Fine Structure of Giant Resonances Revisited ...
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S-DALINAC 208 Nature of the pygmy dipole resonance: the case of Pb M2 and spin dipole modes Fine structure and characteristic scales COMEX1, Paris 2003 Fine Structure of Giant Resonances Revisited Experimentally and Theoretically - ISGQR at shell closures 90 - GT resonance in Nb F. Hofmann, Y. Kalmykov, N. Ryezayeva, A. Shevchenko, J. Wambach Darmstadt / Groningen / iThembaLAB / Münster / Osaka Collaborations P. von Neumann-Cosel, V. Ponomarev, A. Richter, Supported by DFG under Contract FOR 272 / 2 - 2
Transcript of Fine Structure of Giant Resonances Revisited ...
S-DALINAC
208Nature of the pygmy dipole resonance: the case of Pb
M2 and spin dipole modes
Fine structure and characteristic scales
COMEX1, Paris 2003
Fine Structure of Giant ResonancesRevisited Experimentally and Theoretically
- ISGQR at shell closures90
- GT resonance in Nb
F. Hofmann, Y. Kalmykov, N. Ryezayeva, A. Shevchenko, J. Wambach
Darmstadt / Groningen / iThembaLAB / Münster / Osaka Collaborations
P. von Neumann-Cosel, V. Ponomarev,A. Richter,
Supported by DFG under Contract FOR 272 / 2 - 2
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Nature of the pygmy dipole resonance: 208the case of Pb
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E1 Response in Nuclei
GDR
p
PDR
E (MeV)
B(E1)
-(2 x 3 )1
+ -
n
x 100
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E1 Response in Nuclei
GDR
p
PDR
E (MeV)
B(E1)
-(2 x 3 )1
+ -
n
x 100
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138Photon Scattering off Ba
A. Zilges et al., Phys. Lett. B 542, 43 (2002)
E1 excitations
Energy (keV)
E = 9.2 MeVmax
4000 0
1000
2000
Co
un
ts / 1
.3 k
eV
5000 6000 7000 8000 9000
138Ba
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...
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5 6 7 80
500
1000
1500E
th
Photon Energy (MeV)
Co
un
ts
x10
208Pb ( γ, γ´)
E0
= 9.0 MeV
qγ = 1300
NRF Spectrum
N. Ryezayeva et al., Phys. Rev. Lett. 89, 272502 (2002)
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208B(E1) in Pb
Shell Model
QPM
Exp208Pb200
100
0
200
100
0
200
100
05.0 5.5 6.0 6.5 7.0 7.5 8.0
Excitation Energy (MeV)
-32
2B
(E1
) (
10
e
fm
)
Ponomarev (2002)
Brown (2002)
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Electric Dipole Responseof Neutrons and Protons
PDR largely isoscalar
Similar results from the Milano and Munich groups
Evidence for surface neutron density oscillations
neutrons
protons
208Pb PDR
GDR
Axial Distance (fm)
2-1
rr(r
) (e
fm
)
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r r
208“Snapshots” of Velocity Distribution in PbPDR GDR
Toroidal (current) mode: zero sound wave Vibrational mode
Restoring force is not of hydrodynamicnature but elastic
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Electric Dipole Strength and Vorticity
Vorticity density: measure for the strength of the transverse current
208Pb
Excitation Energy (MeV)
Vo
rtic
ity (
%)
E1
str
en
gth
(%
)
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E1 Strength vs. Vorticity
QPM208
Pb
Excitation Energy (MeV)
-+
-|<
1|| E
1 || 0
>|
i
-+
|<1
|| V
ort
|| 0
>|
i
0
0
0.5
-0.5
1
-1
5 10 15 20 25
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208Pb(e,e´)
Oq = 180
Form Factors of Toroidal and Skin Modes
toroidal
skin
(dσ/
dΩ
) / (
) Mott
dσ/
dΩ
40
-1010
-910
-810
-710
-610
60 80 100 120E (MeV)0
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M2 and Spin Dipole Modes
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O180 Electron Scattering: Selectivity
Excitation Energy (MeV)
-1C
ou
nts
(m
sr C
ke
V)
90Zr(e,e´)
Oq = 180
E = 42.7 MeV0
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Direct Evidence for the Twist Mode
Excitation Energy (MeV)
58Ni(p,p')
58Ni(e,e') q = 180° E = 65.4 MeV0
q = 6° E = 172 MeV0
2d
σ / d
Ωd
Ep
x
(mb
arn
/ s
r M
eV
)
2d
σ / d
Ωd
Ee
x-5
(10
mb
arn
/ s
r M
eV
)
B. Reitz et al., Phys. Lett. B 532, 179 (2002)
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πThe J = 2 Twist Mode
P. von Neumann-Cosel et al., Phys. Rev. Lett. 82, 1105 (1999)
_
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Orbital Transition Currents of the Twist Mode
Shear module µ/ρ ~ 58Ni~ 6.5 MeV ( )
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Spin Dipole Modes
l Transition operator: r [σ ⊗Y1] 0-, 1-, 2- Strongest
l (p,p') and (p,p'): 58Ni as a test case
l d2σ/dΩdE
l Snn' d2σ/dΩdE
l Snn'
l Comparison with model predictions l EUROSUPERNOVA collaboration
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Target
E = 172 MeV0
VDCs Analyzer MWPCs
FPPFPDS
Vetoscintillator Scintillators
Beam from AGOR
58Ni( p,p’) Reaction: Experimental Setup
O Oq = 4 - 20 unpolarized protonsO Oq = 4 - 11 polarized protons
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Effective NN Interaction
Model I: G-Matrix + Paris Potential a von Geramb
Model II: G-Matrix + Bonn potential a Karataglidis et al.
Model III: t-Matrix a Love and Franey
Ground State and Excited States
2p2h Quasiparticle Phonon Model a Ponomarev
E0 - E5, M0 -M6 transitions up to E = 25 MeVx
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Observations
Quality of model description of experimental observables improves for
2d σ / dΩ dE x
2S d σ / dΩ dE xnn' Snn'
Possible reason: reaction part - in particular the non-spin part of the continuum is not correctly described
Nuclear structure part seems to be correct
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Fine Structure and Characteristic Scales
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Fine Structure of Giant Resonances
208Pb(e,e´)DALINAC
208Pb(p,p´)IUCF
Search for characteristic energy scales of fluctuations:
Multiple Scales of FluctuationsDifferent Probes - Similar Structures2
dσ
/ d
Ω d
E (
arb
itra
ry u
nits
)x
Excitation Energy (MeV) Excitation Energy (MeV)
2d
σ / d
Ω d
E (
arb
itra
ry u
nits
)x
Entropy Index Method
Wavelet Analysis
Local Scaling Dimension: Aiba, Matsuo (1999)
8 9 10 112
6
10
0
10
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Entropy Index Method
+
δE
(Haar Wavelet)
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Entropy Index Method
+
δE
(Haar Wavelet)
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Entropy Index Method
+
δE
(Haar Wavelet)
Define
Define coefficient
sets the scales
Spectrum ∆E divided into n bins
with binwidth
and entropy
D. Lacroix and P. Chomaz, Phys. Rev. C 60, 064307 (1999)
Excitation Energy
;
-
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for statistical fluctuations of around the mean value
for the appearence of characteristic scales
for scales with the most complex configuration
const
varies
is maximal
np-nh mp-mh 1p-1h
change of onset of a new scale
> where n>m> .... >
Entropy Index Properties
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208Scales in (e,e’) and (p,p’): The Example Pb
Experimental evidence for scales at 1.1 MeV, 400 keV, 125 keV
Scales are independent of the probes
0.07 0.1 0.2
0.22
6
10
8 9 10 11
0
10
0.3
0.3
0.4
0.5 0.7Excitation Energy (MeV) Energy Scale δE (MeV)
E = 7.6 - 11.7 MeVx
En
tro
py
Ind
ex
K(δ
E)
2d
σ / d
Ω d
E (
arb
itra
ry u
nits
)x
400 keV
125 keV
Similar scales are found in SRPA: D. Lacroix et al., Phys. Lett. B479 (2000) 15
208Pb(e,e´)208Pb(e,e´)
208Pb(p,p´)
208Pb(p,p´)
S-DALINAC
Scales in the Fine Structure of Giant Resonances
Global phenomenon?
- Other nuclei
- Other resonances
Posters by Shevchenko et al.Kalmykov et al.,
Is the wavelet analysis unique?
Γ , Γ , CRPA, ...Final goal: physics of the scales
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O O 8 - 10 (close to maximum of ∆L=2 transitions)
O O6 - 14 (check contributions of different multipoles)
(p,p´)Reaction:
Recent Experiments
Excitation Energy Range:
Scattering Angles:
E = 0 - 23 MeVx
E = 200 MeV0Beam Energy:
Targets: 208 120 90 89 58
Pb Sn Zr Y Ni82 126 70 50 50 3050 40 39 28
Energy Resolution (FWHM): ∆E = 35 - 50 keV
iThemba LABS in South AfricaPlace:
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Fine Structure of the ISGQR: A Global Phenomenon?
q
q
q
q
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Details of the Fine Structure
Not a Lorentzian
Excitation Energy (MeV)
500011 12 13 14 15 16
7500
10000
Co
un
ts / 1
0 k
eV
Fluctuations of different strength and scales
90Zr(p,p´)
Oq = 9.2p
E = 200 MeV0
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various scales statistical fluctuations
Scales and Fluctuations208
Pb(p,p´)
Oq = 8p
E = 200 MeV0
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Wavelet Analysis
l
a
a
l
Entropy Index Method is limited no information on localization of scales
no reconstruction of original spectrum possible
Another possibility: Discrete Wavelet Transform from signal processing
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Discrete Wavelet Analysis
scale position spectrum wavelet
Wavelets:
WaveletCoefficients:
- 88
xx 0
Steps: 2 with j = 1, 2, 3, ... and j
σ
0
0
1
-15-5
Haar Mexican Hat Morlet Biorthogonal
0
1
0
1
-1
0
1
-10 5-5 0 5-50 5-5
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Decomposition
A2
σ(E)
Highpass FilterSmall scales δE
D1
Lowpass FilterLarge scales δE
A1
D2
A3 D3
σ(E) = + A1 D1
σ(E) = + A2 + D2 D1
σ(E) = + + A3 + D3 D2 D1
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208Decomposition of Pb(p,p´) SpectrumApproximations Ai Details Di
D1
Range of Scales
10 - 20 keV
20 - 40 keV
40 - 80 keV
80 - 160 keV
160 - 320 keV
320 - 640 keV
640 - 1200 keV
1.2 - 2.4 MeV
2.4 - 4.8 MeV
D2
D3
D4D4
D5
D6D6
D7
D8D8
D9
A1
A2
A3
A4
A5
A6
A7
A8
A9
SpectrumSpectrum
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Fine Structure of the Spin-Flip GTR
Excitation Energy (MeV)
90 3 90Zr( He,t) Nb
E = 140 MeV/u0
RCNP
+1
+ 0 IAS
∆E = 50 keV FWHM
Co
un
ts / 1
0 k
eV
Excitation Energy (MeV)
Co
un
ts / 1
0 k
eV
0° < θ < 0.9°
S-DALINAC
Fine Structure of the Spin-Flip GTR
observed for the first time
scales T Γc vs. Γ` and comparison with electric GR’s
Tπ +selectivity: J = 1 level density
90Zr(p,n)90Nb D. Bainum et al., Phys. Rev. Lett., 44 (1980) 1751
Co
un
ts
Channels
90 3 90Zr( He,t) Nb
E = 140 MeV/u0
θ = 0°
RCNP
+1
+ 0 IAS
∆E = 50 keV FWHM
Co
un
ts / 1
0 k
eV
Excitation Energy (MeV)
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90 3 90Decomposition of Zr( He,t) Nb Spectrum
Approximations Ai Details Di Range of Scales
10 - 20 keV
20 - 40 keV
40 - 80 keV
80 - 160 keV
160 - 320 keV
320 - 640 keV
640 - 1200 keV
1.2 - 2.4 MeV
2.4 - 4.8 MeV
A1
A2
A3
A4
A5
A6
A7
A8
A9
D1D1
D2D2
D3D3
D4D4
D5D5
D6D6
D7D7
D8D8
D9D9
SpectrumSpectrum
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Discrete Wavelet Transform: Reconstructed Spectra
σ (E)r = + A8 + + + D8 D6 D4 D3 σ (E)r = + A8 + + + D7 D5 D2 D1
- Experiment
- Reconstruction
- Experiment
- Reconstruction
S-DALINAC
ConclusionPDR:
neutron surface density oscillations
toroidal (current) mode might be present
M2 and Spin Dipole Modes:
direct evidence for twist mode
extraction of spin dipole strength from proton scattering
comparison with model predictions
Fine structure of GR's and characteristic scales:
fine structure is a global phenomenon
preliminary results of fast wavelet analysis are encouraging
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Photon Scattering(Nuclear Resonance Fluorescence)
Electrons
Target
Detectors
EnergyEnergy
Inte
nsity
Inte
nsity
Radiator
Collimator Bremsstrahlung
