Coulomb Breakup and Pairing Excitation

of Two-Neutron Halo Nucleus 11Li

Niigata University S . AoyamaRCNP T. MyoHokkaido Univeristy K. KatoRiken K. Ikeda

S. Aoyama, K. Kato, T. Myo and K. Ikeda, PTP 107(2002).

T. Myo, S. Aoyama, K. Kato and K. Ikeda, PLB576(2003).

Neutron Halo Structure

neutronneutron

9Li-core

Neutron Halo

9Li+n subsystem 　⇒ unbound

9Li+n+n　⇒ loosely bound

n+n subsystem ⇒unbound

Borromean system

B.V. Danilin et al. PRC43, 2835(1991)

Complex Scaled Cluster Orbital Shell Model

9Li+n+nthreshold

4He+n+n: S. Aoyama, S. Mukai, K. Kato and K. Ikeda, PTP93 (1995).

Many higher orbits

Gamow Shell Model (Complex Scaled Shell Model)N. Michel, W. Nazarewicz, M. Ploszajczak , J. Okolowicz, PRC67(2003).R. ID Betan, R.J. Liotta, N. Sandulescu, T. Vertse, PRL89(2002).

E. Balslev and J.M. Combes, Commun. Math. Phys. 22(1971), 280.J. Aguilar and J.M. Combes, Commun. Math. Phys. 22(1971), 269.

Proof of ECR for CSM was given in

Giraud and Kato, Ann. of Phys.308(2003).

Giraud et al., J. Phys. A37(2004).

Gamow Shell Model is also based on ECM.

Core-n: Folding potential

n-n: Minnesota(u=0.95)

V-type T-type

Cluster Orbital Shel Model (Hybrid TV model )

＋ψJM=φJM(V)+φJM(T)

・ wave function

・ Core+n+n Hamiltonian

・ potential

Gaussian-type potential

VFcore-n=Vcnt +Vls

S. Aoyama, K. Kato and K. Ikeda, PTP. Suppl. No.142 (2001).

Energy Convergence of 3/2- state in 11Li

Channel of COSM (V-type)[1] (p1/2)2

[2] (p1/2)2+ (s1/2)2

[3] ・・・・・

Channel of ECM (T-type) l=L=S=0

9Li-n potential: HN1,δ= 0.245, δp= 0.0866n-n potential: Minnesota, u=0.95

V-type

V-type T-type

+

COSM

Hybrid -TV

S. Aoyama, K. Kato and K. Ikeda, PTP. Suppl. No.142 (2001)

28 shell-like orbits (l=14)

Shell-like bases can not accurately describe halo! !

Partners of mixed configurations of (1s1/2)2 and (0p1/2)2 in 11Li

1s1/2

0p1/2

10Li

9Li+n threshold

Ground 3/2- state

11Li

9Li+n+nthreshold

(0p1/2)2+ (1s1/2)2 　 +　・・・

(1s1/2)2+ (0p1/2)2 　 +　・・・

Excited 3/2- state

loosely bound state

three-body resonance

Pairing excited 9Li+n+n resonance

Calculations with the Hybrid TV model

A peak is observed at 0～1MeV in the Coulomb (E1) breakup experiments.

⇒ Soft dipole resonance?

(E1 or 1- resonance)

Neutron Halo

9Li-core

Dipole oscillation

K. Ikeda, INS Report JHP-7(1988).

P.G. Hansen and B. Jonson , EPL4(1987).

Separation of the Strength Function for Eλ-trandition

Complex scaled Hamiltonian

In this calculation, we deveop COSM in order to include the core excitation.

No three-body resonant states which correspond to the soft dipole mode!

Summary(1)As an excited resonance in 11Li, by using CSM, we predict the pairing type three-body resonance at low energy region (0～ 1MeV).

(2)For the peak of the E1 strength in 11Li, we understand that the experimental peak is considered to be from the 10Li+n breakup and the 9Li+n+n breakup rather than the three-body resonance.

Next problem

We will study new Riken data.