dineutron formation and breaking in 8 he

Dineutron formation and breaking in 8He

2013 10th Sep.

The 22nd European Conference on Few-Body Problems in Physics 1

Department of Physics, Kyoto University　　　　　　　　　　　 Fumiharu Kobayashi

　　 Yoshiko Kanada-En’yo

arXiv:1305.4323 [nucl-th]

Introduction

2013 10th Sep.

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Dineutron correlation2013 10th Sep.

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A dineutron : A compact spin-singlet pair of two neutrons.

Dineutron correlation is enhanced in some situations.

(e.g. in the low-density region of the nuclear matter,

in the neutron-halo and -skin region of neutron-rich nuclei; 6He, 11Li…)

M. Matsuo, PRC 67 (2006)…

G. F. Bertch and H. Esbensen, Ann. Phys. (NY) 209 (1991) M. V. Zhukov et al., Phys. Rep. 231 (1993)

core

dineutron

To make clear the mechanism of the dineutron formation, andthe universal properties of the dineutron correlation.

Our aim

The 22nd European Conference on Few-Body Problems in Physics

8He2013 10th Sep. 4

a + four valence neutrons

a

(0p3/2)4-shell

6He

developed one-dineutron

a

developed two-dineutron

the 0+1 state

(Y. Kanada-En’yo, PRC 76 (2007), N. Itagaki et al. PRC 78 (2008))

the 0+2 state

Framework

2013 10th Sep.

The 22nd European Conference on Few-Body Problems in Physics 5

In order to describe 8He, we superpose two kinds of wave functions, extended 6He + 2n cluster wave functions

and 8He dineutron condensate (DC) wave functions.

Description of 8He2013 10th Sep.

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F.K. and Y. Kanada-En’yo. PTP 126 (2011)

N. Itagaki et al, PRC 71 (2005)

a6He

a 6He

The 22nd European Conference on Few-Body Problems in Physics

Extended 6He+2n cluster w.f.2013 10th Sep. 7

The 8He system is composed of 6He(H.O.(0p)2) core and two neutrons around it.

The dissociation effect in 2n cluster due to the spin-orbit interaction can be taken into account.6He

2n*

We mainly describe H.O.(0p3/2)4 and one dineutron at the surface.

The 22nd European Conference on Few-Body Problems in Physics

8He DC wave function2013 10th Sep. 8

We assume that the system is composed of the core and one dineutron.

One dineutron (spin-singlet 2n)is distributed around the corein the S-wave.

The DC wave function has two characteristic parameters, the dineutron size, bn, the expansion from the core, b.

b2bn

a

2n*

dineutron

We describe one- or two- developed dineutrons.

Result

2013 10th Sep.

The 22nd European Conference on Few-Body Problems in Physics 9

The 22nd European Conference on Few-Body Problems in Physics

8He(0+1,2)

2013 10th Sep. 1

0

a+4n threshold

EXP. CAL.

0+1 0+

1

0+2

(0p3/2)4 6He+

Poster session

(0p3/2)4-componentand one-dineutron oneare important.

Dineutron condensate state

The 22nd European Conference on Few-Body Problems in Physics

Two-dineutron condensation in 0+2

2013 10th Sep. 1

1

In 8He(0+2),

valence neutrons form two compact dineutrons.

Two dineutrons and an a are expanded largely with little correlation each other.

Two-dineutron condensation characterized by a gas-like structure of a+2dineutron.

~3fm

~5fm

Summary

2013 10th Sep.

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2

The 22nd European Conference on Few-Body Problems in Physics

Summary2013 10th Sep. 1

3

We investigated the dineutron correlation in 8He(0+).

In the excited 0+ state of 8He, the two-dineutron condensation would exist, characterized by a gas-like structure of an a and two dineutrons.

[Poster session 12th Sep. (Thu.)]In 8He(0+

1), (0p3/2)4- and developed one-dineutron components are mixed, but developed two-dineutron one is minor because of the fragility of the dineutrons.

The 22nd European Conference on Few-Body Problems in Physics

2013 10th Sep. 1

4

Description of 8He2013 10th Sep.

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5

6He+2n* → (0p3/2)4 sub-shell closure 6He in (0p)2 + one dineutron around

6He

DC → 6He in (0p)2 + one developed dineutron a + two developed dineutron

1-DC wave function2013 10th Sep.

The 22nd European Conference on Few-Body Problems in Physics 1

6

Assuming that the A-nucleon system is composed of (A-2)-nucleon core and one dineutron.

( Not a dineutron condensate state )

core (Brink) dineutronB

dineutron

Yn

n

~ bn

core

Here assuming that B = Bx = By = Bz .

Transformation to relative and c.o.m. w.f.

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7

(s-wave)

(S-wave)

coordinate transformation Y-integral

relative part

c.o.m. part

size of the dineutron

spatial expantion of the dineutron

n

nb

2bn

core

rrG

Dineutron condensate component2013 10th Sep.

The 22nd European Conference on Few-Body Problems in Physics 1

8

We calculate the overlap with aDC w.f. to see the dineutron condensate components in 8He. Here we approximate aDC w.f. as follows.

replace one of the R-integal by the d-summation

The 22nd European Conference on Few-Body Problems in Physics

One-body density2013 10th Sep. 1

9

Hamiltonian

: LS part of G3RS 　 vLS = 2000 MeV

: Volkov No.2 m=0.55, b=h=0.125 (2n unbound) or m=0.59, b=h=0.0 (2n bound)

2013 10th Sep.

The 22nd European Conference on Few-Body Problems in Physics 2

0

0+ energy spectra

6He+n+n

a+n+n+n+n

(2n bound)

(2n unbound)

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1

0+1

competition of (0p3/2)4 andone-dineutron

0+2

Two-dineutronin the S-wave

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R.m.s. radii2013 10th Sep. 2

2

The neutron expansion (halo, skin) in 6,8He(0+1) is

reproduced.8He(0+

2) has much larger neutron radius than that of 8He(0+

1).

Three body model

(a) K. Arai et al, PRC 59 (1996)

The 22nd European Conference on Few-Body Problems in Physics

Degree of shell-model component2013 10th Sep. 2

3

We calculate the squared spin and the 0p3/2-shell component.

(a) K. Arai et al, PRC 59 (1996)(b) K. Hagino et al, PRC 72 (2005)

Dineutron is major.

Shell-model and dineutron compete.

Dineutron is dominant.

in (0p3/2)2

in (0p3/2)4

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one-dineutron componentDineutron component in 0+

1

2013 10th Sep. 2

4

two-dineutron component

b : dineutron expansionb n :

dine

utro

n siz

e

(fm)

(fm)

Not only one but also two compact dineutrons are formedat the surface. (b, bn)~ (2.0, 1.5)

However, the tail component(b ≥ 4 fm) diminishesin two-dineutron one.

A dineutron is fragile.

6Heb

2bn

In the ground state,(0p3/2)4 -componentand developed one-dineutron componentare significant.

(0p3/2)46He+

b

2bna

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One-dineutron component in 8He(0+1)

2013 10th Sep. 2

5

bbn

core

In m55 (strong a-n interaction), the dineutron is more dissociated. In m59 (strong n-n interaction), the dineutron correlation is enhanced.

b : dineutron expansion(fm)b n :

dine

utro

n siz

e

(fm) m55 m59

The 22nd European Conference on Few-Body Problems in Physics

Comparison of 8He(0+1) with 6He(0+

1)2013 10th Sep. 2

6

bbn

core

b : dineutron expansion(fm)b n :

dine

utro

n siz

e

(fm) 8He 6He

In 6He, a dineutron is formed at the surface. In 8He, a dineutron is dissociated at the surface due to the spin-orbit interaction.

The 22nd European Conference on Few-Body Problems in Physics

Two-dineutron component in 8He(0+1)

2013 10th Sep. 2

7

The peak component is similar, but the tail component is reduced in 2DC.

(fm) 1DC 2DC

b n :

dine

utro

n siz

e

b : dineutron expansion(fm)b

bn

The component of two developed dineutrons is suppressed.

The 22nd European Conference on Few-Body Problems in Physics

two-dineutron component

b : dineutron expansionb n :

dine

utro

n siz

e

(fm)

(fm)

Dineutron condensation in 0+2

2013 10th Sep. 2

8

b

2bn

This state has a gas-like structure ofone a and two compact dineutrons expanded very largely.

Two-dineutron condensate state

The 22nd European Conference on Few-Body Problems in Physics

Two-dineutron condensation in 8He(0+2)

2013 10th Sep. 2

9

bbn8He(0+2) contains swelled dineutrons

expanded largely from the origin.

(fm)

b n :

dine

utro

n siz

e

b : dineutron expansion(fm)

m59 m55

Two-dineutron condensation