Charge Exchange Excitations and the r_n - r_p issue in relativistic RPA

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Charge Exchange Excitations and the r_n - r_p
issue in relativistic RPA

• Nguyen Van Giai
• Institut de Physique Nucléaire
• Université Paris-Sud

Collaborators Haozhao Liang, Jie Meng
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Contents

• Introduction
• Theory background
• Relativistic Hartree-Fock (RHF)
• Charge-exchange RPA
• Results and discussions
• Self-consistency check isospin restoration
• Isobaric Analog States (IAS)
• Gamow-Teller Resonances (GTR)
• Spin-dipole (SD) excitations and r_n - r_p
  values
• Summary

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Introduction
What is charge exchange excitations?
example 208Pb (3He, t) 208Bi
H. Akimune et al. PRC 1995.
IAS ?S0 ?L0 GTR ?S1 ?L0 SDR ?S1 ?L1

• Charge exchange excitations can
• provide direct information on the spin and
  spin-isospin properties of the effective nuclear
  interaction.
• determine the neutron rms radius by SDR or other
  spin-isospin modes.
• determine the GT ß-decay rates to decide the path
  of the r-process.

A. Krasznahorkay et al. PRL 1999 K. Yako et al.
PRC 2006 D. Vretenar et al. PRL 2003.
J. Engel et al. PRC 1999.
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• The relativistic Hartree-Fock (RHF) context

Early attempts A. Bouyssy et al., 1985, 1987
S. Marcos et al, 1993,
2004
Recent progress W.H. Long et al., 2006, 2007,
2008

• exchange (Fock) terms included
• explicit effects of pion- and rho-tensor
  couplings
• density-dependent couplings
• quantitative description of ground state
  properties

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Relativistic charge-exchange RPA

• About 30 years ago, Skyrme-RPA model was extended
  to the charge exchange channel.
• Recently, fully self-consistent CE Skyrme-QRPA
  models have been developed.
• CE Relativistic (Q)RPA calculations have been
  performed within the relativistic mean field
  (RMF) framework.
• Our goal establish a fully self-consistent CE
  RRPA model based on relativistic Hartree-Fock
  (RHF) approach.

N. Auerbach, N. Van Giai and A. Yeverechyahu,
1980.
S. Fracasso and G. Colo, PRC 2005.
C. De Conti et al., PLB 1998 D. Vretenar et al.,
PRL 2003 N. Parr et al., PRC 2004.
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Theory framework - DDRHF

• Lagrangian density

where,

• Density-dependent meson-nucleon couplings
• s- and ?-meson
• ?- and p-meson

W.H. Long et al., PLB 2006.
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Theory framework - DDRHF

• Hamiltonian

where represent the corresponding
meson propagators,
and the interacting matrices read,

• RHF can take the exchange contributions and
  pion-induced interaction into account explicitly.

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Theory framework RPA equations

• 1p-1h configurations

t channel
t- channel
X amplitude
Y amplitude
X amplitude
Y amplitude

• RPA equations combining t- and t channels

where A and B are the matrix elements of
particle-hole residual interactions.

• Orthogonality condition

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CE RPA in relativistic framework

• Self-consistent RPA the particle-hole residual
  interaction is derived from the same Lagrangian
  as ground state.

one meson exchange
RMF RPA
RHF RPA
p
p
p
h
h
h
-
h
p
h
p
p
h
exchange terms
?
?
?
?
?
no in-medium effect
re-fitting
? g1/3
?
?
C. De Conti et al. PLB 1998. D. Vretenar et al.
PRL 2003. N. Parr et al. PRC 2004.
For the first time, a fully self-consistent RRPA
model is established.
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IAS checkContributions from different channels

• The IAS would be degenerate with its isobaric
  multiplet partners, if the nuclear Hamiltonian
  were completely charge-independent.

• The self-consistency of our model is satisfied.
• The isoscalar mesons play an extremely important
  role through the exchange terms.
• The rho meson is important as expected.
• The coupling strength of pion and g coefficient
  are somewhat under control, g' is no longer a
  free parameter.

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IAS and GTR
IAS

• IAS excitation energies are mainly shifted from
  zero energy by the repulsive Coulomb potential.
• It is not sensitive to the model effective
  nucleon-meson or nucleon-nucleon interactions.

• In RHFRPA, the isoscalar mesons play an
  essential role through the exchange terms. The
  pion little affects the GTR position.

GTR
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IAS and GTR

• RHFRPA results for excitation energies of IAS
  and GTR. All units are in MeV.

exp aD.J. Horen et al. 1980 H. Akimune et al.
1995. bD.E. Bainum et al. 1980 T. Wakasa et al.
1997. cB.D. Anderson et al. 1985.
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Spin Dipole Resonance and neutron skin

• Neutron skin thickness can be determined by
  model-independent SD sum rule.
• RHFRPA calculations reproduce the strength
  distributions well up to around 30 MeV in both
  channels.
• 2p-2h configurations are missing.

exp K. Yako et al. PRC 2006.
neutron skin thickness of 90Zr from calculated
and experimental SD sum rules
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Summary

• A fully self-consistent charge-exchange RRPA
  approach has been established
• Accuracy of the method checked by degeneracy of
  isobaric analog and parent states
• Isoscalar mesons play important role in
  charge-exchange modes via exchange interactions
• Gamow-Teller resonances are correctly described
  
• Spin-Dipole strength distributions in both
  channels are well reproduced up to the giant
  resonance region
• The Spin-Dipole excitations, and other
  charge-exchange excitations, can be used as
  probes of the thickness of neutron skins in nuclei

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CollaboratorsWenhui LONG (PKU)Haozhao LIANG
(PKU/IPN Orsay)Jie MENG (PKU)

• Thank you!