1. Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
Mateusz Krzysiek
Joint COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

2. Soft dipole mode - PDR
The electric dipole (E1) response is one of the basic properties of atomic nucleus.
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

3. Soft dipole mode - PDR IVGDR
The electric dipole (E1) response is one of the basic properties of atomic nucleus.
IVGDR
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

4. Soft dipole mode - PDR PDR
The electric dipole (E1) response is one of the basic properties of atomic nucleus.
Oscillation of the neutron skin vs core of the nucleus
PDR
two-phonon state
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

5. Soft dipole mode - PDR PDR
The electric dipole (E1) response is one of the basic properties of atomic nucleus.
or interplay between
… PDR ?
… vortical toroidal flow ?
... compression mode ?
... p-h excitations of skin neutrons ?
Oscillation of the neutron skin vs core of the nucleus ?
PDR
two-phonon state
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

6. Izovector excitations, ΔT =1 Isoscalar excitations, ΔT = 0
PDR – transition densities
Macroscopic
PDR E1
ΔT = ?
IVGDR E1
ΔT = 1
Izovector excitations, ΔT =1
Isoscalar excitations, ΔT = 0
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

7. PDR – transition densities
Macroscopic
Microscopic
Neutron and proton transition densities
Contribution of proton and neutrons in given excitation with respect to nucleus radius
PDR E1
ΔT = ?
PDR
IVGDR
IVGDR E1
ΔT = 1
Opposite sign in n and p transition densities associated to the oscillations in opposite phase (isovector)
Izovector excitations, ΔT =1
Isoscalar excitations, ΔT = 0
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

8. RQRPA model calculations Neutron and proton transition densities
PDR – transition densities
RQRPA model calculations
N. Paar et al., PRL 103 (2009)
Microscopic
Neutron and proton transition densities
E1 strength function
140Ce
PDR
IVGDR
4.14 % of ISEWSR
(isoscalar energy-weighted sum rule)
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

9. PDR and symmetry energy
E1 strength correlated with the symmetry energy of equation of state
The neutron skin thickness itself is determined by the symmetry energy of the equation of state (EOS)
Dipole polarizability αD correlated to neutron-skin thickness ?
PDR stronger correlated to neutron-skin thickness?
𝛼 𝐷 = ℏ𝑐 2 𝜋 2 𝑒 𝜎 𝛾 𝜔 2 𝑑𝜔
σγ - photo-absorbtion cross section
J. Piekarewicz, PRC 83 (2011)
Precise PDR strength identification needed!
… which is not trivial…
A. Carbone, PRC 81 (2010) (R)
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

10. Pygmy states (PDR) in 140Ce isospin character
PDR – isospin mixing
Pygmy states (PDR) in 140Ce isospin character
D. Savran et al., PRL 97 (2006)
All states
Selectivity
Why ?
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

11. Pygmy states (PDR) in 140Ce isospin character
PDR – isospin mixing
Pygmy states (PDR) in 140Ce isospin character
Photon scattering
Dominant isovector excitations
Interaction with whole nucleus
Inealstic scattering
Isoscalar probe e.g. alpha, heavy ion
Dominant isoscalar excitations
Dominant surface interactions
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

12. Pygmy states (PDR) in 140Ce isospin character
PDR – isospin mixing
Pygmy states (PDR) in 140Ce isospin character
D. Savran et al., PRL 97 (2006)
High-energy states are of isovector nature and associated to the transitions towards IVGDR
Low-energy states are of predominantly isoscalar nature and their transition density is peaked on the surface
Further need to study the PDR states with heavy ions
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

13. Experimental setup
Inelastic scattering of 20 MeV/u on 90Zr, 124Sn, 140Ce, 208Pb target
LNL-Legnaro, spokepersons: Maria Kmiecik (Krakow), Fabio Crespi (Milan)
Idea of experiment:
Expected excitation of high-energy states of low spins
Sensitivity to angular momentum – measurement of emitted gamma rays
17O as a projectile:
isoscalar probe1, expected mostly surface interaction
further study on isospin character of PDR
no background from projectile excitation in PDR region
weakly bound projectile (4.1 MeV) is required
17O
140Ce γ
(1) A. Bracco, F.C.L. Crespi, E. Lanza, EPJ A 51 (2015) 99
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

14. Experimental setup
Inelastic scattering of 20 MeV/u on 90Zr, 124Sn, 140Ce, 208Pb target
AGATA campaign in LNL-Legnaro
Demonstrator
AGATA
LaBr3:Ce γ
LaBr3:Ce γ Si
17O Si
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

15. Experimental setup
Inelastic scattering of 20 MeV/u on 90Zr, 124Sn, 140Ce, 208Pb target
Demonstrator
AGATA
LaBr3:Ce γ
AGATA Demonstrator: 5 triple clusters of HPGe detector
Pulse Shape Analysis
Tracking Algorithm
LaBr3:Ce γ Si
17O
HECTOR+: 9 Large volume LaBr3: Ce
High efficiency
Cylindrical shape, volume up to 9 x 20 cm
Good energy resolution Si
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

16. Experimental setup
Inelastic scattering of 20 MeV/u on 90Zr, 124Sn, 140Ce, 208Pb target Si
17O Si
TRACE array: 2 ΔE-E telescopes
Si-pad technology (5 x 12 pixels)
Pixel area: 4x4 mm2
Active area: 20 x 50 mm 2
Thickness: ΔE detector – 200 um
E detector – 1 mm
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

17. Selection of the 17O channel
Data analysis
Selection of the 17O channel O F
18O N
17O
16O C B
140Ce(17O, 17O'γ) – coincidence matrix
E2+ → g.s.
E3+
E2+
E3+ → E2+
Ex = TKE – MeV
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

18. Results – decay of PDR PDR General conclusions:
Spectrum measured with AGATA in „pygmy” energy region
Gating conditions: Time coincidence peak 17O channel Decays to ground state
Two-phonon
2+ ⊗ 3-
PDR
General conclusions:
Excitation pattern similar to (α,α’) – discrete peaks in low energy-region
Some excitations in high-energy part of rather continuous character
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

19. Results – angular distributions
Due to position sensitivity of AGATA (1 deg) and TRACE arrays (3 deg) it is possible to measure the angle of gamma emission with remarkable accuracy.
Gating conditions: Time coincidence peak 17O channel Decays to ground state
1596keV
2+ → 0+
868 keV
3- → 2+
After demonstrating the sensitivity to mulipolarity , it is possible to study the „pygmy” energy region …
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

20. Results – multipolarity of PDR
Multipolarity of the „pygmy” transitions ?
Calculated distributions
E1 character in the „pygmy” energy region confirmed
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

21. Results – differential cross sections
12.5 deg scattering angle
Cross sections for population of 1- states
Differential cross sections:
number of gammas
𝒅 𝟐 𝝈 𝒅𝑬𝒅𝛀 = 𝑵 𝜸 (𝑬 𝝐(𝑬) 𝑵 𝒃𝒆𝒂𝒎 𝑵 𝒕𝒂𝒓𝒈𝒆𝒕 𝒅𝛀
solid angle
number of target nuclei
detection efficiency
number of beam nuclei
How to theoretically interpret the PDR excitations ?
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

22. Results – DWBA DWBA (Distorted Wave Born Approximation) calculations
Accurate to describe the inelastic scattering of heavy ions Ebeam < 50 MeV / u
DWBA calculations with Fresco code – ingredients:
Elastic scattering - Optical model (Woods-Saxon potential)
Inelastic excitations:
Deformation using B(E1), B(E2), B(E3)
Appropriate form factor for a given excitation
Elastic scattering
reaction V
[MeV] Rv rc
[fm] av W Rw aw
Ref.
16O + 90Zr at 25 MeV/u 40
1.15
1.20
0.671 26
[Sjo84]
17O + 90Zr at 20 MeV/u
[Hor91]
17O + 124Sn at 20 MeV/u 50
1.16
0.670 32
[Pel14a]
16O + 208Pb at 25 MeV/u 60
1.17
0.665 38
17O + 208Pb at 20 MeV/u
0.767
42.5
[Cre14]
V, W – depth of the real and imaginary potential
Rv, Rw – radii of the real and imaginary potential
av, aw – diffuseness of the real and imaginary potential
rc – Coulomb radius parameter
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

23. Results – differential cross sections and DWBA
Elastic scattering (a)
DWBA calculations to normalize exp. data
influence of beam current and target thickness
used for inelastic excitations
2+ and 3- states of 140Ce (b,c,d)
DWBA calculations to describe the inelastic scattering
using optical model potential parameters
known B(E2) and B(E3) used
Collective form factor
Good agreement between experimental cross sections and DWBA calculations
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

24. Results – differential cross sections and DWBA
Total strength in low- and high-energy regions
6.2 – 7.8 MeV
4 – 6.2 MeV
DWBA using „standard” form factor of IVGDR does not reproduce the experimental data, especially in low-energy part !
It suggests its predominantly isoscalar character
More accurate form factor is needed !
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

25. Results – microscopic form factor
Calculation of form factor - double folding method1 B
𝐹 0 = 𝛿 𝜌 𝑛 𝐴 𝑟 1 +𝛿 𝜌 𝑝 𝐴 𝑟 1 × 𝜈 0 𝑟 12 𝛿 𝜌 𝑛 𝐵 𝑟 2 +𝛿 𝜌 𝑝 𝐵 𝑟 2 𝑟 1 2 𝑑 𝑟 1 𝑟 2 2 𝑑 𝑟 2
(isoscalar part)
𝐹 1 = 𝛿 𝜌 𝑛 𝐴 𝑟 1 −𝛿 𝜌 𝑝 𝐴 𝑟 1 × 𝜈 1 𝑟 12 𝛿 𝜌 𝑛 𝐵 𝑟 2 −𝛿 𝜌 𝑝 𝐵 𝑟 2 𝑟 1 2 𝑑 𝑟 1 𝑟 2 2 𝑑 𝑟 2
(isovector part) A γ
Proton and neutron transition densities
(calculated with RQRPA2 for PDR state)
Interaction
(M3Y)
p and n densities for projectile
E = 8.4 MeV
ISEWSR = 4.14%
(1) E. Lanza et al.,PRC 91 (2015) (2) N. Paar et al., PRL 103 (2009)
M. Krzysiek et al., PRC 93 (2016)
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

26. Results – differential cross sections and DWBA
… Then, for given PDR excitation, the form factor is scaled taking into account the energy and deduced fraction of ISEWSR in order to reproduce the differentia cross sections
DWBA with
„pygmy” FF
Isoscalar energy weighted-sum rule (ISEWSR):
Low energy part: 1.42(22)%
High-energy part: 0.61(14)%
(1) E. Lanza et al.,PRC 91 (2015) (2) N. Paar et al., PRL 103 (2009)
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

27. Results – differential cross sections and DWBA
Calculation of ISEWSR for single peaks
Comparison with previous experiments
ISEWSR
(17O, 17O’) 124Sn1 140Ce2
in peaks 2.2% 0.44% 5
Cross sections [mb/sr]
(α, α’) 124Sn3 140Ce4
in peaks
... and calculations ISEWSR
RQRPA %
RQTBA %
𝟏𝟐𝟒 𝐒𝐧 𝟏𝟒𝟎 𝐂𝐞
0.014%
0.039%
0.029%
0.05%
0.03%
0.033%
0.053%
0.038%
0.075%
0.076%
𝟏𝟐𝟒 𝐒𝐧 𝟏𝟒𝟎 𝐂𝐞
Very consistent data !
Using different techniques and models
Isoscalar energy weighted-sum rule (ISEWSR):
For sum of the peaks: 0.44(12)%
For total strength: 2.03(26)%
Reasonably good agreement with RQTBA
(1) L. Pellegri et al., PLB 738 (2014) (2) M. Krzysiek et al., PRC (2016) (submitted) (3) J. Endres et al., PRL 105 (2010)
(4) J. Endres et al., PRC 80 (2009) (5) N. Paar et al., PRL 103 (2009)
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

28. Results – all nuclei Comparison with other nuclei Nucleus Selection
Energy range [MeV]
ISEWSR [%]
B(E1)↑
[10-3 e2fm2]
90Zr
in peaks
6.3 – 6.9
4.0(6) 87
124Sn
5.5 – 9.0
2.2(3)
228
total
7.8(7)
140Ce
4.1 – 7.8
0.44(12)
307
2.03(26)
208Pb
4.8 – 7.3
9.0(1.5)
1084
Increase of B(E1) with the mass
No clear correlation for IS excitations
Influence of nuclear structure
N/Z =50/40=1.25
N/Z =74/50=1.48
N/Z = 82/58 = 1.41
N/Z = 126/82 = 1.54
(1) F.C.L. Crespi et al., Phys. Rev. C 91, (2015). (2) L. Pellegri et al., PLB 738 (2014) (3) M. Krzysiek et al., PRC 93 (2016)
(4) F.C.L. Crespi et al. Phys. Rev. Lett. 113 (2014)
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

29. PDR studies - perspectives
Stable nuclei:
Different nuclei using inelastic scattering of 17O
Inelastic scattering of fast protons (RCNP-Osaka and CCB-Krakow)
Gamma beams in ELI-NP (Romania): (γ,γ’), (γ,n)
Neutron-rich nuclei
Relativistic Coulomb excitations – strength functions determination via measurement of:
neutrons (e.g. 132Sn – LAND collaboration),
high-energy gamma rays (e.g. 68Ni - RISING collaboration)
Inelastic scattering of neutron-rich radioactive beams on e.g. 13C – inverse kinematics
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

30. Conclusions
Inelastic scattering of 20 MeV/u has been used to study low-lying E1 response for a different nuclei: 90Zr, 124Sn, 140Ce and 208Pb
Applied setup allowed for:
precise Doppler correction
reduction of background
high sensitivity to multipolarity – angular distributions
Results for 140Ce:
E1 states in the region of PDR with predominantly isoscalar character
ISEWSR was estimated:
for discrete peaks to be 0.44%
for total region, including unresolved strength to be 2.03%
Results consistent with the 124Sn nucleus studied with (17O, 17O’ γ) and (α‚ α’ γ)
Experimentally obtained ISEWSR for total strength (considered as upper limit) is reasonably well reproduced by RQTBA calculations
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy

31. A. Gadea, T. Huyuk, D. Barrientos IFIC, Valencia, Spain
Collaboration
M. Kmiecik, A. Maj, P. Bednarczyk, M. Ciemala, B. Fornal, J. Grębosz, M. Krzysiek, K. Mazurek, W. Męczyński, M. Ziębliński The Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, Poland
F.C.L. Crespi, A. Bracco, G. Benzoni, N. Blasi, C. Boiano, S. Brambilla, F. Camera, A. Giaz, S. Leoni, B. Million, A. Morales,
R. Nicolini, L. Pellegri, S. Riboldi, V. Vandone, O. Wieland Università degli Studi e INFN sezione di Milano, Italy
G. De Angelis, D. R. Napoli, J.J. Valiente-Dobon INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy
D. Bazzacco, E. Farnea, A. Gottardo, S. Lenzi, S. Lunardi, D. Mengoni, C. Michelagnoli, F. Recchia, C. Ur Università di Padova e INFN, sezione di Padova, Padova, Italy
A. Gadea, T. Huyuk, D. Barrientos IFIC, Valencia, Spain
B. Birkenbach, K. Geibel, H. Hess, P. Reiter , T. Steinbach, A. Wiens Institut fur Kernphysik der Universitat zu Koln, Germany
A.Bürger, A. Görgen, M. Guttormsen, A.C. Larsen, S. Siem Department of Physics, University of Oslo, Norway
Study on the pygmy dipole states in 140Ce using inelastic scattering of 17O
COLL-AGAIN, COPIGAL and POLITA workshop, , Catania, Italy