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Diproton correlation in the
proton-rich Borromeannucleus 17Ne
Tomohiro OishiA,Kouichi HaginoA, Hiroyuki SagawaB
ATohoku Univ., BUniv. of Aizu
1. Introduction2. Model3. Results4. SummaryT.Oishi, K.Hagino, and H.Sagawa, PRC82,024315(2010)
1.1 Dineutron correlation
Dineutron 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
r
2
r
1
z12rr 21
1.2 17Ne nucleus
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.
emit)-(p [s] 10F)T( 2016
2.1 Three-body-model ppO Ne 1517
1 )(
2
, ),(
),()()(),(
)(2
)(
2121)2()1(
212)2(
1)1(
2121
C
Ci
iNC
iiNC
NNC
NCNC
NNNCNCCore
A
mArV
ph
rrVmA
pphh
rrVrVrVTTTrrH
Off-diagonal
Core
r
2
r
1
z
),(V 2 1 NN rr
)(V 1 NC r
)(V 2 NC r
12rr 21
Parameters are fixed to output g.s.energy of 17Ne:-0.944 MeV.
210
2
21)(
21
1
4),(),(
rr
errVrrV N
pppp
2.2 Pairing interaction
Density-dependent contact
Explicit Coulomb
),(V 2 1 NN rr
])(exp[1)(
1021
)(
aRr
vvrrV N
pp
22111
22100
)( )(exp)(exp rrbvrrbvV Npp
OR
Minnesota
2.3 Single-particle states
5/2-15 1dp1/2O
21 944.0
2
10 )(2s1/2 23
675.0
344.0
2125
(MeV) 964.0
820.0
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
Fixed to reproduce averaged resonanceenergies
)()(1
)()()( ClmbpC,2
00pC rVrfdr
d
rsVrrfVrV ls
Woods-Saxon + Coulomb potential for p-Core
Note;In actual calculation,1) We set cutoff-energy:ECUT = 60 MeV.2) Continium states are discretized by setting infinite wall at RBOX = 30 fm.
2.4 Expansion with basis
),(~),( 21'' ,
'21g.s. rrrr ljnnnn jl
ljnn
)()()()(
0,0|,;,)1(2
1),(~
21'2'1
'21'
rrrr
mjmjrr
mnljljmnmljnnljm
mnnljnn
Determined by H-diagonalization
)ˆˆ( , ),,(),(),(:density
)2(2
1
)2(
2
2
|4/)(|:distance Core-2N square-mean
|)(|:distance N-N square-mean
11221
2
21..21
2222
2
2
22
..2
21..2
2
..2
21..2
zrrrrrrr
rA
rA
Ar
A
Arr
rrr
rrr
sg
NNCNAA
sgsgCN
sgsgNN
0+ configuration for g.s.
calculation
3.1 Results (1)
)(ppwithout
,contact
adjusted-re
CV
0.14 )(
)(
N
pp
Cpp
V
V
2NNr
22 CNr
Core22
222
2
22
)2(2
1
)2(
2
2 NNCNAAr
Ar
A
Ar
A
Arr
Corer
2
221 CNrz
z
3.2 Results (2)
1222
1221 sin24),( rrrrr
1222122222
1/2221 sin , cos , ), ; z( rxrzxzrr CN
Ne17C16
“Diproton correlation”
3.3 Minnesota v.s. Contact (1)
2NNr
22 CNr
Core
3.4 Minnesota v.s. Contact (2)
Minnesota Contact
4. Summary
We performed three-body-model calculation for 17Ne with two types of pairing plus explicit Coulomb interaction.
1. Coulomb repulsion contributes about 14% reduction to pairing energy.
2. Existence of strong “diproton correlation”.
Future work: application to 2p-emission.
1.2 17Ne nucleus (1)
p] p O[15
p
n
2.3 Single-particle basis
smillm
lmsmsliljm
iljminljinljm
rYmjmmlr
rrRr
)ˆ(,|,21;,),ˆ(
, ),ˆ()()(
,
)()(1
)()(
)()()(
200 rVrf
dr
d
rsVrrfV
rVrVrV
Clmbls
ClmbWSpC
])(exp[1
1)(
CoreCore aRrrf
)( 4
1
)( 32
1
4
1)(
2
0
22
0
CoreC
CoreCoreCore
CClmb
Rrr
eZ
RrR
r
R
eZrV
Woods-Saxon + Coulomb potential for p-Core
Put infinite wall at r=Rbox: Continuum states are discretized.
2.4 Box-approximation
0)( boxnlj RrR
Resonances of 16F at 0.675 MeV (s1/2) and at 1.129 MeV (d5/2) are reproduced.
])(exp[1)(
1
4)()(),(
101
210
2
12121pp
aRr
vvrg
rr
ergrrrrV
2.2 Pairing interaction
Density-dependent contact interaction
Explicit Coulomb interaction
2
22
0 ,2
22
mE
kak
a
mv C
CnnC
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
S.Hilaire et al., Phys.Lett.B531(2002)
protons neutrons
Pairing gap of protons and neutrons
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
