Transcript Diapositiva 1 - Dipartimento di Fisica

The physics of nuclear collective states:
old questions and new trends
G. Colò
Congresso del Dipartimento di Fisica
Highlights in Physics 2005
October 2005, Dipartimento di Fisica,
Università di Milano
An old question: the nucleon-nucleon (NN) interaction
QCD
Fit to observables
(scattering
data)
Problem not yet solved,
despite recent progress
(cf., e.g., chiral PT)
free NN interaction
Knowing the free interaction, we still have to describe
the hierarchy of the many-body correlations inside the
nucleus. Through them, the interaction is very strongly
renormalized.
Since quite recently, it is possible to perform ab-initio
calculations using the free NN interaction for light nuclei
up to A ~12. (Price to be paid: 103-104 CPU hours…).
For medium-heavy systems, this is simply not possible
and one is obliged to resort to an effective force.
We are simply forced to simplify the force (B.R. Mottelson)
Building directly an effective NN interaction
free NN interaction
Fit to observables
effective NN interaction
relativistic models (RMF)
non-relativistic models:
Skyrme, Gogny
What observables ?
• Nuclear matter properties (saturation point)
• Properties of a limited set of nuclei (total binding
energy, charge radii)
After that, we dispose of Veff and Heff = T + Veff.
The Density
effectivefunctional
interaction defines an energy
functional like
in DFT
theory
E   Hˆ    Hˆ eff   Eˆ 

Slater determinant
  A (1 (r1 )     A (rA ))
Mean field:
E
ˆ
h
ˆ
 ˆ
density matrix
A
ˆ (r, r' )   i (r ) i (r' )
i 1
Interaction:
2

E
ˆ
V 
ˆˆ
h[ρ] = δE / δρ = 0 defines the minumum of the energy
functional, that is, the ground-state mean field (through
the Hartree-Fock equations).
=
Z protons + N neutrons
The small oscillations around this minimum are obtained
within the self-consistent Random Phase Approximation
(RPA) and the restoring force is: δ2E / δρ2 .
Coherent superpositions of 1p-1h
=
Modes of nuclear excitations
MONOPOLE
In the isoscalar
resonances, the
n and p oscillate
in phase
In the isovector
case, the n and
p oscillate in
opposition
of
phase
DIPOLE
QUADRUPOLE
Normally in many spectra, both a giant resonance (GR)
and a low-lying state show up. The GR is made up with
high-lying transitions and it has a smooth A-dependence,
whereas the low-lying states depend critically on the
detailed shell structure around EFermi.
2hω
1hω
0hω
Nuclear vibrations = phonons
described as p-h superpositions (e.g.,
dipole, quadrupole, monopole)
Excited in inelastic scattering
Exp: GANIL
(Caen, Francia)
Theory: D.T. Khoa et al., NPA 706 (2002), 61
Charge-exchange excitations
They are induced by charge-exchange reactions, like (p,n) or (3He,t), so
that starting from (N,Z) states in the neighbouring nuclei (N,Z±1) are
excited.
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
decay, 2005
on
(p,n)
Z+1,N-1
(n,p)
Z,N
Z-1,N+1
double-β,
Cf. Poster (S. Fracasso)
Can we go towards “universal” functionals ?
• Ground-state properties of nuclei -
Cf. Poster (S. Baroni)
• Vibrational excitations (small- and large-amplitude)
• Nuclear deformations
• Rotations -
Cf. Talk (S. Leoni)
• Superfluid properties -
Cf. Talk (R.A. Broglia)
Nucleons →
Cooper pairs
If pairing is introduced, the energy functional depends on
both the usual density ρ=<ψ+(r)ψ(r)> and the abnormal
density κ=<ψ(r)ψ(r)> (κ=<ψ+(r)ψ+(r)>).
The system is described in terms of quasi-particles.
HF becomes HF-BCS or HFB, RPA becomes QRPA.
This kind of research is immersed in a blooming experimental
effort, aimed to finding the limits of nuclear existence, and
therefore where are the so called drip-lines.
…need to know
the drip lines for Z
larger than 10.
What is the most critical part of our
functional ?
In the nuclear systems there are neutrons and protons.
usual (stable) nuclei
neutron-rich (unstable) nuclei
neutron stars
The largest uncertainities
concern the ISOVECTOR,
or SYMMETRY part of the
energy functional.
The nuclear matter (N = Z and no Coulomb interaction) incompressibility
coefficient, K∞ , is a very important physical quantity in the study of nuclei,
supernova collapse, neutron stars, and heavy-ion collisions, since it is
directly related to the curvature of the nuclear matter (NM) equation of state
(EOS), E = E[ρ].
E/A [MeV]
ρ = 0.16 fm-3
E/A = -16 MeV
ρ [fm-3]
A compressional (“breathing”) mode is the Isoscalar Giant
Monopole Resonance (ISGMR).
Its first evidences date back to the early 1970s. More data
collected in the 1980s already showed that:
• the ISGMR manifests itself systematically in nuclei, and
• it corresponds to a well-defined single peak (~80 A-1/3
MeV) in heavy nuclei like Sn or Pb and is more fragmented
in lighter systems like Ca or Ni.
Recent data from Texas A&M University have better
precision than all previous ones (± 2% on the moments of
the strength function distribution).
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[ρ].
K∞ in nuclear matter (analytic)
IT PROVIDES AT THE SAME TIME
EISGMR (by means of selfconsistent RPA calculations)
EISGMR
RPA
Eexp
Skyrme
Gogny
RMF
220
240
260
Extracted value of K∞
K∞ [MeV]
SLy4 protocol, α=1/6
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.
K∞ around 230-240 MeV.
The ISGMR and the nuclear incompressibility:
In the past, large uncertainities plagued our knowledge of
K∞ for which values as low as 180 MeV or as large as 300
MeV have been proposed.
First attempts of microscopic calculations suffered from
many approximations.
Recent careful work has been carried out.
Relativistic mean field (RMF) plus RPA: lower limit for K∞
equal to 250 MeV.
Together with our results, this leads to
→ K∞ = 240 ± 10 MeV.
Photon absorbtion excites the dipole
states in an exclusive way
escape width Γ↑
Γexp = Γ↑ + Γ↓
spreading width 
Is there a soft dipole ?
Only in light nuclei ?
excess neutrons
“core” with p and n
11Li
on different targets
GSI : 280 MeV/nucleon
NPA 619 (1997) 151
From the astrophysicist’s point of view, the importance of the
low-lying dipole stems from its role in the nucleosynthesis: the
(,n) or (n,) cross sections affect the formation rate in the rprocess. Claim of the importance of the “pygmy” states:
Red: empirical
Blue: no pygmy
Green: with pygmy
IT IS IMPORTANT TO HAVE RELIABLE
MEASUREMENTS AND MODEL PREDICTIONS !
The effective Hamiltonian Heff is diagonalized in a
larger space including not only the particle-hole
configurations, but also the more complicated states
made up with 2 particle-2 hole-type states.
Going beyond the mean field (i.e., the description in
terms of the simple one-body density), we can obtain
agreement with the experimental dipole strength in
different nuclei - including the width.
ANHARMONICITIES !
D.Sarchi,P.F.Bortignon,G.Colò (2004)
D. Sarchi et al., PLB
601 (2004) 27.
The high energy state (the usual giant dipole resonance) shows n and p in
opposition of phase, while the lowest states are pure neutron states at the
surface.
The amount of strength at low energy seems in agreement with preliminary
data from GSI.
Conclusions and prospects
Microscopic nuclear energy functionals: overall
reasonable, if one does not look too much at details.
properties
are
Problem: extrapolation far from stability. The study of exotic nuclei is
still in its infancy. It should help to fix the isovector part of the
functional, and allow to make predictions also for astrophysics.
Other challenges:
• Exotic modes ? Breaking of irrotationality.
• Pairing in drip-line systems.
• Relativistic or non-relativistic functionals ?
• Merging structure and reaction theories ?
The symmetry energy (Esym or S)
At saturation:
J=24-40 MeV