Dipole Polarizability of 120 Sn and 208 Pb T. Hashimoto et al ., to be published in PRC 208 Pb calc. by P.-G. Reinhard SkM* SV-min SkP SV-bas SkT6 RD-min SG-II SkI3 SLy6 Total: α D = 20.1 ± 0.6 fm 3 BSk4 UNEDF2 120 Sn (p, p’) DD-PC-min ( γ , n) DD-ME-min ( γ , xn) FSU ( γ , xn) FSU2 α D (fm 3 ) 135 MeV 1.12 ± 0.07 7.00 ± 0.29 0.82 ± 0.12 Total: α D = 8.93 ± 0.36 fm 3
Plans in Near Future • Measurements on 112 Sn, 124 Sn and on 92 Zr, 94 Zr, 96 Zr, have been done in May-June, 2015. • Data analyses on 48 Ca, 90 Zr, 96 Mo, and 154 Sm Zr isotopes: presentation by C. Iwamoto on Tuesday
Spin-M1 Responses and Quenching of IS/IV Spin-M1 Strengths H. Matsubara et al., PRL 115 , 102501 (2015) 1
Self-Conjugate ( N = Z ) even-even Nuclei ground state: 0 + ; T =0 We focus on these nuclei. Stable self-conjugate even-even nuclei: ( 4 He), 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, 32 S, 36 Ar, 40 Ca
Energy spectra at 0-degrees 28 Si 12 C 24 Mg 32 S 36 Ar
IS/IV-spin-M1 distribution
Spin-M1 SNME H. Matsubara et al., PRL 115 , 102501 (2015) ・ Summed up to 16 MeV . ・ Compared with shell-model predictions using the USD interaction bare-g effective-g Squared Nuclear Matrix elements Non-quenching Isoscalar spin-M1 SNME is NOT quenching.
np Spin Correlation Function Shell-Model: USD interaction = (IS-IV)/16 p effective quenching n i S ! (g eff /g) is SNME S !
np spin correlation function ! ! N ! Z ! ∑ ∑ S n ≡ S p ≡ s n , i s p , i i i ! ! ! ! 2 − S ! ! ( ) ( ) p = 1 2 n ⋅ S n + S n − S S S p p 4 ( ) ! " ! " ( ) ( ) = 1 ∑ ∑ 2 2 M σ − M σ τ z 16 : np spin correlation function of the nuclear ground state spin aligned np -pair s n ⋅ ! ! s p > 0 hints isoscalar np -pairing
np Spin Correlation Function Shell-Model: USD interaction � Correlated Gaussian Method: W. Horiuchi � Non-Core Shell Model: P. Navratil p n i S ! S !
np Spin Correlation Function Shell-Model: USD interaction � ab-initio type calc. � Correlated Gaussian Method: W. Horiuchi � with realistic NN int. Non-Core Shell Model: P. Navratil p n i S ! S !
np Spin Correlation Function Shell-Model: USD interaction � ab-initio type calc. � Correlated Gaussian Method: W. Horiuchi � with realistic NN int. Non-Core Shell Model: P. Navratil p n i S ! S ! Further theoretical studies are interesting: large scale shell model, non-core shell model, coupled cluster calc, etc.
Spin Susceptibility Very Preliminary Inversely energy-weighted sum rule N of the spin-M1 strengths magnetization S H 2 N (spin part) χ σ = 8 1 ∑ ∑ σ i f 0 ω 3 N S f i M = χ σ H χ σ : spin magnetic susceptibility. Spin Susceptibility of N = Z Nuclei 0.006## 0.005## 0.0044(7) MeV -1 at ρ =0.16 fm -3 χ σ (MeV − 1 ) 0.004## Neutron matter calc. 0.003## by AFDMC model 0.002## 0.001## G. Shen et al., PRC 87 , 025802 (2013) 0.000## 10# 15# 20# 25# 30# 35# 40# • magnetic response of nuclear matter � • ν -emissivity � A • ν -transportation
Conclusion/Future CAGRA+GR Campaign Exp. in 2016 • Study on PDR by ( p , p ’ γ ) and ( α , α ’ γ ) *1 isospin/surface property, transition density ang. dep. • ( 6 Li, 6 Li’ γ ) for IV spin-flip inelastic ex. *2 CAGRA(Clover Ge Array) E. Ideguchi and M. Carpenter for γ -coincidence measurements also plans for LaBr3 detectors spokespersons: *1 A. Bracco, F. Crespi, V. Derya, M.N. Harakeh, T. Hashimoto, C. Iwamoto, P. von Neumann-Cosel, N. Pietralla, D. Savran, A. Tamii, V. Werner, and A. Zilges et al . *2 S. Noji, R.G.T. Zegers et al .,
Conclusion/Future CAGRA+GR Campaign Exp. in 2016 E441 5.0 days ( 6 Li, 6 Li' γ ) for IV spin-flip inelastic excitation E450 25.0 days (p,p' γ ) and ( α , α ' γ ) for PDR (p,p' γ ) and ( α , α ’ γ ) for PDR in E454 6.0 days (p,p' γ ) at 300 MeV and ( α , α ' γ ) for PDR 64 Ni, 90,94 Zr, 120,124 Sn, 206,208 Pb Total 36.0 days. Transition densities by QPM 208 Pb( p , p ’) at E p =80 MeV PDR like transition density d σ /d Ω (mb/sr) Estimated size of the n p statistical uncertainties GDR like transition densities P.-G. Reinhard and W. Nazarewicz PRC87, 014324 (2013) Collaborators A. Bracco*, F. Crespi*, F. Camera*, O. Wieland*, … θ cm (deg) D. Savran*, A. Zilges*, V. Derya*, J. Isaak*,… M.N. Harakeh*, A. Tamii*, C. Iwamoto*, T. Hashimoto, N. Nakatsuka*… *Participants in COMEX5 P. von Neumann-Cosel, N. Pietralla, V. Werner, … A. Maj*, B. Wasilewska*, M. Krzysiek*, … A new collaborative project of Angela and Adam. R.G.T. Zegers*, S. Noji, S. Lipscutz*, …
Conclusion/Future • Electric dipole response of 208 Pb and 120 Sn: (p, p’) Measured precisely by proton inelastic scattering. ( γ , n) ( γ , xn) IV properties of the effective interaction: ( γ , xn) • Constraints on the symmetry energy • Neutron skin thickness, pygmy dipole excitations Isotope dependence on Sn and Zr have been measured. T. Hashimoto et al ., to be published in PRC. • Non-quenching IS spin- M1 matrix elements in sd -shell. Quenching of IV spin- M1 and GT matrix elements. • Requires further knowledge on the quenching phenomena. H. Matsubara et al ., PRL115, 102501 (2015) • Hints IS np -pairing correlation in the ground state.
RCNP-282 Collaboration 208 Pb RCNP, Osaka University A. Tamii, H. Matsubara, H. Fujita, K. Hatanaka, H. Sakaguchi Y. Tameshige, M. Yosoi and J. Zenihiro Dep. of Phys., Osaka University IKP, TU-Darmstadt Y. Fujita P. von Neumann-Cosel, A-M. Heilmann, � Y. Kalmykov, I. Poltoratska, V.Yu. Ponomarev, Dep. of Phys., Kyoto University A. Richter and J. Wambach T. Kawabata � KVI, Univ. of Groningen CNS, Univ. of Tokyo T. Adachi and L.A. Popescu K. Nakanishi, IFIC-CSIC, Univ. of Valencia Y. Shimizu and Y. Sasamoto B. Rubio and A.B. Perez-Cerdan � Sch. of Science Univ. of Witwatersrand CYRIC, Tohoku University J. Carter and H. Fujita M. Itoh and Y. Sakemi iThemba LABS � F.D. Smit Dep. of Phys., Kyushu University Texas A&M Commerce M. Dozono C.A. Bertulani Dep. of Phys., Niigata University GSI Y. Shimbara E. Litivinova 33
RCNP-316 Collaboration 120 Sn T. Hashimoto†, A. M. Krumbholz 1 , A. Tamii 2 , P. von Neumann-Cosel 1 , N. Aoi 2 , O. Burda 2 , J. Carter 3 , M. Chernykh 2 , M. Dozono 4 , H. Fujita 2 , Y. Fujita 2 , K. Hatanaka 2 , E. Ideguchi 2 , N. T. Khai 5 , C. Iwamoto 2 , T. Kawabata 6 , D. Martin 1 , K. Miki 1 , R. Neveling 7 , H. J. Ong 2 , I. Poltoratska 1 , P.-G. Reinhard 8 , A. Richter 1 , F.D. Smit 6 , H. Sakaguchi 2,4 , Y. Shimbara 9 , Y. Shimizu 4 , T. Suzuki 2 , M. Yosoi 1 , J. Zenihiro 4 , K. Zimmer 1 � †Institute for Basic Science, Korea 1 IKP, Technische Universität Darmstadt, Germany 2 RCNP, Osaka University, Japan 3 Wits University, South Africa 4 RIKEN, Japan 5 Institute for Nuclear Science and Technology (INST), Vietnam 6 Kyoto University, Japan 7 iThemba LABs, South Africa 8 Institut Theoretical Physik II, Universität Erlanen-Nürnberg, Germany 9 CYRIC, Tohoku University, Japan
RCNP-E241 & E299 Collaboration spin-M1 50
Thank you
Fine Structure of GDR and its direct g.s. gamma decay (under discussion) fine structure of GDR d σ ( ) (p,p’) Coulomb-Ex. d Ω 0 ° γ -decay B.R. GDR g.s. d σ ( ) → B E 1 ( ) → Γ 0 The total width Γ will be determined d Ω 0 ° for each part of the GDR. B . R . = Γ 0 pioneering works: 52 J. R. Beene et al.,PRC41, 920(1990) Γ A. Bracco et al., PRC39, 725(1989)
Unit cross section (UCS) ・ Conversion factor from cross-section to Squared Nuclear Matrix Elements (SNME) ・ Calibration from β and γ -decay measurements (on the assumption of the isospin symmetry). d σ 2 ( ) ˆ ( ) ( ) 0 F q , E M O ° = σ ( T = IS or IV) T x f d Ω UCS Kinematical factor SNME ( ) 1 / 3 ˆ ( A ) N exp xA σ = − T T.N. Taddeucci, NPA469 (1987). ・ Function taken from the mass dependence of GT UCS
Summary • Electric dipole response of 208 Pb and 120 Sn have been precisely measured. Proton inelastic scattering was used as an electro- magnetic probe (relativistic Coulomb excitation). α D ( 208 Pb) = 20.1 ± 0.6 fm 3 α D ( 120 Sn) = 8.93 ± 0.36 fm 3 • Electric dipole polarizability ( α D ) is sensitive to the difference between the proton and neutron distributions. • The neutron skin thicknesses and the constraints on the symmetry energy parameters have been extracted with the help of mean field calculations.
Backup Slides 27
核子当たりのエネルギー Nuclear Equation of State (EOS) Neutron matter ( δ =1) E/N (MeV) E/A (MeV) Neutron matter ( δ =1) Symmetry Energy (+ Coulomb) Nuclear matter ( δ =0) Neutron Density (fm -3 ) Nucleon Density (fm -3 ) Steiner et al., Phys. Rep. 411 325(2005) Prediction of the neutron matter EOS is much model dependent.
Neutron Skin and Density Dependence of the Symmetry Energy For larger L : Smaller S δ 2 at higher ρ Larger S δ 2 at lower ρ larger neutron skin Neutron skin thickness Energy minimum Density dependence of the symmetry energy (equilibrium)
Neutron Skin and Density Dependence of the Symmetry Energy For smaller L : Larger S δ 2 at higher ρ Smaller S δ 2 at lower ρ smaller neutron skin Neutron skin thickness Energy minimum Density dependence of the symmetry energy (equilibrium)
Neutron Skin Thickness Measurement by Electroweak Interaction PREX PREX Result: S. Abrahamyan et al. , PRL 108 , 112502 (2012) Theor. Calc.: X. Roca-Maza et al. , PRL 106 , 252501 (2011) Future measurements: PREX-II: factor of 3 smaller statistical uncertainty for 208 Pb CREX: for 48 Ca The model independent determination of δ R np by PREX important but the present accuracy is limited.
Electric Dipole Polarizability ( α D ) α D ! " ! " = α NE P Restoring force ← symmetry energy α : dipole polarizability of an atom Inversely energy weighted sum-rule of B(E1) ( ) σ abs ω 2 d ω = 8 π α D = ! c E 1 dB E 1 ∫ ∫ Requires the B ( E1 ) 2 π 2 ω distribution 9
CREX WS, March 17-19, 2013 (Electric) ¡Dipole ¡Polarizability balanced symmetry ¡ restoring ¡force E1-‐‒field energy
CREX WS, March 17-19, 2013 (Electric) ¡Dipole ¡Polarizability with ¡neutron ¡skin w/o ¡neutron ¡skin smaller ¡restoring ¡force larger ¡restoring ¡force
CREX WS, March 17-19, 2013 (Electric) ¡Dipole ¡Polarizability thicker ¡neutron ¡skin smaller ¡restoring ¡force larger ¡displacement with ¡neutron ¡skin w/o ¡neutron ¡skin smaller ¡restoring ¡force larger ¡restoring ¡force larger ¡dipole ¡polarizability
CREX WS, March 17-19, 2013 (Electric) ¡Dipole ¡Polarizability Sensitive ¡to ¡the ¡ difference ¡between ¡the ¡ proton ¡and ¡neutron ¡ density ¡distribution. with ¡neutron ¡skin w/o ¡neutron ¡skin smaller ¡restoring ¡force larger ¡restoring ¡force
Neutron Skin Thickness and Dipole Polarizability ( α D ) P.-G. Reinhard and W. Nazarewicz, ( Δ r np ) PRC 81, 051303(R) (2010). Covariance analysis with SV-min interaction in the framework of energy density functional. Strong correlation between the α D and the neutron skin of 208 Pb ( α D ) X. Roca-Maza et al ., PRC 88 , 024316(2013) 208 Pb Correlations observed in various interaction sets. insights from the droplet model
Electric Dipole (E1) Response of Heavy Nuclei neutron separation energy GR and Continuum (Main Strength) Discrete (Small Strength) NRF B(E1) ( γ ,xn) ( γ , γ ’) (p,p’) Low-lying E1 IVGDR ( PDR) 0 g.s. S n S p
NuSym13,July 22-26, 2013 at NSCL X. Roca-Maza et al., arXiv:1307.4806 a D J is a strong isovector indicator. Insights from the droplet model
Two Approaches for the Neutron Skin Thickness Probing the matter/neutron/weak-charge distribution Takes the difference from the charge (or p ) distribution → ∆ R np • Less/no model dependence � PREX • Data must be highly accurate p elastic scattering ( ) coherent π production σ Δ R np ~ 0.02 fm 5.45 fm ~ 4 × 10 − 3 Both approaches are important. R p Probing the difference between the p/n distribution • Requires theoretical models � Dipole Polarizability • Data can be less accurate PDR ( ) σ Δ R np ~ 0.02 fm GDR 0.2 fm ~10 − 1 68 Δ R np
Two Approaches for the Neutron Skin Thickness Probing the matter/neutron/weak-charge distribution Takes the difference from the charge (or p ) distribution → ∆ R np • Less/no model dependence � PREX • Data must be highly accurate p elastic scattering ( ) coherent π production σ Δ R np ~ 0.02 fm 5.45 fm ~ 4 × 10 − 3 Both approaches are important. R p Probing the difference between the p/n distribution If n diffuseness is changed, the • Requires theoretical models � Dipole Polarizability E1 response would change. • Data can be less accurate PDR ( ) σ Δ R np ~ 0.02 fm GDR 0.2 fm ~10 − 1 69 Δ R np
Electric Dipole Response of Nuclei oscillation between oscillation of neutron B ( E1 ) neutrons and protons skin against core? 1 - Low-Lying core Dipole Strength neutron skin PDR GDR g.s. 0 S n S p
Proton inelastic scattering as an electro-magnetic probe of the electric dipole response Missing Mass Spectroscopy with Virtual Photon Only the scattered Insensitive to the decay channel. protons are measured. Total strengths are measured. detector p p virtual photon ( q , ω ) * A A Excited State Target Nucleus Select low momentum transfer (q~0) kinematical condition, i.e. at zero degrees EM Interaction is well known Coulomb Excitation at 0 deg. (model independent)
Relativistic Proton Inelastic Scattering at Forward Angles as a probe of electric dipole response of nuclei •An electromagnetic probe (Coulomb excitation) • High-resolution (20-30 keV) , high/uniform det. efficiency in E x •Covers a broad E x of 5-22MeV •Insensitive to the decay channels (sensitive to the total strength ) •Requires a small amount of target material (several mili-gram) and a few days of beam time •Applicable to stable nuclei (Coulomb excitation/dissociation in inverse kinematics for unstable nuclei)
CREX WS, March 17-19, 2013 RCNP, Osaka Univ. J-PARC RIKEN KYOTO TOKYO OSAKA July 28 2008 seminar @ LNL
Research Center for Nuclear Physics (RCNP), Osaka University Polarized p beam at 295 MeV High-resolution WS beam-line (dispersion matching) High-resolution Spectrometer Grand Raiden
Spin Precession in the Spectrometer g θ p : precession angle with respect to the beam direction ( 1 ) θ = γ − θ p b 2 θ b : bending angle of the beam g: Lande’s g-factor γ : gamma in special relativity ≅ 162 ≅ 180 θ ° θ ° b b
Setup for E282&E316
Distribution of B(E1) I. Poltoratska, PhD thesis low-lying discrete states GDR region Excellent agreement between (p,p’) and ( γ , γ ’) below ~ S n
B(E1): low-lying discrete states Excellent agreement between (p,p’) and ( γ , γ ’) below ~ S n I. Poltoratska, PhD thesis
B(E1): GDR Excellent agreement among three measurements in the GDR region I. Poltoratska, PhD thesis
Excellent agreement with ( γ , γ ’) below Sn, and with ( γ ,n) and ( γ ,abs) in the GDR region AT et al., PRL107, 062502(2011)
CREX WS, March 17-19, 2013 Electric Dipole Polarizability up ¡to ¡130 ¡MeV 20.1±0.6 ¡fm 3 /e 2 I. ¡Poltoratska, ¡PhD ¡thesis
Electric Dipole Response of 208 Pb Low-lying Dipole Strength Giant Dipole Resonance (Pygmy Dipole Resonance) Dipole Polarizability (fm 3 ) 20"# 15"# 10"# 5"# Integrated 0"# 5" 10" 15" 20" Excitation Energy (MeV)
Electric Dipole Response of 208 Pb Low-lying Dipole Strength Giant Dipole Resonance (Pygmy Dipole Resonance) alpha_D'in'208PbA α D in 208 Pb Dipole'Polarizability'alpha_D'(fm^3) � Dipole Polarizability α D (fm 3 ) 20.0#$ Dipole Polarizability (fm 3 ) 20"# DP is saturating at around ~40 MeV. 15.0#$ 15"# 10"# 10.0#$ 5"# Integrated 5.0#$ 0"# 5" 10" 15" 20" 0.0#$ 0.0## 20.0## 40.0## 60.0## 80.0## 100.0## 120.0## Excitation Energy (MeV) Excitation'Energy'(MeV) �
Energy Weighted (TRK) Sum-Rule of 208 Pb E10EWSR'in'208Pb 7 1.8#$ Energy'Weighted'Sum0Rule'(TRK'unit) 7 1.6#$ 1.4#$ 1.2#$ 1.0#$ 0.8#$ 0.6#$ 0.4#$ 0.2#$ 0.0#$ 0.0## 20.0## 40.0## 60.0## 80.0## 100.0## 120.0## Excitation'Energy'(MeV) �
Quasi-Deuteron Excitation Contribution? Absorption of a photon by a virtual deuteron in nuclei. 208 Pb 120 Sn α D ( 208 Pb) = 20.1 ± 0.6 fm 3 quasi- d : 0.51 ± 0.15 fm 3 120 Sn quasi- d contribution α D ( 120 Sn) = 8.93 ± 0.36 fm 3 quasi- d : 0.34 ± 0.08 fm 3 The contribution is small but is included in the numbers. it is unclear whether it should be removed it for comparison with theoretical predictions. 85
(Electric) Dipole Polarizability X. Roca-Maza et al ., PRC 88 , 024316(2013) 208 Pb P E = α
Neutron Skin Thickness of 208 Pb X. Roca-Maza et al . PRC88, 024316 (2013) ¡Δ r np ¡= ¡0 ¡.165 ¡± ¡(0 ¡.009) expt ¡± ¡(0 ¡.013) theor ¡± ¡(0 ¡.021) est ¡fm ¡ for ¡the ¡estimated ¡ J =31 ¡± ¡(2) est
Neutron Skin Thickness of 208 Pb ¡Δ R np ¡= ¡0 ¡.165 ¡± ¡(0 ¡.009) expt ¡± ¡(0 ¡.013) theor ¡± ¡(0 ¡.021) est ¡fm ¡ for ¡the ¡estimated ¡ J =31 ¡± ¡(2) est X. Roca-Maza et al ., PRC 88 , 024316(2013)
Neutron Skin Thickness of 208 Pb X. Roca-Maza et al., PRC88, 024316 (2013) C.J. Horowitz et al., JPG41, 093001 (2014)
PDR strength E1 Response of 208 Pb and α D core ? neutron skin PDR AT et al., PRL107, 062502(2011)
Application of the PDR : constraints on the symmetry energy • Theoretical dependences of pygmy EWSR on J and L are determined using relativistic energy density functionals spanning the range of J and L values. Available experimental data provide constraints on theoretical models. DD-ME Similar approach but different theory ➔ A. Carbone et al, PRC 81, 041301(R) (2010) Exp. Data: 68 Ni : O. Wieland et al, PRL 102, 092502 (2009) 132,130 Sn: A. Klimkiewicz et al., PRC 76, 051603 (R) (2007) 208 Pb: I. Poltoratska et al., PRC 85, 041304 (R) (2012) Courtesy of N. Paar
Determination of Symmetry Energy AT et al., EPJA 50 , 28 (2014). C.J. Horowitz et al., to be published in JPG. DP: Dipole Polarizability HIC: Heavy Ion Collision PDR: Pygmy Dipole Resonance IAS: Isobaric Analogue State FRDM: Finite Range Droplet Model (nuclear mass analysis) n-star: Neutron Star Observation c EFT: Chiral Effective Field Theory QMC by S. Gandolfi et al QMC M.B. Tsang et al. , PRC 86 , 015803 (2012) I. Tews et al., PRL110, 032504 (2013) 208 Pb PDR EWSR Analysis with DD-ME by N. Paar Model uncertainty should be evaluated.
Cluster Dipole Sum-Rule of PDR Assuming that the PDR is formed by the dipole oscillation of the neutron skin against the other part (core), PDR core ? neutron skin Y. Alhassid, M. Gai and G.F. Bertsch, PRL49, 1482(1982) Cluster Dipole Sum-Rule H. Sagawa and M. Honma, PLB251,17(1990) R. de Diego, E. Garrido et al., PRC77, 024001 (2008) ( ) 2 60 Z s A c − Z c A s + = AA s A c ( ) ( ) TRK: 60 NZ A , N , Z A s , N s , Z s = 0 A c , N c , Z c = Z A Number of neutrons in the skin: N s 2% TRK → N s (skin) ~ 12 R n =5.66 ¡and ¡δR np ¡= ¡0.168±0.022 ¡ → ¡ N s ¡ = ¡10.9±1.4 The numbers look consistent to each other
Electric Dipole Response of 208 Pb Low-lying Dipole Strength (Pygmy Dipole Resonance) Value up to E x (TRK unit) Integrated TRK Sum Rule 0.10#$ The amount of E1 strength which 0.08#$ corresponds to the neutron skin oscillation 0.06#$ predicted by the cluster sum-rule. 0.04#$ 0.02#$ 0.00#$ The correlation between the PDR strength 5" 6" 7" 8" 9" 10" 11" and the neutron skin thickness will be Excitation Energy E x (MeV) discussed by the next speaker, Dr. Inakura.
Dipole Polarizability of 120 Sn T. Hashimoto et al ., submitted α D ( 208 Pb) (fm 3 ) α D ( 120 Sn) (fm 3 )
Dipole Polarizability of 120 Sn T. Hashimoto et al ., submitted
Dipole Polarizability of 120 Sn T. Hashimoto et al ., submitted
PDR in 120 Sn A.M. Krumbholtz et al ., PLB744, 7(2015)
PDR in 120 Sn A.M. Krumbholtz et al ., PLB744, 7(2015) ( γ , γ ’): B. Özel-Tashenov, et al ., PRC90, 024304(2014)
PDR in Deformed Nuclei: 154 Sm A. Krugmann et al. in the INPC2014 Proceedings PDR Bumps?
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