Nuclear excitations in relativistic nuclear models

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Nuclear excitations in relativistic nuclear models

• 1Akihiro Haga, 1Hiroshi Toki,
• 1Setsuo Tamenaga, and 2Yataro Horikawa
• 1. RCNP Osaka University
• 2. Juntendo University

8/1-8/3 ????????-??????????????_at_KEK
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Introduction

• The relativistic nuclear model has succeed to
  describe the nuclear ground-state properties,
  mainly due to the large spin-orbit force arising
  from the (small) relativistic effective mass.
• Recently, however, it is reported that there are
  discrepancies in the nuclear excitations
  calculated by the relativistic model, and it
  presumably originated by the relativistic
  effective mass.
• In the conventional relativistic model, the
  negative-energy state is not used for the
  construction of ground state (no-sea
  approximation). This treatment is crucial to lead
  to small effective mass.

We thought important to reconsider the
negative-energy contribution (vacuum
polarization)
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What is the vacuum polarization?
Vacuum of electron-positron field is polarized by
electromagnetic field generated by nuclear charge.
Vacuum of nucleon-anti-nucleon field is also
polarized by nuclear force!
e -
e
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Vacuum polarization in Walecka model
?
s?
potential for the positive-energy state
-?
s
s-?
potential for the negative-energy state
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Instability of vacuum polarization
Nucleons
Total
No solution
Vacuum
Scalar potential as a function of coupling
constant gs in nuclear matter.
Effective mass,
should be large!!
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Computation of the Dirac-sea effect Derivative
expansion
One-loop vacuum contribution to Lagrangian
is expanded in terms of the derivatives of meson
fields as,
Then, the functional coefficients are given as,
A. Haga et. al., Phys. Rev. C70, 064322(2004)
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Effective Lagrangian of the Walecka modelwith
the vacuum contribution
Tensor coupling term
G. Mao, Phys. Rev. C67, (2003) A. Haga,
nucl-th/0601041
Leading-order derivative expansion
Parameters, gs , g? , g? , ms are selected with
nuclear matter properties and ground-state
properties of finite spherical nuclei (binding
energy and charge radius).
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Fully-consistent RPA calculation
RPA equation
Uncorrelated polarization tensor obtained by
RHA Green function
Density part
Feynman (vacuum polarization) part
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Vacuum-polarization (Feynman) part
Effective action
Mesons at initial and final vertices
Vacuum polarization is given by the functional
derivatives of the effective action.
A
B
A. Haga et al., Phys. Rev. C72 (2005)
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Isoscalar giant quadrupole resonances
The model with the vacuum polarization reproduces
the data on the ISGQR !
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Excitation energies of ISGQR as a function of the
relativistic effective mass.
The relativistic effective mass m/m0.8 is
required to reproduce experimental ISGQR
energies.
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Two-body Interaction
fp0.08, mp139MeV
g is obtained by fitting with the peak of the
Gamow-Teller resonance in 208Pb. Then, the value
of g is model-dependent as,
RHAT RHAT RHA TM1 NL3
g 0.69 0.89 0.96 0.69 0.55
which is the strength of tensor force.
g is sensitive to the value of
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GTR Distribution
Fitting g with the GTR peak, 19.2MeV, the shape
becomes very similar.
RHAT TM1 NL3
Ikeda sum 90.5 89.0 88.4
Exp. 60-70
Cut Off energy 50MeV. The rest comes from the
excitations larger than 50MeVantinucleon states.
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Magnetic dipole (M1) resonance
Using the same interaction (and g) as GTR
analysis,
RHAT can reproduce the excitation energy !
On the other hand,
RHAT TM1 NL3
Strength 27.6 28.9 31.5
Exp.17.5
Strength is still overestimated though it is
suppressed by the vacuum effect.
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Shell structure for unstable nuclei
76Fe RHA BCS calculation
NL3 ?E -5.045 MeV (0.734) RHAT ?E -6.382
MeV (0.710)
76Fe
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ß-decay life times in 78Ni
78Ni
T1/2 2.0 sec (NL3)
T1/2 0.6 sec (RHAT)
f0
Exp. T1/2 0.3 sec
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Summary

• We have developed the calculation method of the
  vacuum polarization in relativistic Hartree
  approximation and fully-consistent RHA RPA
  calculation using the derivative-expansion
  method.
• The RHA calculation produces the enhanced
  effective mass naturally, because the inclusion
  of vacuum effect makes meson fields weak.
• We have found that the relativistic effective
  mass is about 0.8 to reproduce the ISGQR
  excitation energies.
• The quenching of the Gamow-Teller sum rule still
  remains with the vacuum polarization. In
  addition, we found the quenching of the M1
  resonance caused by the vacuum polarization.
• The inclusion of the vacuum polarization affects
  the shell structure around the Fermi level. As a
  result, the beta-decay life time in 78Ni is
  improved by this effect.

The beta-decay and nuclear polarization analyses
in unstable nucleus give us the evidence of the
large effective mass, that is, a role of the
vacuum polarization.