite nuclei
l=1 M*/M E0(p) E0(n) E0(p) +E0(n)
ES EV
Pb208 0.755 15.53 6.57 22.1 22.5 13.5+-0.2
Zr90 0.742 15.56 11.37 26.93 _ 16.5+-0.2
Ca40 0.7 19.58 19.58 39.16 _ 19.8+-0.5
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Giant quadrupole resonances of finite nuclei
l=2 M*/M E0(p) E0(n) E0(p) +E0(n)
ES EV
Pb208 0.742 15.02 5.84 20.86 10.9+-0.1 22.0
Zr90 0.742 13.16 8.27 21.43 14.41+-0.1 _
Ca40 0.69 18.54 18.54 37.08 17.8+-0.3 32.5+-1.5
O16 0.69 18.54 18.54 37.08 20.7 _
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Mixture of different L state (M*/M=0.742, kF=1.36fm-1)
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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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Thanks for your attention!