Reaction dynamics of slow collisions in light neutron excess systems － Unified studies from bounds to continuum in Be isotopes 伊藤 誠 関西大学 システム理工学部 物理応用物理学科 I. Introduction II. Framework III. Varieties of structures in 12 Be and Be isotopes IV. Enhancements induced by large amplitude motions V. Summary and feature plan
IKEDA Diagram Cluster structures in 4N nuclei Ikeda’s Threshold rules Molecular structures will appear close to the respective cluster threshold. Be isotopes Molecular Orbital : Itagaki et al., Abe et al,…. α ‐ Particle ⇒ Stable ― 3 H+p ～ 20 MeV Systematic Appearance + of cluster structures PRC61,62 (2000)
Studies on Exotic Nuclear Systems in (E x ,N, Z,J) Space Slow RI beam Unbound Nuclear Systems Ex. energy Systematics of 8 ～ Decays in Is Threshold Continuum Rule valid ?? 16 Be Structural Change Low ‐ lying Molecular Orbital : ― 、 ＋ ‥ N ( N,Z ) : Two Dimensions
Interests from the viewpoints of large amplitude collective motions Reactions are extreme limits of large amplitude collective motions ! Combined states Binary states How to characterize … Breakup Reaction path in adiabatic energy surfaces (AESs) Scattering Subjects 1. Pursuit of structural changes over a wide region in AESs 2. Investigation of reaction path in AESs and enhancements in connection to AESs structures Today’s report 1. Global features of structures in 12 Be and Be isotopes 2. Non ‐ adiabatic phenomena in large amplitude reactions
Extension of microscopic cluster model (Test calculation for 10 Be) 10 Be= + +N+N 6 He 5 He 5 He Mol. Orb. Combine Unified model between M.O. and He clusters :PLB588 (04) ... S + + C2 C3 C1 S, Ci : Variational PRM. 0Pi (i=x,y,z) Coupled channels with Atomic orbitals Absorbing B.C. Scattering B.C. Tr. densites < | | > → + 6 He + 6 He Cross sections Decay widh 10 Be PTP113 (05) PLB636 (06) Breakup ｰ i W(R)
： 12 Be= + +4N Femto Molecules 7 He 5 He Covalent Ionic )(0p L ) ( + ) 2 + 8 He ⇒ 6 He+ 6 He (0p R 8 6 He 6 He + 0 6 + 0 5 Atomic 4 0 4 + 6 He + 6 He Neutrons’ ex. Energy ( MeV ) 0 3 + 0 + 8 He 8 He Clusters’ Relative ex. ( ‐ ) 2 ( ‐ ) 2 −4 Ionic 0 2 + −8 Various structures are 0 1 + generated by excitation ( ‐ ) 2 ( + ) 2 of ‐ 0 4 8 12 and neutron degree α − α Distance ( fm ) α − α α − α α − α of freedom.
Be isotopes from bounds to continuums : J = 0 + 8 Be 10 Be 12 Be 14 Be 16 Be 1 − Re S el 2 0 1 − Re S el 1 − Re S el 1 − Re S el 1 − Re S el 2 0 2 0 2 0 2 0 8 8 8 8 8 4 4 4 4 4 Energy ( MeV ) Energy ( MeV ) Energy ( MeV ) Energy ( MeV ) Energy ( MeV ) 0 0 0 0 0 −4 −4 −4 −4 −4 −8 −8 −8 −8 −8 Deformed states (Clusters) Excitation of y He x He ‐ rel. motion Compact states (Shell model)
Global behaviors of Level Crossings in Be isotopes C + D E + F* Internal E + F States A + B Energy Clusters ( Intruder ) Level Crossing Asymptotic States Compact ( Normal ) Small Large Core ‐ Core distance
Level Crossings in 12,14 Be= + +XN (X=2,6) 10 Be 14 Be 20 20 (0p) 2 (sd) 4 Excitation Energy ( MeV ) Excitation Energy ( MeV ) 10 10 + 6 He g.s. 8 He g.s. + 6 He g.s. 0 0 (sd) 2 4 He + 6 He 6 He + 8 He Level Crossing Level Crossing (0p) 2 (0p) 4 (sd) 2 −10 −10 0 2 4 6 8 10 12 0 2 4 6 8 10 12 α − α Distance ( fm ) α − α Distance ( fm )
10 Be (0+) case : M.I., PLB636, 236 (2006) Adiabatic surfaces (J = 0 + ) Energy spectra ( J = 0 + ) Adiabatic energy surfaces (J P = 0 + ) Adiabatic energy surfaces (J P = 0 + ) 20 20 Weak + 6 He(2 1 + ) Coupling Excitation Energy ( MeV ) Excitation Energy ( MeV ) 10 10 − − ) − − ) 2 2 2 2 ( π ( π 1/2 ( π ( π ) ) 1/2 1/2 1/2 − ) − − − ) 2 2 2 2 ( π ( π ( π ( π 1/2 ) ) 1/2 1/2 1/2 α + 6 He(2 1 + ) α α α ｰ i W(R) Cluster 0 0 + + + + ) ) 2 2 2 2 4 He + 6 He g.s. ( σ 1/2 ( σ ( σ ( σ ) ) 4 He + 6 He g.s. 1/2 1/2 1/2 + ) + + + ) 2 2 2 2 ( σ ( σ 1/2 ( σ ( σ ) ) 1/2 1/2 1/2 − ) − − − ) 2 2 2 2 ( π 3/2 ( π ( π ( π ) ) 3/2 3/2 3/2 − − − − ) ) 2 2 2 2 ( π 3/2 ( π ( π ( π ) ) 3/2 3/2 3/2 −10 −10 0 4 8 12 0 4 8 12 α − α Distance ( fm ) α − α Distance ( fm )
Nuclea breakup : 10 Be + 12 C ⇒ 10 Be(0 + + 12 C (CDCC cal.) conti.) Smat.( Conti. ← G.S. ) Smat.( Poles ← G.S.) S ‐ matrices to continuums S ‐ matrices to Poles Pole contribution in decays to 4 He+ 6 He(2 1 + ) Psude states <− ground state 0.5 0.002 4 He + 6 He(2 1 + ) Cluster 4 He + 6 He(2 1 + ) Cluster 0 3 + | S f<−i | 2 | S f<−i | 2 1st Peak ( Single ) 0 3 + 0.25 0.001 2nd Peak ( Coherent ) 0 4 + − ) 2 (π 1/2 + 0 4 − ) 2 (π 1/2 0 0 0 4 8 12 16 0 4 8 12 16 Decay energy ( MeV ) Decay energy ( MeV )
Reaction path in 10 Be → x He + y He Breakup reaction (Positive Parity) 10 Be(0 + ) → [ + 6 He(2 1 + ) ] 0 + Reaction Path in Breakup Adiabatic energy surfaces (J P = 0 + ) Adiabatic energy surfaces (J P = 0 + ) Adiabatic energy surfaces (J P = 0 + ) 20 20 20 Weak Coupling 4 He + 6 He(2 1 4 He + 6 He(2 1 + ) + ) Excitation Energy ( MeV ) Excitation Energy ( MeV ) Excitation Energy ( MeV ) 10 10 10 − ) − ) 2 2 − − 2 2 ( π 1/2 ( π ( π ( π ) ) 1/2 1/2 1/2 α + 6 He(2 1 + ) α α α 0 3 + × 0 0 0 4 He + 6 He g.s. 4 He + 6 He g.s. 4 He + 6 He g.s. + + + + ) ) 2 2 2 2 ( σ ( σ 1/2 ( σ ( σ ) ) 1/2 1/2 1/2 − ) − − − ) 2 2 2 2 ( π 3/2 ( π ( π ( π ) ) 3/2 3/2 3/2 + 0 1 − − ) − − ) 2 2 2 2 ( π ( π ( π ( π 3/2 ) ) 3/2 3/2 3/2 −10 −10 −10 0 4 8 12 0 4 8 12 0 4 8 12 α − α Distance ( fm ) α − α Distance ( fm ) α − α Distance ( fm ) → 0 3 0 1 + + is the dominant transition. Non ‐ adiabatic path is main process.
⇒ + 6 He(2 1 + 6 He g.s. + ) scattering (Negative Parity) + 6 He(0 1 + ) → + 6 He(2 1 + ) + 6 He g.s. Adiabatic energy surfaces (J P = 1 − ) Adiabatic energy surfaces (J P = 1 − ) 20 20 [ α + 6 He(2 1 + ) ] [ α [ α [ α Excitation Energy ( MeV ) Excitation Energy ( MeV ) 10 10 [ α + 6 He g.s. ] [ α [ α [ α 0 0 α + 6 He g.s. 4 He + 6 He g.s. α α α − σ − − − + ) + + + ( π ( π ( π ( π 3/2 σ σ σ 1/2 ) ) ) 3/2 3/2 3/2 1/2 1/2 1/2 0 4 8 12 0 4 8 12 α − α Distance ( fm ) α − α Distance ( fm ) Avoided crossing at the surface Landau ‐ Zener type enhancement
Level Crossing in 12 Be (1) Un correlated AESs Correlated AESs 10 10 Energy ( MeV ) Energy ( MeV ) + 8 He g.s. + 8 He g.s. ( ‐ ) 2 ( + ) 2 0 0 + ( ‐ ) 2 ( + ) 2 + 8 He g.s. + ( ‐ ) 2 ( + ) 2 ( ‐ ) 2 ( ‐ ) 2 S=1 corr. ( ‐ ) 2 ( ‐ ) 2 −10 −10 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 Distance ( fm ) Distance ( fm ) Two AESs are almost degenerated due to correlations ⇒ Crossing occurs at inner region !
Level Crossing in 12 Be (2) Correlated AESs AESs with full coupling 10 10 + 8 He g.s. Energy ( MeV ) Energy ( MeV ) Coupling with all configurations 0 0 Conjunction G.S. ⇔ + 8 He G.S. −10 −10 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 Distance ( fm ) Distance ( fm ) Lowest minimum smoothly connected to + 8 He g.s. ⇒ Formation of adiabatic conjunction
Monopole transition of 12 Be Adiabatic conjunction enhances the monopole transition ! A 2 0 M ( E 0 , IS ) 0 r 2 f i 1 M ( E 0 , IS ) i 1 a. u. 0 8 8 8 He 5 He + 7 He 4 4 Energy ( MeV ) 6 He + 6 He Energy ( MeV ) + 0 3 0 0 4 He + 8 He + → 0 3 + 0 1 is enhanced. −4 −4 ( ‐ ) 2 ( + ) 2 −8 −8 + 0 1 2 3 4 5 6 7 8 Distance ( fm )
Contents of present report 1. Unified studies form bounds to continuums in Be isotopes 2. Reactions with large amplitudes in connection to adiabatic energy surfaces Results 1. There appears a wide variety of structures in excited states (Cluster + excess N) 2. Enhancements occur depending on the structures of AESs. 10 Be : Non ‐ adiabatic path is dominant in monopole breakup and slow scattering. 12 Be : Adiabatic path is dominant in monopole b.u. (Formation of conjunction) Feature studies Recently, we have just succeeded in extending the model to general two centers. O= + 12 C+XN 、 Ne= + 16 O+XN ⇒ Extension to SD shell Generalities and Specialities : hybrid structures of clusters + excess neutrons in O and Ne
Systematics based on the Cluster Picture 10 Be 14 Be ) － 4 L:(0P 3/2 L:(0P 3/2 ) 4 Similar R:(0P 3/2 ) － 2 ) 2 R:(0P 3/2 8 Be 16 Be ) － 4 L:(0P 3/2 ) 4 L:(0P 3/2 Similar ) － 4 R:(0P 3/2 ) 4 R:(0P 3/2 We are now analyzing wave functions. Special feature in 12 Be 12 Be= 6 He+ 6 He, + 8 He is a self conjugate when atomic p ‐ h are exchanged. ⇒ This is a special nucleus in even Be isotopes
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