Diproton correlation in aproton-rich Borromean

nucleus 17NeTomohiro OishiA,Kouichi HaginoA, Hiroyuki SagawaB

ATohoku Univ., BUniv. of Aizu1. Introduction2. Model3. Results4. Summary

http://arxiv.org/abs/1007.0835

1.1 Dineutron correlationDineutron correlation in 2n-Borromean nuclei (theoretically predicted):

He6 Li11

K.Hagino, and H.Sagawa, PRC72(‘05)044321

Remarkable localization of two neutrons“dineutron correlation”.How about two protons in a weakly bound system?

Core

r2

r1

z12

rr 21

1.2 17Ne nucleus (1)

p] p O[15

p

n

1.2 17Ne nucleus (2)

O15 p p p

F16 proton-di

O15 p p

Ne17

Typical “2p-Borromean” nucleus;

proton-unbound,

stable for proton emission.

17Ne is an ideal system to analyze diproton correlation.

eak[ms].....w 109Ne)T(

emit-[s].....p 10F)T(17

2016

2.1 Three-body-model ppO Ne 1517

1 )(

2

, ),(

),()()(),(

)(2

)(

2121)1()2(

212)2(

1)1(

2121

C

Ci

iNC

iiNC

NNC

NCNC

NNNCNCCore

AmArVph

rrVmApphh

rrVrVrVTTTrrH

Off-diagonal

Core

r2

r1

z

),(V 2 1 NN rr

)(V 1 NC r

)(V 2 NC r

12rr

21

])(exp[1)(

14

)()(),(

101

210

2

12121pp

aRrv

vrg

rrergrrrrV

2.2 Pairing interaction

Density-dependent contact interaction

Explicit Coulomb interaction

2

22

0 ,2

22

mEkak

am

v CC

nnC

nn

(fm) 5. 18

, ) 2(

') 1(

nn

C lj n nlj

a

E

We need cutoff:EC to determine v0 (pairing in vacuum).

Other parameters are fixed to obtain g.s.energy of 17Ne:-0.944 MeV.

),(V 2 1 NN rr

2.3 Single-particle basis

smillmlmsm

sliljm

iljminljinljm

rYmjmmlr

rrRr

)ˆ(,|,21;,),ˆ(

, ),ˆ()()(

,

)()(1)()(

)()()(

200 rVrf

drd

rsVrrfV

rVrVrV

Clmbls

ClmbWSpC

])(exp[11)(

CoreCore aRrrf

)( 4

1

)( 321

41)(

2

0

22

0

CoreC

CoreCoreCore

CClmb

RrreZ

RrRr

ReZrV

Woods-Saxon + Coulomb potential for p-Core

5/2-15 1dp1/2O

21 944.0

2

10 )(2s1/2 23

675.0

344.0

2125

(MeV) 964.0820.0

3

535.0

722.0

951.0

(MeV) 257.1

)(1d5/2

129.1

p2O15

0 0

F16 Ne17

pO15

1/2-15 2sp1/2O

AveragedResonances

Put infinite wall at r=Rbox: Continuum states are discretized.

2.3 Box-approximation0)( boxnlj RrR

Resonances of 16F at 0.675 MeV (s1/2) and at 1.129 MeV (d5/2) are reproduced.

2.5 Expansion with s.p.basis

),(~),( 21'' ,

'21g.s. rrrr ljnnnn jl

ljnn

)()()()(

0,0|,;,)1(2

1),(~

21'2'1

'21'

rrrr

mjmjrr

mnljljmnmljnnljm

mnnljnn

Determined by diagonalization

)ˆˆ( , ),,(),(),(:density

)2(21

)2(2

2

|4/)(|:distance Core-2N square-mean

|)(|:distance N-N square-mean

112212

21..21

2222

22

22

..2

21..2

2

..2

21..2

zrrrrrrr

rA

rA

ArAArr

rrr

rrr

sg

NNCNAA

sgsgCN

sgsgNN

0+ configuration for g.s.

3.1 Results (1)

(C)ppV excluding

, (fm) 81.7ppa

0.14 )(

)(

N

pp

Cpp

V

V

2NNr

22 CNr

Core

22

22

C

C12

1-12

32A

AE1 , coscos CNC reZB

S.Hilaire et al., Phys.Lett.B531(2002)

protons neutrons

Pairing gap of protons and neutrons

Corer2

221 CNrz

z

3.2 Results (2)12

221221 sin24),( rrrrr

12221222221/22

21 sin , cos , ), ; z( rxrzxzrr CN

Ne17C16

“Diproton correlation”

4. SummaryWe performed three-body-model calculation for 17Ne with density-dependent contact pairing and the Coulomb interaction.

1. Coulomb repulsion contributes about 14% reduction to pairing energy.

2. Existence of strong “diproton correlation”.

Future works: application to 2p-emission.

Table of Nuclides , http://atom.kaeri.re.kr/ton/nuc6.html

[MeV] 5.47C)BE(-C)BE(S

[MeV] 0.944O)BE(-Ne)BE(S1416

2n

15172p

C and Ffor )( 1516rVNC