Couplage de phonons = state of the art of

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Couplage de phonons
state of the art of extended RPA calculations
Espace de Structure Nucléaire Théorique SPhN,
Saclay, January 11-12, 2005
G. Colò
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Many talks in this workshop have shown the
progress in the field of self-consistent mean
field calculations which employ effective
nucleon-nucleon interactions. Ground state
vibrational states HF
plus RPA extended to HF-BCS or HFB plus
QRPA (Skyrme or Gogny forces)
Aim of this talk is (a) to provide motivations to
introduce correlations which go beyond mean
field, (b) to review some of the calculations
along this line, and (c) to stress some open
problems and challenges.
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Photoabsorbtion cross section ? GDR
Kamerdzhiev et al.
120Sn
Berman-Fultz
Continuum-RPA ? escape width G? Gexp G? G?
spreading width
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IV dipole
IS quadrupole
The spreading width is due to the coupling of the
simple 1p-1h configurations (or 2 quasiparticle)
with more complex states.
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Second RPA Gn S Xph ph-1gt - Yph p-1hgt
Xphph ph-1ph-1gt - Y phph p-1hp-1hgt
The theory is formally sound (e.g., EWSRs are
conserved). Handling an explicit 2p-2h basis is
feasible only in light nuclei. Projecting the
SRPA equations in the 1p-1h space, one gets a
RPA-like equation.
S (E)


the interaction among 2p-2h states is neglected
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a
ß
Nucleons are coupled to phonons, mainly density
vibrations (2,3-). In other words, the nuclear
mean field undergoes fluctuations which are felt
by the particles.
To deal with these phenomena, a nuclear field
theory has been developed by the Copenhagen
group. Phenomenological particle-vibration
coupling of the type lt a VPV ß gt ? dr
ua(r) C(dU/dr) uß(r) lt p YL p gt One
can work out the particle-vibration coupling with
effective forces and microscopic
phonons Removal of simple approximations
(assumption of good isospin for vibrations).
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The phonon coupling has been known for many years
to be important for the understanding of s.p.
states around the 208Pb core.
Exp. HF HF
phonons
C.Mahaux et al., Phys. Rep., 1985 ? PV coupling
increases m
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Spin-orbit splitting ?E(?h9/2-?h11/2) MeV
HF HFphon. SLy4 9.44
8.52 SGII 7.44 6.78 Exp.
value is 6.75
HF HFphon. Exp.
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The state a is not a 2p-2h state but 1p-1h plus
one phonon
Sphph(E)
Pauli principle ! Re and Im S
cf. G.F.Bertsch et al., RMP 55 (1983) 287
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In the last decade we have developed, within a
Milano-Orsay collaboration, a microscopic model
aimed to a detailed description of GR excitation
and decay G. Colò et al. Phys. Rev. C50, 1496
(1994). The model includes the coupling with
1p-1h plus 1 phonon configurations and with the
continuum (allowing the description of particle
decay). The model has been able to reproduce the
total width of the GMR, and total and partial
decay widths of GTR and IAR in 208Pb. Recently,
we have extended the model to include pairing
correlations (without the continuum coupling).
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The IAS a stringent test
The measured total width (Gexp230 keV) is well
reproduced. The accuracy of the symmetry
restoration (if VCoul0) can be established.
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Extension starting point is HF-BCS QRPA
2qp states are coupled to configurations made up
with 2qp plus a phonon. Compared to the case
without pairing, more diagrams arise.
NPA 696 (2001) 427
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Cross section integrated up to 15 MeV
Experiment A. Leistenschneider et al. Phys.
Rev. Lett. 86, 5442 (2001) Theory G. Colò and
P.F. Bortignon QRPA phonon coupling
Nucl. Phys. A 696, 427 (2001)
H. Sagawa and T. Suzuki large scale shell
model Phys. Rev. C 59,
3116 (1999)
The phonon coupling shifts strength down
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S B(E1) in e2fm2 lt 6 MeV lt 8
MeV Exp. 0.53 0.80 Th.
0.52 1.27
D. Sarchi et al. PLB 601 (2004) 27. (QRPA-PC)
N. Ryezayeva et al., PRL 89 (2002) 272502
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Other models

• QPM (Quasi-particle phonon model)
• It has been developed in Dubna (V. Soloviev and
  collaborators). It is not a self-consistent
  model.
• Woods-Saxon basis
• Separable force
• A basis of 1 phonon AND 2 phonon states is
  constructed
• The interaction among phonons is diagonalized

Continuum ?
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Microscopic description of low-lying 2
In NZ nuclei, isospin is a good quantum number
and the lowest states are purely isoscalar. In
most vibrational nuclei, after the first 2, a
triplet of two-phonon states 0, 2, 4 is
found. H based on Woods-Saxon plus a separable
interaction. Beyond RPA ? diagonalization in a
space including 1, 2 and 3 phonon states (QPM).
92Zr
N.Lo Iudice,Ch.Stoyanov (2004)
Both 21 and 22 are one-phonon states. The p-n
symmetry is broken, mainly in the second state.
Mixture of collective and non-collective
components. Simplistic pictures (pure boson) or
numerical truncation of the relevant model space
would fail !
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A.Severyukhin, V.Voronov, N. Van Giai

• Skyrme Hartree-Fock
• Finite-rank separable approximation for the
  Skyrme residual force

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• S. Kamerdzhiev et al.
• Woods-Saxon basis ? but they need to undress
  the states
• Separable force

The model has been extended so that it includes
continuum and pairing also, it includes the
so-called ground-state correlations (GSC).
Sometimes, there are large violations of the sum
rules (GSC induce sizeable strength at
low-energy).
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F.Barranco et al. (2004)
Diagonalizing the v14 interaction within the
generalized BCS (on a HF basis) account for only
half of the experimental gap in 120Sn.
The remaining part comes from renormalization due
to the particle vibration coupling.
it is possible to treat on the same footing
and
Cf. P. Schuck !
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Some final remarks
While in the case of the pairing channel we
dispose of a clean scheme to handle at the same
time the bare force and the polarization
contributions (i.e., PV coupling), this is not
the case in the particle-hole channel (i.e.,
vibrational states, GR). The interactions have
been adjusted at the mean field level. Although
the shifts induced by the PV coupling are often
not large, in principle consistency would require
to go beyond RPA in a more coherent scheme ?
DFT. Relativistic theories for phonon coupling ?