Dineutron condensate state in 8 He

Dineutron condensate state in 8He

12 Mar. 2013 Coexistence of weak and strong binding in unstable nuclei and its dynamics 1

Kyoto University, Department of Physics,　　　　　　　　　　　 Fumiharu Kobayashi　　 Yoshiko Kanada-En’yo

Outline• Introduction

• Dineutron correlation, cluster condensation•Part I

• Dineutron behavior in dineutron condensation of light nuclei

•Part II• Excited state of dineutron condensation in

8He•Summary


Introduction


Dineutron correlation12 Mar. 2013 Coexistence of weak and strong binding

in unstable nuclei and its dynamics 4

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) .

What is the mechanism of the dineutron formation?What is the universal properties of the dineutron correlation?

Cooper pair

dineutron

Cluster condensation12 Mar. 2013 Coexistence of weak and strong binding


a Condensation :some as in the lowest s-orbit.

Such a state is characterized by clusters weakly interacting each other and expanded largely.

The a condensate states are being investigated theoretically and experimentally.

a a a 0s

a

a

a

12C(0+2); Hoyle state

“a gas”

Some studies suggested that • a dineutron becomes compact in neutron-rich

nuclei

and

• dineutrons in light neutron-rich nuclei (8He, 7H) may condensate.

Is the dineutron condensation formed?How do the dineutrons behave in dineutron condensate state?

Dineutron condensation12 Mar. 2013 Coexistence of weak and strong binding


(Y. Kanada-En’yo, PRC 76 (2007), N. Itagaki et al. PRC 78 (2008), S. Aoyama et al. PRC 80 (2009))

(G. F. Bertsch et al. Ann. Phys. (NY) 209 (1991), M. V. Zhukov et al. Phys. Rep. 231 (1993) K. Hagino et al. PRC 72 (2005 ） … )

8He12 Mar. 2013 Coexistence of weak and strong binding


a + four valence neutrons

In this work, we investigate1. the behavior of two dineutrons

in dineutron condensate states of 8He, 6,10He and 7H using a and dineutron condensate (aDC) w.f..

part Ipart II

2. the dineutron condensate state in realistic 8He considering 0p3/2-orbits superposing 6He+2n cluster w.f. and 8He DC w.f..

higher than 0p3/2

aDC w.f. (including two dineutrons explicitly)

6He + 2n cluster w.f.

6He 2n(*)

8He DC w.f. (including dineutron explicitly)

core

Part I


• Introduction of a new framework; aDC w.f.

• Investigation of the dineutron behavior in a+2dineutron condensate state (8He)

• Comparison the dineutron behavior in 8He with those in 6,10He and 7H

Condensate wave function12 Mar. 2013 Coexistence of weak and strong binding


As a framework to describe an a condensate state in 4N nuclei, a condensate wave function (THSR wave function) is very useful.

Our framework, a and dineutron condensate (aDC) wave functionoriginates from a condensate wave function.

A. Tohsaki et al. PRL 87 (2001)

a

a

a

a condensate wave function of 12C12 Mar. 2013 Coexistence of weak and strong binding


In an a condensate wave function, a clusters move in the lowest s-orbit around an origin.

Ri; centers of the ai

b ; size of asB ; spatial expansion of as

{same for all the as

a

a

a

BO

~b

Energy surface on B-b plane12 Mar. 2013 Coexistence of weak and strong binding


An a cluster is rigid.The valley at b~1.4 fm is the indication of the Hoyle state.

B : a expansion

b : a

size

A. Tohsaki et al. PRL 87 (2001)

B

b

aDC wave function of 8He12 Mar. 2013 Coexistence of weak and strong binding


One a and two dineutrons move in the s-orbit around an origin.

Ri; centers of the cluster ibi ; size of the cluster iBi ; spatial expansion of the cluster i

βbn2

aOBa

Bn1

bn1(ba = 1.4 fm){

different for each clusterbut here Bn1 = Bn2, bn1 = bn2

Bn2

Hamiltonian12 Mar. 2013 Coexistence of weak and strong binding


: Volkov No.2 m=0.59, b=h=0.0 (2n is bound)

or m=0.55, b=h=0.125 (2n is unbound){

m = 0.55

Energy surface on Bn-bn plane12 Mar. 2013 Coexistence of weak and strong binding


m = 0.59

Bn : dineutron expansion

b n :

dine

utro

n siz

e

There is a valley (bn~1.7 fm) and a repulsive area (Bn~0 fm).

Competition between kinetic and potential energy

ValleyPauli principle between the neutrons in the s-orbit

(Bn~0)Repulsive

area

Compact dineutrons are favorable.

Bn1 = Bn2, bn1 = bn2 two dineutrons have same size and expansion

Comparison between 6,8,10He12 Mar. 2013 Coexistence of weak and strong binding


Bn1 = Bn2=Bn3, bn1 = bn2=bn3 m=0.596He (1DC) 8He (2DC) 10He (3DC)


b n :

dine

utro

n siz

e

Qualitatively similar, but, as neutrons are added, • compact dineutrons become unfavorable,• the repulsive area grows.The valley becomes clear. = Dineutrons become rigid.

(The number of dineutrons is 1,2 and 3.)

Comparison between 8He and 7H


6

(7H is described by replacing an a with t.)

8He (a+2dineutrons)


b n :

dine

utro

n siz

e

7H (t+2dineutrons)

In 7H, the attraction is so weak that the 2n correlation is close to that in free space.

Bn1 = Bn2, bn1 = bn2, m=0.59

The valley is unclear. = Dineutrons disperse.

Summary of part I12 Mar. 2013 Coexistence of weak and strong binding


We analyzed the dineutron behavior in dineutron condensate states by using a toy model of aDC w.f..

We discussed about the mechanism of the dineutron condensation

the systematics of the dineutron behavior in He isotopes

the essence for the formation of a dineutron condensation

Energy valley and repulsive region

strong attraction is essential

Qualitatively similar but dineutron size changes

Part II


8

• Introduction of 6He+2n cluster w.f. + 8He DC w.f.

• Energy spectra of the 0+1,2 states

• Dineutron component in the 0+1,2 states

Description of 8He12 Mar. 2013 Coexistence of weak and strong binding


0p3/2-configurations are important for description of 8He (g.s.).

In order to describe these configurations, we superpose two kinds of wave functions, that is6He + 2n cluster wave functions (for (0p3/2)4)

and8He DC wave functions (for dineutron configurations). F.K. and Y. Kanada-En’yo. PTP 126

(2011)




6He 2n(*)

8He DC w.f. (including one dineutron explicitly)

core

6He + 2n cluster w.f.12 Mar. 2013 Coexistence of weak and strong binding


6He cluster is described with an a core plus two balance neutrons in 0p-orbits.

The other two neutrons have two kinds of configurations,

dc

a

6He2n

dc

a6He 2n*

{R = (dc ,0,0) (dineutron-like)R = (dc,±0.5i,0) (dissociated)

dineutron-like dissociated

DC w.f. (one dineutron case)


2

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

(s-wave)

(S-wave)

size of the dineutron

n

nb

2bn

core

rrG

relative part

c.o.m. part

spatial expantion of the dineutron

Core of 8He DC w.f.12 Mar. 2013 Coexistence of weak and strong binding


As in the 6He + 2n cluster w.f., we describe a + 2n core, and distribute a dineutron around the core.

a 2n* a 2n

same size




a 2n

8He DC w.f. I

a 2n*

8He DC w.f. II

dc = 1 – 4 fm, dI = 1 – 4 fm, dII = 1 – 8 fm, b = 2 – 8 fm, bn ; 5 values

a

Hamiltonian

: LS part of G3RS 　 vLS = 2000 MeV

: Volkov No.2 m=0.59, b=h=0.0

or m=0.55,

b=h=0.125


5

Energy spectra

0+1

0+1 0+

1

0+2

0+2

a+n+n+n+na+n+n+n+na+2n+2n

We consider the dineutron component in the 0+1,2

states.

(2n bound) (2n unbound)


6

Two dineutron condensate component


7

In order to see the two dineutron condensate (2DC) component, we calculate the overlap with aDC w.f.,

Two dineutrons with the same size (bn) and expantion (b) move in the s-orbit.

We show the overlap of the 0+1,2

states.

Ground state (0+1)


8

Compact dineutrons are at the nuclear surface, but the tail amplitude is not so large.Four neutrons are strongly

bound.

b : dineutron expansion

b n :

dine

utro

n siz

e

(fm)

(fm)

Dineutron condensate state (0+2)


9

This state would be a dineutron condensate state.

Compact dineutrons are expanded largely and freely, which is the feature of a condensate state.

b : dineutron expansion

b n :

dine

utro

n siz

e

(fm)

(fm)

Summary


0

Summary12 Mar. 2013 Coexistence of weak and strong binding


We investigated the dineutron behavior in dineutron condensate states of 8He and 6,10He, 7H, and the possibility of a dineutron condensate state in 8He.

Compact dineutrons are formed and a long tail of dineutrons stretches when the system is bound strongly to some extent.

In 8He, we found a candidate for a dineutron condensate state, which contains compact dineutron clusters expanded spatially.

Outlook12 Mar. 2013 Coexistence of weak and strong binding


In future, we will invesitgate the component of 6He + one dineutron in 8He(0+

1,2).

We will also investigate realistic 6,10He and 7H and make clear whether or not dineutron condensate states existand the systematics of the dineutron behavior.


3

Comparison between 6,8,10He12 Mar. 2013 Coexistence of weak and strong binding


m=0.596He (1DC) 8He (2DC) 10He (3DC)


b n :

dine

utro

n siz

e

m=0.55

m = 0.55

Energy surface on Bn-bn plane12 Mar. 2013 Coexistence of weak and strong binding


m = 0.59


b n :

dine

utro

n siz

e

Bn1 = Bn2, bn1 = bn2 two dineutrons have same size and expansion

Center of mass motion12 Mar. 2013 Coexistence of weak and strong binding


In the aDC w.f., the center of mass motion can be separated from the intrinsic motion, when

mass of the cluster i (a; 4, dineutron; 2) (for all i)

When ba = 1.4 fm (fixed), Bn1 = Bn2 and bn1 = bn2,

1-DC wave function12 Mar. 2013 Coexistence of weak and strong binding


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.


8

(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 component12 Mar. 2013 Coexistence of weak and strong binding


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

b : dineutron expansionb n :

dine

utro

n siz

eGround state (0+

1)12 Mar. 2013 Coexistence of weak and strong binding


m = 0.59

m = 0.55

b : dineutron expansionb n :

dine

utro

n siz

eDineutron condensate state (0+

2)12 Mar. 2013 Coexistence of weak and strong binding


m = 0.59

m = 0.55

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Dineutron condensate state in 8 He