What can we learn from vibrational states

1
What can we learn from vibrational states ? the
isoscalar and the charge-exchange excitations
ECT Workshop The Physics Opportunities
with 16-21/1/2006
G. Colò
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Modes of nuclear excitations
MONOPOLE
In the isoscalar resonances, the n and p
oscillate in phase
DIPOLE
In the isovector case, the n and p oscillate in
opposition of phase
QUADRUPOLE
3
Self-consistent mean field calculations (and
extensions) are probably the only possible
framework in order to understand the structure of
medium-heavy nuclei. The study of vibrational
excitation is instrumental in order to constrain
the effective nucleon-nucleon interaction.

• Both the non-relativistic Veff (Skyrme or Gogny)
  and RMF Lagrangians are fitted using
• Nuclear matter properties (saturation point)
• G.s. properties of a limited set of nuclei
  (total binding energy, charge radii).

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Density functional theory
The effective interaction defines an energy
functional like in DFT
Slater determinant
density matrix
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Can we go towards universal functionals ?

• Ground-state properties of nuclei
• Vibrational excitations (small- and
  large-amplitude)
• Nuclear deformations
• Rotations
• Superfluid properties

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What is the most critical part of the nuclear
energy functional ?
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The Isoscalar Monopole and the nuclear
incompressibility
The nuclear matter (N Z and no Coulomb
interaction) incompressibility coefficient, K8 ,
is a very important physical quantity in the
study of nuclei, supernova collapse, neutron
stars, and heavy-ion collisions.
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Microscopic link E(ISGMR) ? nuclear
incompressibility
Nowadays, we give credit to the idea that the
link should be provided microscopically. The key
concept is the Energy Functional E?.
Skyrme Gogny RMF
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Until 2 years ago The extraction of the
nuclear incompressibility from the monopole data
was plagued by a strong model dependence the
Skyrme energy functionals seemed to point to
210-220 MeV, the Gogny functionals to 235 MeV,
and the relativistic functionals to 250-270 MeV.
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Results for the ISGMR Cf. G. Colò, N. Van Giai,
J. Meyer, K. Bennaceur and P. Bonche,
Microscopic determination of the nuclear
incompressibility within the non-relativistic
framework, Phys. Rev. C70 (2004) 024307.
Full agreement with Gogny before we had SC
violations
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We have increased the exponent in the density
dependence of the Skyrme force We have also
increased the density dependence of the symmetry
energy (Kt) By-product decrease of m
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Ksurf cK? with c -1 (cf. Ref. 1). KA K?
(non rel.)(1cA-1/3) Kt (non rel.) d2 KCoul
(non rel.) Z2 A-4/3 KA K? (rel.)(1cA-1/3)
Kt (rel.) d2 KCoul (rel.) Z2 A-4/3 KCoul
should not vary much from the non-relativistic to
the relativistic description. But since both the
terms which include K? and Kt contribute, a more
negative Kt can lead to a the extraction of a
larger K? (and vice-versa). Remember Kt is
negative and depends on the density dependence
of the symmetry energy ! 1 M. Centelles et
al., Phys. Rev. C65 (2002) 044304
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CONCLUSION FROM THE ISGMR
Fully self-consistent calculations of the ISGMR
using Skyrme forces lead to K8 230-240
MeV. Relativistic mean field (RMF) plus RPA
lower limit for K8 equal to 250 MeV. It is
possible to build bona fide Skyrme forces so that
the incompressibility is close to the
relativistic value. ? K8 240 10 MeV. To
reduce this uncertainity one should fix the
density dependence of the symmetry energy.
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How to experimentally discriminate between models
?
E A-1/3 dE/E dA/3A Even if we take a long
isotopic chain of stable, spherical isotopes Sn
? dE/E is of the order of 3, that is, 0.45 MeV
( 2sexp). If we are able to measure outside
this range (that is, we consider unstable nuclei)
we can have a larger variation of the monopole
energy and be able to see the effect of the
symmetry term.
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A word about the energies which are required
The most recent experiments on stable nuclei
employ a particles at 400 MeV, which means 100
MeV/u (e.g., at RCNP, Osaka). However, previous
experiments at lower energies (of the order of 60
MeV/u) had given positive results, although maybe
with larger background and less accurate
determination of the details of the structure of
the vibrational mode.
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Speculations
Problem calculations SO FAR are consistent with
the idea that only light nuclei develop a halo
and halo excitations are not collective.
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Low-energy quadrupole

• The GQR is lower than the systematics (62A-1/3)
  by about 10

• Implications for the effective mass since E
  (m/m)1/2.

• The neutron content is much larger (about 50)
  than N/Z

• It cannot be separated by low-lying pure neutron
  strength

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• The low-lying quadrupole, and to some extent,
  the usual GQR, do not have the standard
  isospin. The low-lying strength is half IS and
  half IV. To reproduce it amounts to testing the
  energy functional in a very different situation
  compared to standard nuclei.
• Relationship with the evolution of the effective
  mass far from stability.
• Low-energy should make the quadrupole a better
  physics case for EURISOL.

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Folding model calculation D.T. Khoa et al., NPA
706 (2002), 61
S isotopes 30,32 S 38,40 S
Use of microscopic (QRPA) transition densities.
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Pairing far from stability
If the collective modes involve excitations not
so far from the Fermi surface, in open-shell
isotopes pairing is obviously important.
Do we have a theory for pairing ?
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Example of an effective pairing force. Surface
pairing ?0 ?sat Mixed pairing ?0 2?sat
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F.Barranco, R.A.Broglia, G. Colò, G.Gori,
E.Vigezzi, P.F. Bortignon (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
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CONCLUSION
Probably EURISOL can be able to provide answers
to the problem of pairing (i.e., how to treat in
a unified way the usual like-particle pairing
in nuclei with usual N/Z ratios and the pairing
in n-rich systems) by means of other experiments
like TRANSFER reactions. However, low-lying
excited states are sensitive BOTH to
particle-hole correlations and pairing
correlations.
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Charge-exchange excitations
A systematic picture of these states is
missing. However, such a knowledge would be
important for astrophysics, or neutrino physics
Nuclear matrix elements have to be evaluated
with uncertainities of less than 20-30 to
establish the neutrino mass spectrum. K. Zuber,
workshop on double-ß, decay, 2005
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Strict connection with the isospin symmetry if
H commutes with isospin, the IAR must lie at zero
energy. BCS breaks the symmetry and only
self-consistent QRPA can restore it. H includes
parts which provide explicit symmetry breaking
the Coulomb interaction, charge-breaking terms in
the NN interaction, e.m. spin-orbit.
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Can the energy difference GT-IAR provide a
measure of the neutron skin ?
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Non spin-flip IAR, isovector monopole, dipole
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The IV monopole (r2t)
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Can we see the problem ?
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Self-consistent CE RPA based on Skyrme have been
available for many years. On the other hand,
essentially all the calculations made for
open-shell systems are phenomenological QRPA
based on Woods-Saxon plus a simple separable
force with adjustable gph and gpp parameters. ?
Need of a self-consistent QRPA !
31
IAR energies in 104-132Sn
Exp K. Pham et al., PRC 51 (1995) 526.
S. Fracasso and G. Colò, The fully
self-consistent charge-exchange QRPA and its
application to the Isobaric Analog Resonances,
Phys. Rev. C72 (2005).
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CONCLUSION

• In the charge-exchange sector, the energy below
  about 60 MeV/u seems more favourable for the non
  spin-flip excitations, in contrast with the fact
  that the GT window is above 100 MeV/u.
  Complementarity of EURISOL with respect to
  higher-energy facilities.
• The charge-exchange modes have been always quite
  elusive in this channel, with the exception of
  the IAR.
• If RIA starts, certainly emphasis will be given
  to these kind of studies (JINA Nuclear
  Astrophysics).
• Inverse kinematics ?