Analyses for four-body breakup reactions of 6He

Takuma Matsumoto (RIKEN Nishina Center)

T. Egami1, K. Ogata1, Y. Iseri2, M. Yahiro1 and M. Kamimura1

(1Kyushu University, 2Chiba-Keizai College)

50th Anniversary Symposium on Nuclear Sizes and Shapes 23 June – 25 June, 2008

Nuclear and Coulomb

Target

Unstable Nuclei

Introduction

The unstable nuclear structure can be efficiently

investigated via the breakup reactions. Elastic cross section

Breakup cross section

Momentum distribution of emitted particles

An accurate method of treating breakup processes

is needed.

Structure information

n + n + core

Region of Interest

In a simplified picture, light neutron rich nuclei can be described by a three-body model

n

p 2H 3H

3He 4He 6He 8He

7Li6Li 8Li 9Li

7Be 9Be 10Be

8B 10B 11B

10C9C 11C 12C 14C13C 15C 16C

13B12B 14B 15B

12Be11Be 14Be

11Li

17B 19B

18C17C 19C 20C

Neutron

drip line

n

p 2H 3H

3He 4He 6He 8He

7Li6Li 8Li 9Li

7Be 9Be 10Be

8B 10B 11B

10C9C 11C 12C 14C13C 15C 16C

13B12B 14B 15B

12Be11Be 14Be

11Li

17B 19B

18C17C 19C 20C

Neutron

drip line

core

n

n

1

2

3

4

Four-Body Breakup

S2n < 1 MeV

Continuum-Discretized Coupled-Channels The Continuum-Discretized Coupled-Channels method (CDCC)

Developed by Kyushu group about 20 years ago M. Kamimura, M. Kawai, et al., PTP Suppl. 89, 1 (1986) Fully-quantum mechanical method Successful for nuclear and Coulomb breakup reactions

Essence of CDCC

Continuum

Bound

Breakup threshold

discretization Discretized states Breakup continuum states

are described by a finite number of discretized states

A set of eigenstates forms a complete set within a finite model space that is important for breakup processes

Four-body breakup reactions

Three-body breakupcontinuum

We have to calculate three-body discretized continuum states

Ground and Breakup States of 6He

6He : n + n + 4He (three-body model)

Channel 1 Channel 2 Channel 3

n n nn

nn

4He 4He 4He

Hamiltonian

Vnn : Bonn-A

Vn : KKNN int.

Gaussian Expansion Method : E. Hiyama et al., Prog. Part. Nucl. Phys. 51, 223 An accurate method of solving few-body problems. A variational method with Gaussian basis functions Take all the sets of Jacobi coordinates

I=0+ I=1- I=2+

Exc

itat

ion

en

ergy

of

6 He

[MeV

]

6He+12C, 6He+209Bi Scattering

4Hen

n

6He

4He

n

n

6He

6He+12C scattering 6He+209Bi scattering

209Bi

Breakup: Nuclear Breakup: Nuclear and Coulomb

12C

Coupling potential : Double folding with DDM3Y

Coupling potential : Cluster Folding

Breakup channel : 0+, 2+ Breakup channel : 0+, 1-, 2+

Nuclear Breakup Reactions of 6He on 12C

E >> Coulomb barrier : Negligible of Coulomb breakup effects Elastic cross section

Nuclear and Coulomb Breakup of 6He on 209Bi E ~ Coulomb barrier : Coulomb breakup effects are to be significant Elastic cross section

THO-CDCC calculation : M. Rodriguez-Gallardo et al., arXiv:0710.0769v2

Breakup Cross Section

g.s → 2+ cont.

g.s → 1- cont.

g.s → 0+ cont.

Nuclear and Coulomb BreakupNuclear Breakup6He+12C @ 229.8 MeV

resonance

nn[MeV] nn[MeV]

B

U [m

b]

B

U [m

b]

Discrete S matrix Continuum S matrix

E1 Transition Strength : B(E1)

ground state

I = 1- Discretized B(E1) strength

Smoothing procedure

prelim

inary

Calculated by T. Egami (Kyushu University)

Summary

We propose a fully quantum mechanical method called four-body CDCC, which can describe four-body nuclear and Coulomb breakup reactions.

We applied four-body CDCC to analyses of 6He nuclear and Coulomb breakup reactions, and found that four-body CDCC can reproduce the experimental data.

Four-body CDCC is indispensable to analyse various four-body breakup reactions in which both nuclear and Coulomb breakup processes are to be significant

In the future work, we are developing a new method of calculation of energy distribution of breakup cross section and momentum distribution of emitted particle.