Nucleon transfer reaction in low-Nucleon transfer reaction in low-

energy energy ++66He collisions and He collisions and

continuum structures of continuum structures of 1010BeBe

M. ItoM. Ito, K. Yabana, K. Yabana

Institute of Physics, University of TsukubaInstitute of Physics, University of Tsukuba

K. Kato K. Kato

Div. of Phys., Grad. Sc. of Sci., Hokkaido UnivDiv. of Phys., Grad. Sc. of Sci., Hokkaido Univ

K. IkedaK. Ikeda

Institute of physical and chemical research, RIkenInstitute of physical and chemical research, RIken

Unified studies from the nuclear structures and the nuclear reactions

IntroductionIntroductionCluster structure (N=Z)Cluster structure (N=Z)

88Be = 2Be = 2, , 1212C = 3C = 3, , 2020Ne = Ne = ++1616OO

Clusters + Valence neutronsClusters + Valence neutrons　　 Be = 2Be = 2+Xn : Molecular Orbital+Xn : Molecular Orbital　　 C = 3C = 3+Xn : Linear chain, D+Xn : Linear chain, D3h 3h SymmetrySymmetry

　　 　　 N. Itagaki et al.N. Itagaki et al.

　　 Ne = Ne = ++1616O+Xn : O+Xn : deformationdeformation　　 　　 W. von. OertzenW. von. Oertzen

g.s.g.s.Ex.Ex.

Dynamics in the Two cores + XN systemDynamics in the Two cores + XN system

Collisions

Decays

Breakup

G.S.

Res.

Excitations

Nuclear Structures

Nuclear Reactions

Should be combine !!

ER,

(E), d(E), d/d/d

Be isotopesBe isotopes 　　 ( ( + + + n + n + + n + n +…. )…. ) Low-lying statesLow-lying states : Molecular Orbital : Molecular Orbital

Resonant statesResonant states : : 66He or He or 88He ??He ??

-- ++

1010Be = (Be = (--))22

1212Be = (Be = (--))2 2 ((++))22

1010Be=Be= + +66HeHe 1212Be=Be=66He+He+66HeHe

BeBe 　→　　→　 He + He + HeHe

M. Freer et al.M. Freer et al.A.A. Saito et al.Saito et al.

++66He collisionsHe collisionsR. Raabe et al.R. Raabe et al.

ClusteringClustering !! !!

Our approach ( Our approach ( 1010Be=Be=+++n+n )+n+n )

Description of the internal and asymptotic statesDescription of the internal and asymptotic states Generalized Two-center Cluster Model (GTCM)Generalized Two-center Cluster Model (GTCM)

Resonance parameters in compound systemResonance parameters in compound system Absorbing-kernels in Generator Coordinate (AGC)Absorbing-kernels in Generator Coordinate (AGC) ( Absorbing Boundary Condition )( Absorbing Boundary Condition )

Reaction cross sectionReaction cross section Kohn-Hulthen-Kato’s method (KHK)Kohn-Hulthen-Kato’s method (KHK)　　　　 ( Incident and exit channels )( Incident and exit channels )

ｰ i W(R)

M.O. A.O.

OurOur Model ( Model ( 1010Be = Be = + + + n+ n ) + n+ n )

PJMK

=

ORI

L

Mol. Orb. Weak coupling

I x L ＝ J

0Pi (i=x,y,z)

PJMK + +

..

.+ +

Generalized Two-center Cluster Model ( I )Generalized Two-center Cluster Model ( I )

Basis functionBasis function

JJKK((S) = PS) = PJJ

MK MK A A { { LLRR}}SS

particle, (0s)particle, (0s)44 in H.O. in H.O. NeutronsNeutrons ( Left or Right, 0p( Left or Right, 0pxx,0p,0pyy,0p,0pz z

)) S

Generalized Two-center Cluster Model ( II )Generalized Two-center Cluster Model ( II )

Total wave functionTotal wave function

JJ = = S S KK f(f(S,K) S,K) JJKK((S)S)

= = S S JJ(S)(S)

Eigenvalue ProblemEigenvalue Problem

<< JJKK((R) | H – R) | H – EE | | JJ > = 0> = 0

Adiabatic Energy SurfacesAdiabatic Energy Surfaces

<< JJKK((S) | H – S) | H – E(S)E(S) | | JJ(S)(S) > = 0> = 0

( H = t i + v ij )

Adiabatic energy surfaces (Volkov No2. + G3RS)Adiabatic energy surfaces (Volkov No2. + G3RS)

+ + 66He ( I ) He ( I ) ] ] LJLJ

[[ 55He(IHe(I11) + ) + 55He (IHe (I22)) ]] LJLJ

Blue Dots

Red Dots

+ 6He(01+)

Results of GTCM + AGC for Results of GTCM + AGC for 1010Be(0Be(0++) )

Adiabatic surfaces (J= 0+) Energy spectra ( J= 0+ )

Results of GTCM + AGC + KHK for Results of GTCM + AGC + KHK for 1010Be(0Be(0++) )

+6He(01+) → +6He(21

+)( + 6He) + (5He + 5He) :

6He→01+,21

+,02+,22

+, 5He→3/2-,1/2-

Crossing of adiabatic surfaces in Crossing of adiabatic surfaces in 1010BeBeJ= 0+ (Gradual Coupling) J= 1- (Pseudo Crossing)

Coupled ch. In adiabatic basis for Coupled ch. In adiabatic basis for 1010Be(0Be(0++))

+6He g.s. Elastic scattering

Adiabatic process is dominant.

Coupled ch. In adiabatic basis for Coupled ch. In adiabatic basis for 1010Be(1Be(1--) )

+6He g.s. Elastic scattering

Non-adiabatic transition strongly occurs.

Summary and ConclusionSummary and Conclusion 1. Studies on Clustering and the valence nucleons1. Studies on Clustering and the valence nucleons It is very interesting and important to study the It is very interesting and important to study the

nuclear structures and their enhancements in nuclear structures and their enhancements in reactions.reactions.

2. GTCM + AGC + KHK2. GTCM + AGC + KHK It is possible to study from the point of view of the nuclear reaction and structures..

3. Applications to 3. Applications to 1010Be Systematic studies !!⇒Be Systematic studies !!⇒

Excitation of 0Excitation of 033++ and 0 and 044

++ ⇔ ⇔ Intrinsic structuresIntrinsic structures

11-- Non-adiabatic process is dominant due to ⇒ Non-adiabatic process is dominant due to ⇒ the appearance of the appearance of + + 66He clustersHe clusters. .