6 Oct. 2011 DCEN2011 1

A new framework to investigate dineutron correlation in neutron-rich nuclei

Kyoto University, Department of Physics,

　　　　　　　　　　　 Fumiharu Kobayashi

　　 Yoshiko Kanada-En’yo

F.K. and Y. Kanada-En’yo, PTP 126 (2011), 457

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Outline

Introduction

Framework : The dineutron condensate (DC) wave

function

Result : Dineutron formation in simplified systems

Summary, Outlook

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Introduction

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Dineutron correlationA dineutron is a compact spin-singlet pair of two neutrons.

Dineutron correlation is enhanced in the low-density region of the nuclear

matter.

Some neutron-rich nuclei have low-density structure, such as neutron-halo and -skin.

Is the strong dineutron correlation formed in neutron-rich nuclei?

Does the dineutron condensate state exist?

core

n

ndineutron

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Dineutron in finite nuclei

In finite nuclei,

what is the universal properties of the dineutron at the nuclear surface?

To answer this question, it is necessary to investigate dineutron correlation in various nuclei systematically.

We constructed a new model, the “dineutron condensate (DC) wave function”

Today’s talk : one-dineutron formation at the nuclear surface is investigated.

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Framework

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Framework (one-dineutron case)

With AMD+DC w.f., we describe the nuclear states which includes dineutron correlation.

AMD+DC =

AMD

+

DC

AMD+DC wave function 　　　　　　　　　　　　　　　　　　　 ( = superposition of AMD w.f. and DC w.f. )

core (AMD)

states NOT including a dineutron explicitly

states including a dineutron explicitly

A A-2

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1-DC wave function

spatial part

( Not a dineutron condensate state )

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

core (AMD)

dineutron

relative part c.o.m. part

size of dineutron

spread of dineutron

(s-wave)

(S-wave)

β

n

dineutron

core

n

bn

rrG A-2

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Result

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2α+2n DC w.f.

2α dineutron

relative part

β

bn

α α

d

size of dineutron

spread of dineutron

c.o.m. part

describing the system decomposed of a dineutron around the 2 core

We have analyzed dineutron energy

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Energy surface ( bn)

The dineutron can extend far from the core keeping a compact size.

: dineutron energy

When the dineutron is distributed near the nuclear surface, its energy has a “valley and barrier” structure.

α α

d

bn

β

bn

: si

ze o

f din

eutr

on (fm) (MeV)

(fm) : spread of dineutron

(1.9, 1.5)

d = 2fm

bn : size of dineutron

E :

din

eutr

on e

nerg

y

β = 5 : far from the core

β = 3 : near the core

(MeV)

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(MeV)

bn : size of dineutron (fm)

E :

din

eutr

on

energ

yValley and barrier in dineutron energy

s-wave neutrons in the core

angular correlated two-neutron in the higher wave

strong Pauli effect

weak Pauli effect

Near the nuclear surface, uncorrelated two-neutron has higher energy due to the Pauli principle and a compact dineutron is favorable.

uncorrelated two-neutron in the s-wave

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t+2n

Energy surface of core+2n systems

+2n

2+2n

: spread of dineutron

bn

: si

ze o

f din

eutr

on

(fm)

(fm) (MeV)

As the core becomes lighter, the “valley and barrier” structure disappears. It originates in a decrease of the potential from the core.

barrier

valley

The potential from the core is essential to

dineutron formation.

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dineutron dineutron

2-DC wave function

core

Distributing two same size dineutrons in the S-wave around the core

size of dineutron

spread of dineutron

same parameters

β

n

dineutron

core

n

bn

r1rG1 bn

r2

rG2

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Energy surface of +2n+2n system +2n+2

n

+2n

: spread of dineutron

bn

: si

ze o

f din

eutr

on

(fm)

(fm) (MeV)

In the two-dineutron case, the compact dineutron is unfavored at the nuclear surface, compared to the one-dineutron case.

under the analysis

: two-dineutron energy

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Summary

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Summary

We have proposed a new approach to investigate dineutron correlation in nuclei, the dineutron condensate (DC) wave function. 　　　　　　

When two neutrons are distributed near the nuclear surface, their energy structure has a “valley and barrier”, so that they favor a somewhat compact size.

The potential from the core might be important for correlation between two valence neutrons.

We have applied the AMD+DC method to 10Be and investigated the dineutron components in 10Be(0+

1).

dineutron formation

poster session in YKIS

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Outlook

Application of the AMD+DC method to the various neutron-rich nuclei

where dineutron correlation is expected to be enhanced, and analysis of the dineutron components in them ( for instance, 6He, 11Li and 12,14Be ).

Analysis two-dineutron condensate state in 7H and 8He in detail, and investigation of the behavior of two dineutrons.

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kmax-dineutron DC w.f.

core (AMD) kmax-dineutrons

spatial part

B

n

n

dineutron

core

Yk

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

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core (AMD)

dineutron

spatial partB

n

ndineutron

core

Y

fixiing B = Bx = By = Bz

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

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relative and c.o.m. w.f. of the dineutron

n

n β

core

2bn

coordinate transformation Y-integral

relative part c.o.m. part

size of dineutron

spread of dineutron

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2-DC wave functionDistributing two same size dineutron in the S-wave around the core Approximately replacing one of the Y-integral to the d-sum

dineutrondineutron

same parameters

core (AMD)

B

n

ndineutron

Y1

Y2

core

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Hamiltonian

: Volkov No.2 M=0.60, B=H=0.125

: LS part of G3RS 　 vLS = 1600 MeV

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Energy surface x ≠ z

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Energy surface (d=1,2,3,4 fm)

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Dineutron kinetic energy and potential energy

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Core effect to dineutron kinetic energy