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 finite quantum system in which single-particle and collective degrees of freedom coexist. 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. The evolution of nucleon shell structure and low-energy collective excitations… …structure and dynamics across the chart of nuclides.

Chart of Nuclides ≈ 250 stable nuclides 5000 - 7000 nuclides in Universe ≈ 2000 nuclides synthesized in laboratory

Low-energy Nuclear Theory regions of exotic nuclei far from β -stability connection to low-energy QCD nuclear astrophysics applications

Localization and clustering in atomic nuclei: 20 20 Ne 18 - 7 16 - 7 181 14 - 12 E X [MeV] 5 - 5 10 177 + - 6 2 3 3 8 + - 3 6 156 3 - 1 164(26) 64(10) 6 - 2 155 1 85 6 6 + 1 4 + 4 4 71(6) 89 328 2 + + 2 2 Calc. Exp. 65(3) 54 + + 0 0 0 + - + - K=0 1 K=0 1 K=0 1 K=0 1 RESEARCH LETTER How atomic nuclei cluster ´ 3 & D. Vretenar 3 J.-P. Ebran 1 , E. Khan 2 , T. Niks ˇic 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

Clustering in neutron-rich nuclei ⇒ molecular bonding of α -particles by the excess neutrons. Total nucleon density 14 Be Proton density Neutron density J.-P. Ebran, E. Khan, T. Nik š i ć , and D. Vretenar Phys. Rev. C 90 , 054329

…formation and evolution of exotic cluster states

Shape Quantum Phase Transitions …evolution of nucleonic shells ⇒ phase transitions in equilibrium shapes (QPT) E (MeV) E (MeV) E (MeV) 8 8 8 6 6 6 4 4 4 2 2 2 152 Nd 148 Nd 150 Nd 0 0 0 0.6 0.6 0.4 0.6 0.6 0.4 0.4 0.4 0.2 0.6 0.2 0.2 0.4 0.6 0.2 β 0.4 0.2 β 0 0 β 0 0 0.2 0 0 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.

Transitions between spherical and axially deformed shapes in the chain of Nd-Sm-Gd isotopes.

Experimental evidence for a first-order shape phase transition at N ≈ 90 150 Nd 2.0 + 10 + 10 1 Energy (MeV) 1 1.5 257 + 4 0.12(2) 204(12) 3 + 4 57 80 135 0.38 + 3 4 3.9(12) + + 3 + 8 3 2 + + 4 87 8 1 1 3 135 1 ) 2 1 + + 4 3 + 2 2 1.0 2 0 170(51) 224 . 1 42 0 2 3 3 2 278(25) ( + 0 83 2 7 2.6(20) 0.9(3) 5.4(17) 3.0(8) + 2 + 0 114(23) 6 + 6 2 8.7 1 7.5 + 18 8 1 2 43 0 ) ) 3 1 1 1 39(2) 4.4 2 191 210(2) ( ( 0.5 7 7 1 + + 4 4 ) 1 1 2 ) 4 2.7 9.2 2 2 156 ( 182(2) 1 1 2 2 ( . 9 . + 0 + 1 2 2 1 1 115(2) 101 0.0 + + 0 0 1 1 Coll. Exp. Nik š i ć , Vretenar, Lalazissis, Ring, Phys. Rev. Lett. 99 , 092502 (2007) Li, Nik š i ć , Vretenar, Meng, Lalazissis, Ring, Phys. Rev. C 79 , 054301 (2009)

120 ˆ � e k r 2 T ( E 0) = Nd k 100 k ! 2 (E0) × 10 3 80 2 ⇥ ⇤ � � 2 | ˆ 0 + T ( E 0) | 0 + � � 1 60 ρ 2 ( E 0; 0 + 2 → 0 + � � 1 ) = � � eR 2 � � 40 � � 20 0 84 86 88 90 92 94 96 N q shape invariants: q 2 (0 + n ; k ) = k � B ( E 2; 0 + n → 2 + j ) j =1

Spectroscopy of quadrupole and octupole deformed heavy nuclei

Octupole deformed (pear-shaped) heavy nuclei:

Extrapolation to Superheavy Nuclei

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, Q α -values …

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, Q α -values … Stronger competition between the attractive short-range nuclear interaction and the long- range electrostatic repulsion ➠ Shape transitions! Exotic shapes!

Triaxial energy maps of 254No and 256Rf isotopes in the β – γ plane (0 ≤ γ ≤ 60 ◦ ). 256 Rf 254 No 1.6 1.6 exp. exp. β -band γ -band β -band γ -band + 14 + + 14 + 14 14 + 4 1.4 1.4 + + 6 4 + 2 + 477 + 5 + 2 0 + + 1.2 471 1.2 6 + 4 + 722 685 0 + + 12 + + + 12 12 5 12 3 Energy MeV() Energy (MeV) + + 2 4 1 1 + 3 + 2 706 + + 668 + 26 + 10 0.8 10 0.8 10 26 10 0.6 0.6 + 669 + 648 + 6 + 8 8 8 8 7 4 0.4 0.4 4 + + 645 624 + + 6 6 6 6 0.2 0.2 + + 612 + 591 + 4 4 4 4 + + + 534 552 2 + 2 2 2 385 + 372 + + 0 0 + 0 0 0 0

Harmonic vibrations Isoscalar monopole resonance Isovector dipole resonance Isoscalar quadrupole resonance

Exotic modes of excitations Dipole response of neutron-rich nuclei E1 srength Energy [MeV] 18 Paar, Vretenar, Khan, Colò, Rep. Prog. Phys. 70 , 1 (2007)

Exotic modes of excitations Dipole response of neutron-rich nuclei E1 srength Energy [MeV] In stable nuclei 100% of the E1 strength is absorbed in the Giant Dipole Resonance. 18 Paar, Vretenar, Khan, Colò, Rep. Prog. Phys. 70 , 1 (2007)

Neutron-rich nuclei → weak binding of the excess neutrons, diffuse neutron densities, formation of a neutron skin. E1 srength Energy [MeV] Neutron-rich nuclei → predicted occurrence of a collective soft dipole mode (Pygmy Dipole Resonance) 19

68 Ni photoabsorption cross section E1 strength function

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) 24 KDE0-J 24 FSU Λ NL3 Λ 3 ) 3 ) TAMU-FSU 208 Pb) (fm 208 Pb) (fm 22 DD-ME 22 SAMi-J Skyrmes 20 RCNP 20 RCNP α D ( α D ( 18 18 (b) RCNP r = 0.96 GSI (a) r = 0.96 8 9 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 8.5 9.5 10 10.5 68 Ni) (fm 3 ) 120 Sn) (fm 3 ) α D ( α D (

Neutrino-nucleus reactions Z +1 X ∗ N − 1 + e − ν e + Z X N → Large-scale calculations of supernova neutrino-induced reactions N. Paar, H. Tutman, T. Marketin, and T. Fischer Phys. Rev. C 87 , 025801 (2013) Uncertainties in modeling low-energy neutrino-induced reactions on iron-group nuclei 1000 N. Paar, T. Suzuki, M. Honma, T. Marketin, and D. Vretenar Phys. Rev. C 84 , 047305 (2011) 100 < �� e >[10 -42 cm 2 ] Comparison of the inclusive ν e – 56 Fe cross Table 1. 10 sections averaged with the Michel flux. ⟨ σ ⟩ [10 − 42 cm 2 ] 1 T=4 MeV RNEDF (DD-ME2) 263 SM (GXPF1J) + RPA (SGII) 28,41 259 0.1 all nuclei RPA (Landau–Migdal) 67 240 N/Z < 1 QRPA (SIII) 68 352 N/Z > 1.5 QRPA (G-matrix) 69 0.01 173.5 stable nuclei Theoretical average 258 ± 57 Exp. (KARMEN) 59 256 ± 108 ± 43 0.001 50 100 150 200 250 A

β -decay half-lives of neutron-rich nuclei and matter flow in the r-process Contour maps of experimental and theoretical β -decay half-lives for the Z = 20–50 even–even nuclei. Niu, Niu, Liang, Long, Nik š i ć , Vretenar, Meng, Phys. Lett. B 723 , 172 (2013). 23

β -decay half-lives of neutron-rich nuclei and matter flow in the r-process 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: Niu, Niu, Liang, Long, Nik š i ć , Vretenar, Meng, Phys. Lett. B 723 , 172 (2013). 23

The impact of nuclear β -decay half-lives on the r-matter flow. 24

NuPECC Long Range Plan 2017 Perspectives in Nuclear Physics 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?