Nature of low-energy dipole
states in exotic nuclei
Xavier Roca-Maza
Università degli Studi di Milano, Via Celoria 16, I-20133, Milano
SPES One-day Workshop on "Collective Excitations of Exotic
Nuclei"
December 9, 2013, Milano
1
Motivation
Giant Resonances are collective excitations of atomic nuclei.
The measurement of such (high-energy) excitations has
allowed us to constraint many properties of the nuclear
equation of state
Giant Monopole Resonance → K0
[G. Colò, N. Van Giai, J. Meyer, K. Bennaceur and P. Bonche, Phys. Rev. C 70, 024307 (2004)]
Giant Dipole Resonance → S2 (ρ = 0.1 fm−3 )
[Luca Trippa, Gianluca Colò, and Enrico Vigezzi, Phys. Rev. C 77, 061304(R) (2008)]
Giant Quadrupole Resonance → m∗
[“Nuclear Structure”, Bohr & Mottelson → Ex =
p
2m/m∗ hω]
Experiments on Giant Resonances constitute a basic tool for
the study of fundamental properties of the nuclear strong
interaction.
2
Motivation
What is the Pygmy Dipole Strength (PDS)?
Giant Dipole Resonance
neutron-capture rates in the
r−processes† since the energy
window for both observables is
similar
if collective, it may be correlated with the slope of the
symmetry energy (L): a basic property of the nuclear EoS
that impacts on a variety of physical systems: from the
very big (neutron stars) to the very small (neutron skin)
Pygmy dipole
◮
Low-energy peak in the dipole
response of neutron rich (exotic)
nuclei
It might be relevant in ...
◮
The PDS seems to appear in certain models as a coherent
excitation (resonance), and not in others (shell effect)
†
β−decay rates and radiative neutron capture. In the latter, σ may increase due to the low-energy E1 enhancement
when approaching the neutron drip line. [A. C. Larsen and S. Goriely, PRC 82, 014318 (2010)]
3
Motivation
What is the Pygmy Dipole Strength (PDS)?
Low-energy peak in the dipole
response of neutron rich (exotic)
nuclei
Equation of state for
It uniform
might benuclear
relevantmatter
in ...
Giant Dipole Resonance
neutron-capture rates in the
r−processes† since the energy
window for both observables is
similar
if collective, it may be correlated with the slope of the
symmetry energy (L): a basic property of the nuclear EoS
2
e(ρ, δ) =on
e(ρ,
δ = 0) +
+ Osystems:
δ4 withfrom the
that impacts
a variety
ofS(ρ)δ
physical
ρn − ρp
very big (neutron stars)
δ = to the very small (neutron skin)
Pygmy dipole
◮
◮
ρn + ρp
2
The PDS seems toρ −
appear
in certain
as a coherent
ρ0
ρ − ρ0models
3
+
K
+
O
(ρ
−
ρ
)
S(ρ)
=
J
+
L
sym
0
excitation (resonance),
(shell effect)
3ρ0 and not in others
3ρ0
†
β−decay rates and radiative neutron capture. In the latter, σ may increase due to the low-energy E1 enhancement
when approaching the neutron drip line. [A. C. Larsen and S. Goriely, PRC 82, 014318 (2010)]
3
Motivation
What is the Pygmy Dipole Strength (PDS)?
Giant Dipole Resonance
Low-energy peak in the dipole
response of neutron rich (exotic)
nuclei
It might be relevant in ...
neutron-capture rates in the
r−processes† since the energy
window for both observables is
similar
◮ if collective, it may be correlated with the slope of the
symmetry energy: a basic property of the nuclear EoS
that impacts on a variety of physical systems: from the
very big (neutron stars) to the very small (neutron skin)
The PDS seems to appear in certain models as a coherent
excitation (resonance), and not in others (shell effect)
Pygmy dipole
†
◮
β−decay rates and radiative neutron capture. In the latter, σ may increase due to the low-energy E1 enhancement
when approaching the neutron drip line. [A. C. Larsen and S. Goriely, PRC 82, 014318 (2010)]
4
Motivation: experimentally, the PDS splits
into two parts ...
Alpha-gamma coincidence
experiments allow the
separation of E1 excitations in
...
J. Endres et al. Phys. Rev. Lett. 105, 212503 (2010)
◮
one part excited via
(α, α′ γ) [dominant
isoscalar excitation where
the probe mainly interacts
with the nuclear surface]
and (γ, γ′ )
◮
and the other only via
(γ, γ′ ) [dominant isovector
excitation where the
probe interacts with the
whole nucleus]
5
Motivation: bibliography (non-exhaustive list)
There is a great interest on the PDS ....
... on experiment
◮
Experimental Studies of the Pygmy Dipole Resonance by D. Savran, T. Aumann and A. Zilges, Prog. Part.
Phys. and Nucl. 70 210-245 (2013).
◮
Evidence for Pygmy and Giant Dipole Resonances in 130 Sn and 132 Sn by P. Adrich et al., Phys. Rev.
Lett. 95, 132501 (2005).
Concentration of electric dipole strength below the neutron separation energy in N=82 nuclei by A.
Zilges et al., Phys. Lett. B542, 43 (2002).
◮
◮
◮
The photoresponse of stable N=82 nuclei below 10 MeV by S. Volz et al., Nucl. Phys. A779, 1 (2006).
◮
Search for the Pygmy Dipole Resonance in 68 Ni at 600 MeV/nucleon by O. Wieland et al., Phys. Rev.
Lett. 102, 092502 (2009).
Nature of Low-Energy Dipole Strength in Nuclei: The Case of a Resonance at Particle Threshold in
208Pb by N. Ryezayeva et al., Phys. Rev. Lett. 89, 272502 (2002).
... and theory
◮
Multiphonon excitations and pygmy resonances in tin isotopes by E.G. Lanza, F. Catara, D. Gambacurta
M.V. Andres and Ph. Chomaz, Phys. Rev. C 79 054615 (2009) and Pygmy dipole resonances in the tin
region by N. Tsoneva and H. Lenske, Phys. Rev. C 77 024321 (2008).
◮
Exotic modes of excitation in atomic nuclei far from stability by Nils Paar, Dario Vretenar, Elias Khan and
Gianluca Colò, Rep. Prog. Phys. 70 691 (2007).
◮
Constraints on the symmetry energy and neutron skins from pygmy resonances in 68 Ni and 132 Sn by
Andrea Carbone, Gianluca Colò, Angela Bracco, Li-Gang Cao, Pier Francesco Bortignon, Franco Camera,
and Oliver Wieland, Phys. Rev. C 81, 041301 (2010).
◮
Nuclear symmetry energy and neutron skins derived from pygmy dipole resonances by A. Klimkiewicz
et al., Phys. Rev. C 76, 051603(R) (2007).
◮
Low-lying dipole response: Isospin character and collectivity in 68 Ni, 132 Sn, and 208 Pb by X.
Roca-Maza, G. Pozzi, M. Brenna, K. Mizuyama, and G. Colò, Phys. Rev. C 85, 024601 (2012).
◮
Pygmy resonances and neutron skins by J. Piekarewicz, Phys. Rev. C 83, 034319 (2011).
6
Contents
Microscopic analysis of the PDS: model dependence and
sensitivity to the symmetry energy
We study the PDS within the self-consistent HF+RPA
approach in the exotic 68 Ni and 132 Sn and the stable 208 Pb
nuclei. For that, we use three Skyrme interactions with very
different isovector properties (L ranges from 40 MeV to 100
MeV). We focus on:
◮
RPA and unperturbed dipole strength.
◮
the transition densities.
◮
the isoscalar or isovector nature.
◮
the most relevant p-h contributions.
X. Roca-Maza, G. Pozzi, M.Brenna, K. Mizuyama and G. Colò, Phys. Rev. C 85 024601 (2012)
7
Contents
Microscopic analysis of the PDS: model dependence and
sensitivity to the symmetry energy
We study the PDS within
the self-consistent HF+RPA
L estimates
approach in the exotic 68 Ni and 132 Sn and the stable 208 Pb
nuclei. For that, we use three Skyrme interactions with very
different isovector properties (L ranges from 40 MeV to 100
MeV). We focus on:
χ Lagrangian and
Q. Montecarlo
Neutron-Star
Observations
p & α scattering
charge ex.
Antiprotonic
Atoms
Neutron Matter
Kebeler et al. PRL105 (2010) 161102
and Gandolfi et al. PRC85 (2012) 032801 (R)
Mass-Radius (Neutron Star)
Steiner et al. Astrophys. J. 722 (2010) 33
Lie-Wen Chen et al. PRC 82 (2010) 024321
Neutron Skin
Neutron Skin
Mass
Nuclear
Model Fit
Kortelainen et al. PRC 82 (2010) 024313
Mass
Danielewicz NPA 727 (2003) 233
Empirical
Heavy Ion
Collisions
n−p Emission Ratio
Isospin Diffusion
IVGQR
Agrawal et al. PRL109 (2012) 262501
Famiano et al. PRL 97 (2006) 052701
Tsang et al. PRL 103 (2009) 122701
Roca-Maza et al. PRC 87 (2013) 034301
Dipole Polarizability
◮
Centelles et al. PRL 102 (2009) 122502
Warda et al. PRC 80 (2009) 024316
Neutron Skin
Roca-Maza et al. in preparation (2013)
RPA and unperturbed dipole strength.
Giant
Resonances
Trippa et al. PRC 77 (2008) 061304(R)
GDR
Klimkiewicz et al. PRC 76 (2007) 051603(R)
PDR
PDR
Carbone et al. PRC 81 (2010) 041301(R)
◮
the transition densities.
◮
the isoscalar or20isovector
40 60 80 nature.
100 120
◮
the most relevant p-h contributions.
N−A scattering
Charge Ex. Reactions
Energy Levels
Parity Violating
e-scattering
Optical Potential
Parity Violating Asymmetry
Xu et al. PRC 82 (2010) 054607
PREX Collab. PRL 108 112502 (2012)
L (MeV)
X. Viñas et al. EPJA special volume on the symmetry energy
X. Roca-Maza, G. Pozzi, M.Brenna, K. Mizuyama and G. Colò, Phys. Rev. C 85 024601 (2012)
7
Contents
Microscopic analysis of the PDS: model dependence
and sensitivity to the symmetry energy
We study the PDS within the self-consistent HF+RPA approach
in the exotic 68 Ni and 132 Sn and the stable 208 Pb nuclei. For
that, we use three Skyrme interactions with very different
isovector properties (L ranges from 40 MeV to 100 MeV). We
focus on:
◮
RPA and unperturbed dipole strength.
◮
the transition densities.
◮
the isoscalar or isovector nature.
◮
the most relevant p-h contributions.
X. Roca-Maza, G. Pozzi, M.Brenna, K. Mizuyama and G. Colò, Phys. Rev. C 85 024601 (2012)
8
Dipole strength functions (IV)
50
7
SGII
SkI3
SLy5
0
9
10
11
68
Ni
12
3
30
5
10
20
15
25
SGII
SkI3
SLy5
80
−1
10
9
132
10
Exp. 9.8 MeV [2]
Sn
8
9
208
10
Pb
20
15
Energy [MeV]
15
20
SGII L = 37.6 MeV
SLy5 L = 48.3 MeV
SkI3 L = 100.5 MeV
Exp. 7.37 MeV [3]
10
10
Isovector properties of the interactions:
2
7
0
5
A. Carbone et. al., PRC81 (2010) 041301.
5
0
IV
8
larger L → larger PDS peak
Exp. 13.43 MeV [3]
15
0
5
20
Energy [MeV]
100
40
1
0
10
Energy [MeV]
60
2
IV
IV
Exp. 11 MeV [1]
5
4
2
2
1
0
B (E1) [fm MeV ]
40
−1
15
10
SGII
SkI3
SLy5
6
B (E1) [fm MeV ]
3
2
−1
B (E1) [fm MeV ]
20
20
Experiment:
[1] O. Wieland et. al., PRL 102 (2009) 092502.
[2] P. Adrich et. al., PRL 95 (2005) 132501.
[3] N. Ryezayeva et. al., PRL 89 (2002) 272502.
9
Microscopic analysis of the PDS
RPA versus unperturbed strength
40
35
40
SGII
SkI3
SLy5
68
35
Ni
30
30
25
25
20
20
15
15
10
10
5
5
IV
2
−1
B (E1) [fm MeV ]
Unperturbed
0
0
10
20 0
10
20 0
10
20
0
Energy [MeV]
- No low energy peak in the unperturbed response.
- Indications that the PDS may show some coherency depending
on the model. (RPA peaks do not coincide in energy with the unperturbed peak)
10
Microscopic analysis of the PDS
the transition densities (∼ amplitude of neutron and proton
transition probabilities as a function of r-coordinate)
r [fm]
0
2
r [fm]
6
4
rp rn
0.004
8
10
0
neutrons
protons
E = 9.77 MeV
-0.004
SkI3
E = 10.45 MeV
-0.008
0.004
E = 9.77 MeV
0.005
0
-0.005
SkI3
-0.01
E = 10.45 MeV
0.005
0
0
68
-0.004
-0.008
0
SGII
-0.01
0
10
isovector
isoscalar
0
−3
-0.008
0.004
8
-0.005
δρ(r) [fm ]
−3
δρ(r) [fm ]
SGII
6
4
rp rn
0.005
0
-0.004
2
Ni
2
4
6
r [fm]
-0.005
SLy5
8
68
Ni
-0.01
E = 9.30 MeV
10
0
2
4
6
SLy5
E = 9.30 MeV
8
10
r [fm]
Around the nuclear surface: all models clearly isoscalar.
In the interior: not clear nor definite trends in the studied
models.
11
Microscopic analysis of the PDS
Isoscalar or isovector?
BIV (E1) =
X Z Z
ν
A
drr3 δρn
ν (r) −
30
−1
B (E1) [fm MeV ]
Z
p
drr3 δρν (r)
30
68
SkI3
IS 70%
[0,R]
25
N
A
Ni
IS 70% 25
[R/2,R]
IS 70%
[0,R/2]
20
15
15
10
10
5
5
IV
2
20
0
10
15
20
25 10
15
20
25 10
15
20
0
25
Energy [MeV]
[N. Paar et. al., PRL103 (2009) 032502]
IS nature of the PDS due to outermost nucleons (neutrons in a
neutron-rich nucleus). The ∆rnp is correlated with I and L.
12
2
2
neutrons
protons
68
1f7/2 1g9/2
2d3/2
1f5/2
1g9/2
1f7/2
1g9/2
1f7/2 1g9/2
1f7/2 1g9/2
A
-1
2
Aq
ph (E1) |
ph,q
1f7/2
2p3/2 2d5/2
(E1) [e fm]
0
1f7/2 1g9/2
X
B(E1) ≡|
1
0
q
ph
The most relevant p-h
excitations in the IS and
IV dipole response
1
2p1/2 2d3/2
Ni
Microscopic
analysis of the PDS
SGII
SkI3
SLy5
E = 9.77 MeV
E = 10.45 MeV
E = 9.30 MeV
-2
8
10
12
14 8
10
12
14 8
10
12
-1
14
-2
Eph [MeV]
25
Ni
(E1) [e fm]
20
1f5/2
1f7/2
2p1/2
2p3/2
15
10
2p1/2
2p3/2
1f5/2
2d3/2
1g9/2
2d3/2
2d5/2
1f7/2
2d3/2
3s1/2
2d3/2
1g9/2
25
20
1f5/2
1f7/2
2p1/2
2d3/2
1g9/2
3s1/2
15
2p3/2
2d5/2
10
5
5
A
q
ph
neutrons
protons
68
0
0
-5
E = 10.45 MeV
E = 9.77 MeV
10
15
SLy5
SkI3
SGII
20 10
15
Eph [MeV]
E = 9.30 MeV
20 10
15
-5
20
The largest neutron p-h
contributions (around 8 with
BIS > 1) are coherent and all of
them (except one) correspond
to transitions of the outermost
neutrons → indicates that the
ISPDS is a collective mode
that may be correlated with
N − Z.
13
Collectivity: Coherence of the different
contributions
cumulative sum
cumulative sum
132
Sn
1
-2
0
SGII
π
SkI3
π
ν
10 20 30
nph
0
SLy5
π
ν
10 20 30
nph
0
IS
ph
0
-1
80
132
3
2
(E1) [e fm ]
100
20
SGII
π
ν
SkI3
π
ν
SLy5
π
ν
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 50
nph
nph
nph
10 20 30 40
nph
The largest p-h contributions
are:
40
0
ν
Sn
60
A
A
IV
(E1)
ph
[e fm]
3
◮
coherent in the IS channel,
◮
less coherent in the IV
channel.
14
2
1
0
8
9 10
8
9 10
E [MeV]
8
9 10
16
12
SkI3
SLy5
132
8.64 MeV
8.64 MeV
9.23 MeV
3
Sn
SGII
9.23 MeV
132
5
4
20
SLy5
8.52 MeV
SkI3
B(E1;IS) [s.p. units]
7
6 SGII
8.52 MeV
B(E1;IV) [s.p. units]
Single particle units: qualitative indications
Sn
8
4
0
8
9 10
8
9 10
E [MeV]
8
9 10
If different p-h states are contributing coherently to the PDS,
B(E1) in single-particle units should be clearly larger than 1.
15
Dipole strength functions (IS)
10
10
20
30
E (MeV)
Sn
4
10
20
E (MeV)
30
The response of the
low-energy pygmy state to an
isoscalar probe is comparable
to the high-energy states
corresponding to the ISGDR
20
3
6
−1
B(E1;IS) (10 fm MeV )
132
(b)
pygmy region
208
10
10
8
0
40
30
(b)
pygmy region
3
Ni
0
−1
6
68
0
B(E1;IS) (10 fm MeV )
20
2
6
12
(b)
pygmy region
−1
B(E1;IS) (10 fm MeV )
30
20
E (MeV)
30
Pb
40
16
Conclusions:
PDS in 68 Ni, 132 Sn, 208 Pb:
1 The IV (and IS) dipole response show a low-energy peak
in the strength function for all studied nuclei and models.
2 Such an IV peak (and also IS) increases in magnitude with
increasing values of L [in agreement with other works].
3 The collectivity associated with the RPA states giving rise
to the PDS show up depending on the nature of the probe
used for exciting the nucleus: there is systematically more
collectivity in the IS than in the IV transitions.
4 The low-energy IV and IS responses are basically due to
the outermost neutrons.
5 The isoscalarity displayed by the RPA states giving rise to
the PDS may probe isoscalar properties.
17
Conclusions:
Therefore,
◮
IS probes interacting with the surface of the nucleus
seem to be more suitable for the study of the low-energy
dipole response in nuclei far from the stability valley.
◮
The properties of the PDS may display an involved
correlation with the parameters of the nuclear EoS that it
is not clear enough yet
◮
This puzzle may be solved by performing more studies on
neutron-rich systems
◮
For that, we miss some systematic scattering experiments
(in inverse kinematics) that can excite predominantly IS
states like (α,α′ ) or (16 O,16 O′ )
[See next talk from Prof. Lanza]
18
I would like to kindly thank my collaborators:
Giacomo Pozzi, Marco Brenna, Kazhuito Mizuyama and
Gianluca Colò
19
Thank you for your
attention!
20