CNS, University of Tokyo S. Shimoura
Introduction Structure and Dynamics of Nuclei as functions of N and Z in a wide area of nuclear chart Collectivities / Single-Particle Properties of Nuclear Matter Decoupling of P and N <=> Isospin symmetry New Magic Numbers Shape Coexistence Neutron Skin/Halo Di-neutron correlation Giant/Pigmy Resonances Stable @RIBF Known ~ Available now > 10 3 /s 1-10 3 /s 10-3 - 1 /s Theoretical Prediction
Size/ρ-distribution Skin/Halo Shell Structure New magic # Isospin / Deformation New modes etc. IVE1 ISE0, ISE1 " L, " S, " J " T; q,!,... Size/ρ-distribution σ R, elastic scat. Shell Structure Mass / S n, S 2n Inelastic scatt. Low lying states Knockout / Transfer New modes Coulex Inelastic scatt. CEX etc.
Introduction Structure information of nuclei as functions of N and Z Shell Evolution Collectivities (clustering) / Single particle structure in excited states Nuclear responses 14 O 22 O Disappearance of N=20 magicity 12 Be Disappearance of N=8 magicity Deformation / Cluster structure
Inverse Kinematics w/ RI beam RI beam (0.1 10 5 pps; ΔE~a few %) Exc. States γ rays Decay Fragments Target as probe Interaction Formation of Excited States of Exotic Nuclei Direct reactions and their selectivities In-beam spectroscopy measuring decay products Invariant-mass/γ-ray spectroscopy Particle detectors at forward angles (kin. focus.) Gamma detectors surrounding target (Doppler shift) Missing-mass spectroscopy Recoil & Active Target Measurement Dispersion Matching/Measurement
Probes for direct reactions Heavy Nuclei: Strong Coulomb Field Coulomb Excitation, Coulomb Dissociation E1, E2, (M1) / Isovector H, D, 4 He [Liquid targets] Inelastic Scattering Isovector (H) / Isoscaler(H, D, 4 He) Spin-Flip (H, D) / Spin-Non-Flip (H, D, 4 He) Charge Exchange Fermi type (H) / Gamow-Teller type (H, D) Nucleon Transfer (α,t), (α, 3 He) Reaction Knockout Other (Be, C, ) Inelastic Scattering Knockout / Fragmentation Dirty RI beams and/or Changing Target Same Nucleus can be populated via Different Processes without changing Detector System
Liquid Helium Target (CRYPTA) 100-250 mg/cm 2 24-30 mm φ 7µm Havar window Kept less than 4K sealed with Al cylinder Melting point of helium is 4.2K @ 1atm Developed by CNS/Rikkyo/RIKEN Cold head H. Ryuto et al., NIMA 555 (2005) 1 Target
Observables reaction/decay meas. Yields (Cross Sections) / Lifetime / Width Spectra : As a function of Exc. Energy (+ incident energy) Properties of populated states ( Selectivity) Angular Distribution / Momentum Transfer Assignment of L J π Eikonal Model [Knockout] Virtual Photon / DWBA / Coupled Channels [Coulex, Inelastic, Transfer] Optical Potential / Transition Density Folding Model with Density Dependent Effective Interaction Angular Correlation / Alignments Assignment of J π Cross sections as a function of
Typical Setup of Experiment inverse kinematics 30% Doppler Shift @140 Gamma-ray detector 75 Charged particle detector Plastic scintillator ΔE, E, and position 12 Be vacuum 12 Be, 13 B F3 Beam tracker Position and direction Separate high and low vacuum 120mg/cm 2 4K β 0.3 H. Ryuto et al., NIMA 555 (2005) 1
Analysis of Alpha inelastic excitation WF s of gnd. and exc. states (φ 0 (r), φ(r)) Gnd. State density (ρ 0 (r)) Distorting pot. (V 0 (r)) O.M. analysis Elastic Scat. Data Global Systematics Microscopic Macroscopic BM; Tassie α, β, δ Folding with effective interaction v eff Macroscopic BM β, δ DWBA transition density (ρ tr (r)) Transition pot. (V tr (r)) Experimental Data Integrated C.S., Ang. Distr. Ang. Cor. J π, δ=βr, Transition Matrix Element δ sum rule
Alpha inelastic scattering DWBA by using single folding model with DD interaction Collective form factor Compression mode Tassie model
γ γ spectrum coincident with 12 Be ejectiles 2.1 & 2.7 MeV States excited by (α, α ) DWBA [ col. FF & folding pot.] Angular Distributions of 12 Be* 2 + 1 -
γ γ α α 2.1 & 2.7 MeV States excited by (α, α ) Alignments of 12 Be* Anisotropic Angular Distribution of γ Consistent with Prediction of DWBA calculation assuming 2 + & 1 - excitation, resp. Confirmation of 1 - assignment for 2.7 MeV state
Alpha inelastic scatterings 4 He( 14 O, 14 O*) @ 60 A MeV No bound states in 14 O 14 O* 13 N+p, 12 C+2p, 12 C*+2p, 10 C+α, 10 C*+α Isoscalar E0 & E1 modes (compression) Multipole Decomposition Analysis (MDA) of Isoscalar excitation Effect of Continuum
Compression modes Isoscalar Vibration Compression modes
14 O 14 C (mirror pair; sub magic) No bound state 0 + 1 14 O 14 C 6 bound states 1, 0 +, 3, 0, 2 +, 2
4 He( 14 O, 14 O * ) at 60 A MeV 14 O* 13 N+p, 12 C+2p, 12 C*+2p, 10 C+α, 10 C*+α
4 He( 14 O, 14 O * ) at 60 A MeV G.S. Density of 14 O L=0 L=1 L=2 L=3 Relativistic mean field (TIMORA) HO density Angular distributions for two (Unfold from e-scat. on 14 C) types of 14 O density
4 He( 14 O, 14 O * ) at 60 A MeV (MDA) Angular distributions 1 - state at Ex=5.17 MeV Ex=10.2 10.4 MeV Ex=15 16 MeV
Partial Cross Sections for each Multipole 4 He( 14 O, 14 O * ) - MDA L=0 L=1 L=2 L=3 L>3 13 N+p 5 8 5 25 2010.6.2 Ex (MeV) Ex (MeV) Seminar @ Chiba All L=0 L=1 L=2 L=3 L>3 40% 78% 16% 10% Fraction of EWSR (Ex<25 MeV)
4 He( 14 O, 14 O * ) : Strength distribution Dipole L=0 L=1 RPA Calc. (Sagawa) RPA Calc. (Sagawa) 14 C 14 O 5 Ex (MeV) 20 5 Ex (MeV) 20 One bound 0 + state in 14 C One bound 1 - state in 14 C
Alpha inelastic scattering to highly excited cluster states 4 He( 12 Be, 6 He+ 6 He) & 4 He( 12 Be, 4 He+ 8 He) @ 60 A MeV Cluster states in 12 Be L=0, 2, (4) excitations Multipole Decomposition Analysis (MDA) including decaying process
E x spectra of 6 He+ 6 He & α+ 8 He 6 He+ 6 He α+ 8 He
Angular distribution of (α,α ) Angular correlation of 6 He+ 6 HeDecay (interference) d d & 2 MDA analysis = " ineld" decay l, m 2 * (# ) Y ( )!% l$ lm lm " decay
100% Same method (with odd l) is applied for 4 He+ 8 He channel (preliminary)
6 He+ 6 He α+ 8 He Very preliminary
6 He 6 He α α + 145 kev Freer et al. Bohlen et al. 210 kev 360 kev α n n α + n n α 8 He α α + + -
M. Ito, N. Itagaki, H. Sakurai, and K. Ikeda, Phys. Rev. Lett. 100, 182502 (2008)
4 He( 12 Be, 6 He 6 He), 4 He( 12 Be, 4 He 8 He) MDA. Resonant states including negative parity states Lifetime of 12m Be(0 + ) Large mixing of (p) 2 and (sd) 2 $ "! + #! ~ (π) 2 ~ (σ) 2 #! + "!
Nucleon Transfer from 4 He @ 30-50 A MeV Proton Single particle states in neutron-rich nuclei 4 He( 12 Be, 13 Bγ) [S. Ota et al., Phys. Lett. B 666 (2008) 311] 4 He( 22 O, 23 Fγ), [ 4 He( 23 F, 23 Fγ), 4 He( 24 F, 23 Fγ), He( 25 Ne, 23 Fγ)] utilizing cocktail beams [S. Michimasa et al., Phys. Lett. B 638 (2006) 146] p n
Nucleon (Proton) Transfer from Alpha (d,n), ( 3 He,d), (α,t), Incident energy higher than 30 MeV/u Thicker target (100~200 mg/cm 2 ) Less distortion effect Less multi-step process Same optical potential as inelastic excitation Identification by comparing with other direct reactions But x Momentum mismatch
Momentum Matching Condition (Classical) As if Getting off from the moving train (projectile) to platform (target) Internal motion in the train (Fermi motion in the projectile) along the opposite direction of the train (target) Motion on the platform (Fermi motion of the nucleon on the target) along the direction of the train
Momentum Matching Condition (QM) % % r k c' c' xb T T " [ c] [ c'] a + A! b + B Post PW Prior PW V V = 2 a xb xa b a % % = = c c r k c =! a B!! = ( b + = ( A + c' r & k c' = & = & c' V V xb xa x) + V ( 2$ ) ( 2$ ) r ; k " 2 B xa x) Plane Wave Born Approx. h 2 ; h 2 1 1 + V 3 =! ba ba 2 h 2µ c! c! xb 2 h 3 2µ xa r = k & c a B 2µ xb 2µ Binding energies of a and B xa a x r xb b r c r c r xa B r 2 2 3 r r ikxb ( xb 3 r ( k + " ) d r # ( ) e d r # *( ) xb r 2 2 3 r r ikxb ( xb 3 r ( k + " ) d r # ( ) e d r # *( ) A B xa r k c' a B ' ' xb xb a a xb xb ' ' xa xa B B xa xa A e e r & ik xa r & ik Fourier Components of wave functions of nucleon (x) in a and B Same value but different expressions xa r ( xa r ( xa
Proton Transfer in Momentum Space 2 12 Be(d,n) @ 50 A MeV 2 12 Be(α,t) @ 50 A MeV q (fm -1 ) 1 0-2 12 Be E x =0 13 B*(10MeV) -1 p q z (fm -1 ) 0 d E x =40 n 1 q (fm -1 ) 1 0-2 12 Be E x =0 E x =40 p 13 B*(10MeV) α -1 0 q z (fm -1 ) t 1 13 B* d 13 B* α
DWBA Calculation Example: 22 O(α,t) 23 F 22 O(d,n) 23 F
N-rich N=8 Nuclei Spin-orbit splitting between νp 1/2 & νp 3/2 depend on the number of protons in πp 3/2 orbit attracting νp 1/2 orbit V Τ p n n-rich Boron 8 sd p 1/2 p 3/2 6 p n n-rich Beryllium sd p 1/2 p 3/2 12 Be Low-lying 2 + state Low-lying 1 - state Low-lying 0 + 2 state Magicity loss in N=8 Deformed ground state Change of Boron Proton Shell as a function of configuration sd p 1/2 sd p 1/2 13 B Spherical ground state How about excited states? p n p n 13 B 13 gs B* 2010.6.2 Deformed core + proton? Seminar @ Chiba p 3/2 p 3/2
4 He( 12 Be, 13 Bγ) @ 50 A MeV Deformed 12 Be core + 1 proton? C 2 S(BM) ~ 0.27 for δ=0.4 β( 12 Be(p,p )) ~ 0.6-0.7 8 [101]1/2 Spherical G.S. Deformed Excited 1/2 +? [220]1/2 [101]3/2 ε 2 ~ δ ~ 0.95β 0.3 [110]1/2
Spectra of 14 C, 12 Be, 11 B, and 13 B 2 + 0 + 1-7012 6589 6094 S n =4878 + 1-0 + 2 + 2700 2240 2100 0 + 14 C 11 B 13 B 0 + 12 Be
4 He( 12 Be, 13 Bγ) @ 50 A MeV CNS GRAPE NaI(Tl) array 12 Be beam 4.83 MeV states strongly excited by (α, t) Liq. He target
4 He( 12 Be, 13 Bγ) @ 50 A MeV Angular Distribution of 13 B coin. with 4829 kev γ FR-DWBA (DWUCK5) Optical Potential: 12 C + 4 He (entrance) 12 C + 3 He (exit) L=0 -> J π = 1/2 + C 2 S ~ 0.2 -> Proton single particle state on 12 Be
4 He( 12 Be, 13 Bγ) @ 50 A MeV Proton single particle state on 12 1/2+ Be: 0.30 1/2+ : 0.003?? 1/2+ : 0.03? 1/2- : 0.87 3/2- : 0.15 3/2+ 5/2+ 1/2+ : 0.01 PSDFU 2010.6.2 PSDFU Seminar @ Chiba 3/2- Shell model (3hw)
13 B(1/2 + 1) Present calc. Hyper deformation? 1/ E x + 2 1! 8 MeV! = 0.73 2 3 h# = ( sd) " ( sd)! Proton intruder state in neutron-rich nuclei neutron proton 4He(12Be,13Bγ) Experiments By Ota et al. 1/ 2 + E x! 5 MeV + α - α + 2010.6.2 By Seminar Kanada-Enyo @ Chiba
1/2 + state in 13 B* by AMD Kanada-Enyo prelim.
Exotic Magic Number at N=16 (Z~8) Spin-orbit splitting between νd 3/2 & νd 5/2 depend on the number of protons in d 5/2 orbit attracting νd 3/2 orbit by V στ 16 d 3/2 s 1/2 d 5/2 V Τ 20 p n p n n-rich n-rich Oxygen Fluorine Excitation energy of 3/2 + S.P. state in 17 F & 23 F? d 3/2 s 1/2 d 5/2 Change of Fluorine Proton Shell as a function of Neutron number d 3/2 s 1/2 d 5/2 V Τ p n p n 17 F* 23 F*?
23 F spectra S. Michimasa et al., Phys. Lett. B 638 (2006) 146 Data are taken simultaneously +1p Inel. -1n -1n1p
S. Michimasa et al., Phys. Lett. B 638 (2006) 146 22 O(a,t) 23 F*
νd 5/2 empty νd 5/2 full 2010.6.2 S. Michimasa et al., Phys. Lett. Seminar B 638 (2006) @ Chiba 146
SHARAQ Project @ RIBF Exp. Studies of Nuclear Many-body System Varieties in Detectors Sensitivities Nucleus Sensors Observables Materials Nuclides Probes Interactions Varieties in Nuclei N-/P-rich Nuclei RIBF Varieties in Probes Reactions using various quantum numbers Isospin (T) Spin (J, L, S) Parity (π) Energy & Momentum (ω, q) A (N, Z)... Probe
Motivation Response of Nuclear System using Intermediate-Energy direct reactions Studies using New Quantum Probe RI beam Large Isospin and Mass Excess Various I π ( Excited states ) Controlling Transferred Momenta, Q-values, Spin, Isospin ΔS ΔT q-ω Accessing kinematical area/conditions inaccessible by stable nuclear beam Ordinary kinematics (Missing mass spectroscopy) -> High Resolution Spectrometer + High Quality RI Beam + (Detectors of decaying particles) Asymmetric nuclear System studied using stable probes Inverse kinematics + Invariant Mass / γ-decay / Recoil and High-resolution missing-mass spectroscopy
Int. E Direct reactions (150-400 A MeV) Weak Distortion :Minimal central force Effective Interaction : Spin-Isospin modes d' d$ ~ % fi (& )# C t ( q) " % ( q) r ST ~ v r 3 iq" 2 tr ( q) d r % ( r) e dr r R ( r) j ( qr) Y ( qˆ ) =! fi =! r fi 2 l l k f θ lm q k i
SHARAQ Spectroscopy with Highresolution Analyzer of RadioActive Quantum beams RI Beam (E = 150 400 MeV/A) as a new PROBE beam (stable) to nuclear systems Large Isospin iso-tensor excitations Large internal energy (q,ω) inaccessible by stable beams beam (unstable) (q,ω) ejectile (unstable) large negative Q-value Endothermic (q,ω) ejectile (stable) small Q-value Photon line: q=ω Stable Beam ω IVSMR Multi n s DGT Exothermic Charge Exchange Reactions GT SHARAQ q
Multi-neutron system 3,4 n ; 6,7 H with small q Resonant states? Correlation in multi-body scattering states? Correlation Spectral shape B C He LiBe H n Multi- Neutron Superheavy Hydrogen! (MeV) 2010.6.2 q (MeV/c ) Seminar @ Chiba 8 He 4 He 4n 4 He( 8 He, 8 Be) @ 200 A MeV 8 Be 4 He( 18 O, 18 Ne) @ 40 A MeV
Multi-neutron system 2 n 3,4 He( 8 He, 8 Be) 3,4 n p s p 6,7 Li( 8 He, 8 Be) 6,7 H 4 n Double Dipole α n 2 n 2 n p s p p Dipole x Fermi/GT s n p n 7 Li 7 H
New Spin-Isospin Modes in nuclei: IVSMR IsoVector Spin-Monopole Resonance (IVSMR) β & β + directions ( 12 N (1 + ), 12 C), ( 12 B (1 + ), 12 C) Q=+17 MeV/ +13 MeV ( 11 Li, 11 Be*[1/2 - ]) : Q=+20 MeV Compression mode with στ O ~ r 2 στ Ex, width Spin compressibility of nuclear matter GT strengths @ higher Ex 12 N 12 C (q,ω) small Q-value 2010.6.2 40 MeV/c Seminar @ qchiba ω Single Charge Exchange Reaction IVSMR GTR 50 MeV Sakai-G Project Grant-in-Aid of MEXT ( 12 N, 12 C), ( 12 B, 12 C) @ 250 A MeV (p,n), (n,p) @ 800 MeV
New Spin-Isospin Modes in nuclei: DGTS Double Gamow-Teller States (DGTS) Not yet discovered Two-phonon response E DGTS = 2E GTS? Γ DGTS = 2 1/2 Γ GTS? Nuclear matrix elements for double beta decay ( 20 Mg, 20 Ne) ( 9 C(3/2 ), 9 Be(3/2 )) ω Double Charge Exchange Reaction DGTS 30 MeV Double β decay 30 MeV/c Sakai-G Project Grant-in-Aid of MEXT ( 20 Mg, 20 Ne) @ 200 A MeV ( 12 C, 12 Be) @ 40 A MeV q
Specification dispersion (D) 5.86 m horizontal magnification (M x ) 0.40 D/M x 14.7 m momentum resolution (image size 1mm) 1/14700 vertical magnification (M y ) 0.0 angular resolution < 1 mrad vertical acceptance ± 3 deg for spot size 60mm 10mm (in dispersion matching operation) horizontal acceptance ± 1deg solid angle 2.7 msr for spot size of 10mm 10mm solid angle 4.8 msr
SHARAQ プロジェクト 核反応前後でやりとりされるエネルギー 運動量を高分解能で測定 新しい魔法数 様々な変形 振動状態 中性子物質 高温原子核の反応 SHARAQスペクトロメータの仕様 運動量分解能 Δp/p < 1/15000 高機能 RI ビームライン どれだけ音程が区別できるか 分散測定 最大磁気剛性 Bρ = 6.8Tm (ρ=4.8m) 始めの音の音程を測る どれだけ高い音まで測れるか 分散整合 立体角 ΔΩ =5 msr 始めと終わりの音程差を測る どれだけ小さな音まで測れるか 運動量範囲 +/- 3% 2009年稼働開始 どれだけ音域が広いか 2010.6.2 Seminar @ Chiba
Summary Alpha induced direct Reactions combined with invariant-mass/γ spectroscopy are powerful tools to investigate excited states in exotic nuclei Cluster states Isoscaler responses Nucleon transfer reactions at 30-50 A MeV are useful for searching single-particle states Single particle structure Structure change in excited state Future : SHARAQ spectrometer and gamma-detector GRAPE will be used for studies at heavier exotic nuclei