Nature of low-energy dipole states in exotic nuclei

Nature of low-energy dipole states in exotic nuclei Xavier Roca-Maza Università degli Studi di Milano, Via Celoria 16, I-133, Milano SPES One-day Workshop on "Collective Excitations of Exotic Nuclei" December 9, 13, 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 K [G. Colò, N. Van Giai, J. Meyer, K. Bennaceur and P. Bonche, Phys. Rev. C 7, 2437 (4)] Giant Dipole Resonance S 2 (ρ =.1 fm 3 ) [Luca Trippa, Gianluca Colò, and Enrico Vigezzi, Phys. Rev. C 77, 6134(R) (8)] Giant Quadrupole Resonance m [ Nuclear Structure, Bohr & Mottelson E x = 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 Pygmy dipole 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 (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) 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,σmay increase due to the low-energye1 enhancement when approaching the neutron drip line. [A. C. Larsen and S. Goriely, PRC 82, 14318 ()] 3

Motivation What is the Pygmy Dipole Strength (PDS)? Giant Dipole Resonance Pygmy dipole Low-energy peak in the dipole response of neutron rich (exotic) nuclei Equation of state for It uniform might benuclear relevantmatter 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 (L): a basic property of the nuclear EoS that impacts e(ρ,δ) = one(ρ,δ a variety = )+S(ρ)δ of physical 2 +O [ systems: δ 4] withfrom the very big (neutron stars) δ = to ρ n ρ the very p small (neutron skin) ρ n +ρ p The PDS seems to appear in certain models as a coherent excitation S(ρ) (resonance), = J+L ρ ρ ( ) 2 ρ ρ and +K 3ρ not sym in others 3ρ (shell +O [ (ρ ρ effect) ) 3] β decay rates and radiative neutron capture. In the latter,σmay increase due to the low-energye1 enhancement when approaching the neutron drip line. [A. C. Larsen and S. Goriely, PRC 82, 14318 ()] 3

Motivation What is the Pygmy Dipole Strength (PDS)? Giant Dipole Resonance Pygmy dipole 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) 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, 14318 ()] 4

Motivation: experimentally, the PDS splits into two parts... J. Endres et al. Phys. Rev. Lett. 5, 21253 () Alpha-gamma coincidence experiments allow the separation of E1 excitations in... 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. 7 2-245 (13). Evidence for Pygmy and Giant Dipole Resonances in 13 Sn and 132 Sn by P. Adrich et al., Phys. Rev. Lett. 95, 13251 (5). Concentration of electric dipole strength below the neutron separation energy in N=82 nuclei by A. Zilges et al., Phys. Lett. B542, 43 (2). The photoresponse of stable N=82 nuclei below MeV by S. Volz et al., Nucl. Phys. A779, 1 (6). Nature of Low-Energy Dipole Strength in Nuclei: The Case of a Resonance at Particle Threshold in 8Pb by N. Ryezayeva et al., Phys. Rev. Lett. 89, 27252 (2). Search for the Pygmy Dipole Resonance in 68 Ni at 6 MeV/nucleon by O. Wieland et al., Phys. Rev. Lett. 2, 9252 (9).... 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 54615 (9) and Pygmy dipole resonances in the tin region by N. Tsoneva and H. Lenske, Phys. Rev. C 77 24321 (8). Exotic modes of excitation in atomic nuclei far from stability by Nils Paar, Dario Vretenar, Elias Khan and Gianluca Colò, Rep. Prog. Phys. 7 691 (7). 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, 4131 (). Nuclear symmetry energy and neutron skins derived from pygmy dipole resonances by A. Klimkiewicz et al., Phys. Rev. C 76, 5163(R) (7). Low-lying dipole response: Isospin character and collectivity in 68 Ni, 132 Sn, and 8 Pb by X. Roca-Maza, G. Pozzi, M. Brenna, K. Mizuyama, and G. Colò, Phys. Rev. C 85, 2461 (12). Pygmy resonances and neutron skins by J. Piekarewicz, Phys. Rev. C 83, 34319 (11). 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 8 Pb nuclei. For that, we use three Skyrme interactions with very different isovector properties (L ranges from 4 MeV to 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 2461 (12) 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 χ Lagrangian and approach in the exotic 68 Ni and 132 Kebeler et al. PRL5 () 1612 Q. Montecarlo Neutron Matter Sn and Gandolfi and et al. PRC85 the (12) 3281 stable (R) 8 Neutron-Star Mass-Radius (Neutron Star) Pb Observations Steiner et al. Astrophys. J. 722 () 33 p nuclei. For charge & α scattering that, ex. Neutron Skin Lie-Wen Chen et al. PRC 82 () 24321 we use Neutron three Skin Skyrme Centelles interactions et al. PRL 2 (9) 12252 with very Antiprotonic Atoms Neutron Skin Warda et al. PRC 8 (9) 24316 different isovector properties Mass (L ranges Kortelainen from et al. PRC 82 () 424313 Nuclear MeV to Model Fit Mass Danielewicz NPA 727 (3) 233 Heavy Ion Empirical Agrawal et al. PRL9 (12) 26251 Collisions MeV). We focus on: Dipole Polarizability Giant RPA and unperturbed GDR dipole strength. Resonances N A scattering PDR the transition densities. Charge Ex. Reactions Optical Potential Energy Levels Parity Violating e-scattering IVGQR L estimates n p Emission Ratio Isospin Diffusion Parity Violating Asymmetry the isoscalar or isovector nature. 4 6 8 1 L (MeV) the most relevant p-h contributions. PDR Famiano et al. PRL 97 (6) 5271 Tsang et al. PRL 3 (9) 12271 Roca-Maza et al. PRC 87 (13) 3431 Roca-Maza et al. in preparation (13) Trippa et al. PRC 77 (8) 6134(R) Klimkiewicz et al. PRC 76 (7) 5163(R) Carbone et al. PRC 81 () 4131(R) Xu et al. PRC 82 () 5467 PREX Collab. PRL 8 11252 (12) 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 2461 (12) 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 8 Pb nuclei. For that, we use three Skyrme interactions with very different isovector properties (L ranges from 4 MeV to 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 2461 (12) 8

B IV (E1) [fm 2 MeV 1 ] 15 Dipole strength functions (IV) 5 3 2 1 9 11 12 Exp. 11 MeV [1] SGII SkI3 SLy5 68 Ni B IV (E1) [fm 2 MeV 1 ] 5 4 3 7 6 5 4 3 2 1 8 9 Exp. 9.8 MeV [2] SGII SkI3 SLy5 132 Sn B IV (E1) [fm 2 MeV 1 ] 8 6 4 15 5 7 8 9 15 25 Energy [MeV] Exp. 7.37 MeV [3] Exp. 13.43 MeV [3] SGII SkI3 SLy5 8 Pb 5 15 Energy [MeV] 5 15 Energy [MeV] larger L larger PDS peak A. Carbone et. al., PRC81 () 4131. Isovector properties of the interactions: SGII L = 37.6 MeV SLy5 L = 48.3 MeV SkI3 L =.5 MeV Experiment: [1] O. Wieland et. al., PRL 2 (9) 9252. [2] P. Adrich et. al., PRL 95 (5) 13251. [3] N. Ryezayeva et. al., PRL 89 (2) 27252. 9

Microscopic analysis of the PDS RPA versus unperturbed strength B IV (E1) [fm 2 MeV 1 ] 4 35 3 25 15 5 SGII SkI3 SLy5 Unperturbed 68 Ni 4 35 3 25 15 5 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)

δρ(r) [fm 3 ] Microscopic analysis of the PDS the transition densities ( amplitude of neutron and proton transition probabilities as a function of r-coordinate) r [fm] 2 4 6 8.4 r p r n neutrons protons -.4 -.8.4 -.4 -.8.4 SGII E = 9.77 MeV SkI3 E =.45 MeV -.4 68 Ni SLy5 -.8 E = 9.3 MeV 2 4 6 8 r [fm] δρ(r) [fm 3 ] r [fm] 2 4 6 8.5 r p r n isovector isoscalar -.5 -.1.5 -.5 -.1.5 -.5 -.1 68 Ni SGII E = 9.77 MeV SkI3 E =.45 MeV SLy5 E = 9.3 MeV 2 4 6 8 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? B IV (E1) = ν ( Z drr 3 δρ n A ν(r) N ) drr 3 δρ p A ν(r) B IV (E1) [fm 2 MeV 1 ] 3 25 15 SkI3 IS 7% [,R] IS 7% [,R/2] 68 Ni IS 7% [R/2,R] 3 25 15 5 5 15 25 15 25 Energy [MeV] [N. Paar et. al., PRL3 (9) 3252] 15 25 IS nature of the PDS due to outermost nucleons (neutrons in a neutron-rich nucleus). The r np is correlated with I and L. 12

Microscopic analysis of the PDS The most relevant p-h excitations in the IS and IV dipole response B(E1) (E1) [e fm] A q ph 25 15 5-5 68 Ni ph,q A q ph (E1) 2 2p 1f 5/2 2d 1/2 2d 3/2 3/2 2p 1f 1g 3/2 3s 1/2 7/2 9/2 1f 2d 2p 1/2 2d 5/2 3/2 3/2 2p 3/2 2d 1f 1g 7/2 9/2 5/2 SGII SkI3 (E1) [e fm] A q ph 15 15 15 E ph [MeV] neutrons protons 1f 5/2 2d 3/2 1f 7/2 1g 9/2 2p 1/2 3s 1/2 2p 3/2 2d 5/2 SLy5 E = 9.77 MeV E =.45 MeV E = 9.3 MeV 2 1-1 68 Ni 2p 3/2 2d 5/2 1g 9/2 1f 7/2 1f 7/2 1g 9/2 2d 3/2 2p 1/2 neutrons protons SGII SkI3 SLy5 E = 9.77 MeV E =.45 MeV E = 9.3 MeV -2 8 12 14 8 12 14 8 12 14-2 25 15 5-5 1f 7/2 1g 9/2 1f7/2 1g 9/2 E ph [MeV] The largest neutron p-h contributions (around 8 with B IS > 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 1f 5/2 2d 3/2 1f 7/2 1g 9/2 1f7/2 1g 9/2 2 1-1

Collectivity: Coherence of the different contributions 3 cumulative sum cumulative sum (E1) [e fm] A IV ph 2 1-1 -2 π ν π ν π 3 n ph 132 Sn SGII SkI3 SLy5 3 n ph ν 3 4 n ph A IS ph (E1) [e fm3 ] 8 6 4 3 4 n ph 132 Sn SGII SkI3 SLy5 π ν π ν π 3 4 n ph ν 3 4 5 n ph The largest p-h contributions are: coherent in the IS channel, less coherent in the IV channel. 14

Single particle units: qualitative indications B(E1;IV) [s.p. units] 7 6 5 4 3 2 1 SGII 8.52 MeV 8 9 SkI3 9.23 MeV 8 9 E [MeV] SLy5 132 Sn 8.64 MeV 8 9 B(E1;IS) [s.p. units] SGII 16 8.52 MeV 12 8 4 8 9 SkI3 9.23 MeV 8 9 E [MeV] 8.64 MeV SLy5 132 Sn 8 9 If different p-h states are contributing coherently to the PDS, B(E1) in single-particle units should be clearly larger than 1. 15

B(E1;IS) ( 2 fm 6 MeV 1 ) B(E1;IS) ( 3 fm 6 MeV 1 ) Dipole strength functions (IS) 3 3 pygmy region 68 Ni 3 4 E (MeV) pygmy region (b) (b) 8 Pb 3 4 E (MeV) B(E1;IS) ( 3 fm 6 MeV 1 ) 12 8 4 pygmy region 3 E (MeV) (b) 132 Sn The response of the low-energy pygmy state to an isoscalar probe is comparable to the high-energy states corresponding to the ISGDR 16

Conclusions: PDS in 68 Ni, 132 Sn, 8 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!