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nuclear structure Dario Vretenar University of Zagreb The atomic - - PowerPoint PPT Presentation
nuclear structure Dario Vretenar University of Zagreb The atomic - - PowerPoint PPT Presentation
Static and dynamic aspects of exotic nuclear structure Dario Vretenar University of Zagreb The atomic nucleus is a unique finite quantum system in which single-particle and collective degrees of freedom coexist. The atomic nucleus is a unique
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The evolution of nucleon shell structure and low-energy collective excitations…
The atomic nucleus is a unique finite quantum system in which single-particle and collective degrees of freedom coexist.
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The evolution of nucleon shell structure and low-energy collective excitations… …structure and dynamics across the chart of nuclides.
The atomic nucleus is a unique finite quantum system in which single-particle and collective degrees of freedom coexist.
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≈ 250 stable nuclides ≈ 2000 nuclides synthesized in laboratory 5000 - 7000 nuclides in Universe
Chart of Nuclides
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Low-energy Nuclear Theory
regions of exotic nuclei far from β-stability connection to low-energy QCD nuclear astrophysics applications
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Localization and clustering in atomic nuclei:
How atomic nuclei cluster
J.-P. Ebran1, E. Khan2, T. Niks ˇic ´3 & D. Vretenar3
RESEARCH LETTER
1 9 J U L Y 2 0 1 2 | V O L 4 8 7 | N A T U R E | 3 4 1
2 4 6 8 10 12 14 16 18 20 EX [MeV]
+
4
+
6
+
1
- 2
+
3
- 5
- 7
- 54
89 85
20Ne
156 177 181 1 6 6 2 328 3 3 2 K=01
+
K=01
- +
2
+
4
+
6
+
1
- 3
- 5
- 7
- 65(3)
71(6) 64(10)
164(26) K=01
+
K=01
- Calc.
Exp.
155
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Clustering in neutron-rich nuclei ⇒ molecular bonding of α-particles by the excess neutrons.
Total nucleon density Proton density Neutron density
14Be
J.-P. Ebran, E. Khan, T. Nikšić, and D. Vretenar
- Phys. Rev. C 90, 054329
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…formation and evolution
- f exotic cluster states
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…evolution of nucleonic shells ⇒ phase transitions in equilibrium shapes (QPT)
0.2 0.4 0.6 0.2 0.4 0.6 2 4 6 8
β
E (MeV) 148Nd
0.2 0.4 0.6 0.2 0.4 0.6 2 4 6 8
β
E (MeV) 150Nd
0.2 0.4 0.6 0.2 0.4 0.6 2 4 6 8
β
E (MeV) 152Nd
Nuclear Quantum Phase Transitions: ⇒ the physical control parameter - nucleon number ⇒ order parameters - expectation values of operators that as observables characterize the state of a nuclear system.
Shape Quantum Phase Transitions
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Transitions between spherical and axially deformed shapes in the chain of Nd-Sm-Gd isotopes.
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Experimental evidence for a first-order shape phase transition at N≈90
Nikšić, Vretenar, Lalazissis, Ring, Phys. Rev. Lett. 99, 092502 (2007) Li, Nikšić, Vretenar, Meng, Lalazissis, Ring, Phys. Rev. C 79, 054301 (2009)
0.0 0.5 1.0 1.5 2.0
80 42 0.38 1 18 9.2 8.7 43 . 1 4 2 2 1 2 . 4 3
Energy (MeV) Coll.
101
156 191
150Nd
10
+ 1
8
+ 1
6
+ 1
4
+ 1
2
+ 1 + 1
224 257 135 83
4
+ 2
2
+ 2 + 2
4
+ 3
3
+ 1
2
+ 3
1 8 2
135
57 87 2.7 4.4 7.5 1 . 2 ( 2 ) 9 ( 2 ) 0.12(2) 7 ( 1 ) 0.9(3)
Exp.
115(2)
182(2) 210(2) 278(25) 204(12) 170(51) 114(23) 7 ( 1 3 ) 1 7 ( 3 ) 39(2)
10
+ 1
8
+ 1
6
+ 1
4
+ 1
2
+ 1 + 1
4
+ 2
2
+ 2 + 2
4
+ 3
3
+ 1
2
+ 3
3.9(12) 2.6(20) 5.4(17) 3.0(8)
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84 86 88 90 92 94 96 20 40 60 80 100 120
!2(E0)×103
N
Nd
ˆ T(E0) =
- k
ekr2
k
ρ2(E0; 0+
2 → 0+ 1 ) =
- ⇥
0+
2 | ˆ
T(E0)|0+
1
⇤ eR2
- 2
q2(0+
n ; k) = k
- j=1
B(E2; 0+
n → 2+ j ) q shape invariants:
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Spectroscopy of quadrupole and octupole deformed heavy nuclei
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Octupole deformed (pear-shaped) heavy nuclei:
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Extrapolation to Superheavy Nuclei
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Extrapolation to Superheavy Nuclei
Higher density of single-particle states ➠ the evolution of deformed shells with nucleon number will have a more pronounced effect on energy gaps, separation energies, Qα-values …
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Extrapolation to Superheavy Nuclei
Higher density of single-particle states ➠ the evolution of deformed shells with nucleon number will have a more pronounced effect on energy gaps, separation energies, Qα-values … Stronger competition between the attractive short-range nuclear interaction and the long- range electrostatic repulsion ➠ Shape transitions! Exotic shapes!
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0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Energy MeV()
+
2
+
4
+
6
+
8
+
10
+
12
+ +
2
+
4
+
β -band
2
+
3
+
4
+
5
+
γ-band
14
+
6
+
254No
471 534 591 624 648 372 26 7 4 668 685 exp.
+
2
+
4
+
6
+
8
+
10
+
12
+
14
+
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Energy (MeV)
+
2
+
4
+
6
+
8
+
10
+
12
+ +
2
+
4
+
β -band
2
+
3
+
4
+
5
+
γ-band
14
+
6
+
256Rf
477 552 612 645 669 385 26 6 4 706 722 exp.
+
2
+
4
+
6
+
8
+
10
+
12
+
14
+
Triaxial energy maps of 254No and 256Rf isotopes in the β–γ plane (0 ≤ γ ≤ 60◦).
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Harmonic vibrations
Isoscalar monopole resonance Isovector dipole resonance Isoscalar quadrupole resonance
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18
Dipole response of neutron-rich nuclei Energy [MeV] E1 srength
Paar, Vretenar, Khan, Colò, Rep. Prog. Phys. 70, 1 (2007)
Exotic modes of excitations
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18
Dipole response of neutron-rich nuclei In stable nuclei 100% of the E1 strength is absorbed in the Giant Dipole Resonance. Energy [MeV] E1 srength
Paar, Vretenar, Khan, Colò, Rep. Prog. Phys. 70, 1 (2007)
Exotic modes of excitations
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19
E1 srength Energy [MeV] Neutron-rich nuclei → predicted occurrence of a collective soft dipole mode (Pygmy Dipole Resonance)
Neutron-rich nuclei → weak binding of the excess neutrons, diffuse neutron densities, formation of a neutron skin.
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68Ni photoabsorption cross section
E1 strength function
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Editors' Suggestion
Neutron skin thickness from the measured electric dipole polarizability in Ni 68 , Sn 120 , and Pb 208
- X. Roca-Maza, X. Viñas, M. Centelles, B. K. Agrawal, G. Colò, N. Paar, J. Piekarewicz, and D. Vretenar
- Phys. Rev. C 92, 064304 (2015)
3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 αD(
68Ni) (fm 3)
18 20 22 24 αD(
208Pb) (fm 3) KDE0-J FSUΛ NL3Λ TAMU-FSU DD-ME SAMi-J Skyrmes
r = 0.96 GSI RCNP (a) 8 8.5 9 9.5 10 10.5 αD(
120Sn) (fm 3)
18 20 22 24 αD(
208Pb) (fm 3)
r = 0.96 RCNP RCNP (b)
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Large-scale calculations of supernova neutrino-induced reactions
- N. Paar, H. Tutman, T. Marketin, and T. Fischer
- Phys. Rev. C 87, 025801 (2013)
50 100 150 200 250
0.001 0.01 0.1 1 10 100 1000
all nuclei N/Z < 1 N/Z > 1.5 stable nuclei
<e>[10-42 cm2]
A
T=4 MeV
Table 1. Comparison of the inclusive νe–56Fe cross sections averaged with the Michel flux. ⟨σ⟩ [10−42 cm2] RNEDF (DD-ME2) 263 SM (GXPF1J) + RPA (SGII)28,41 259 RPA (Landau–Migdal)67 240 QRPA (SIII)68 352 QRPA (G-matrix)69 173.5 Theoretical average 258 ± 57
- Exp. (KARMEN)59
256 ± 108 ± 43
νe +Z XN →
Z+1X∗ N−1 + e−
Uncertainties in modeling low-energy neutrino-induced reactions on iron-group nuclei
- N. Paar, T. Suzuki, M. Honma, T. Marketin, and D. Vretenar
- Phys. Rev. C 84, 047305 (2011)
Neutrino-nucleus reactions
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23
β-decay half-lives of neutron-rich nuclei and matter flow in the r-process
Niu, Niu, Liang, Long, Nikšić, Vretenar, Meng, Phys. Lett. B 723, 172 (2013).
Contour maps of experimental and theoretical β-decay half-lives for the Z = 20–50 even–even nuclei.
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23
β-decay half-lives of neutron-rich nuclei and matter flow in the r-process
Niu, Niu, Liang, Long, Nikšić, Vretenar, Meng, Phys. Lett. B 723, 172 (2013).
Contour maps of experimental and theoretical β-decay half-lives for the Z = 20–50 even–even nuclei. ⇒ impact of the predicted β-decay half-lives on r - process abundances:
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24
The impact of nuclear β-decay half-lives on the r-matter flow.
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How does the nuclear chart emerge from the underlying fundamental interactions? Where are the limits of stability and what is the heaviest element that can be created? How does nuclear structure evolve across the nuclear landscape and what shapes can nuclei adopt? How does nuclear structure change with temperature and angular momentum? How can nuclear structure and reaction approaches be unified? How complex are nuclear excitations? How do correlations appear in dilute neutron matter, both in structure and reactions? What is the density and isospin dependence of the nuclear equation of state?