Transcript Tomohiro OishiA, Kouichi HaginoA, Hiroyuki SagawaB ATohoku Univ., BUniv. of Aizu T.Oishi, K.Hagino, and H.Sagawa, PRC82,024315(2010)

Tomohiro OishiA,
Kouichi HaginoA, Hiroyuki SagawaB
ATohoku
Univ., BUniv. of Aizu
T.Oishi, K.Hagino, and H.Sagawa, PRC82,024315(2010)

r2
Dineutron correlation in 2n-Borromean
nuclei (theoretically predicted):
6
He
11
Core
12
Li
 
r 1r 2

r1
K.Hagino, and H.Sagawa, PRC72(‘05)044321
Remarkable localization of two neutrons
“dineutron correlation”.
How about two protons in a weakly
bound system?
zˆ
Typical “2p-Borromean” nucleus;
16
di - proton
F

15
17
O
p
p

proton-unbound,
p
Ne
stable for proton
emission.
 
15
O
p
T(16 F)  1020 [s] (p - emit)
p
17Ne
is an ideal system to
analyze diproton correlation.
17
Ne 15 O  p  p
 
 
(1) 
( 2) 
H (r1 , r2 )  TCore  T1  T2  VNC (r1 )  VNC (r2 )  VNN (r1 , r2 )
 
 
p
(1)
( 2)
1  p2
 hNC  hNC 
 VNN (r1 , r2 ) ,
AC m
Off-diagonal
(i )
NC
h
Core
pi2
(i ) 

 VNC (ri )
2

r2
VNC (r 2 )
12
VNC (r1)

m AC 
  

AC  1 

 
VNN (r1, r 2 )
 
r 1r 2
zˆ

r1
 
VNN (r1, r 2 )
2
 


e
1
(N)
Vpp (r1 , r2 )  Vpp (r1 , r2 ) 
 
4 0 r1  r2
V
(N )
pp

v
  


  (r1  r2 )v0 

1  exp[(r1  R ) a ] 



OR
(N)
pp
V
Explicit Coulomb
Density-dependent contact



  2
  2
 v0 exp  b0 (r1  r2 )  v1 exp  b1 (r1  r2 )

Minnesota
Parameters are fixed to output g.s.energy of
17Ne:-0.944 MeV.
Woods-Saxon + Coulomb potential for p-Core
  1 d

2
VpC (r )  V0 f (r )  r0  Vls (   s )
f (r )  VpC, Clmb (r )
r dr
15
15
3
 
O 1/2 -  p1d 5/2 
2

1
 
O 1/2  p2s1/2 
-
0

1.257 (MeV)
0.951
0.722
0.535
1.129
(1d5/2 )

0.964 (MeV)
12

5 2
0.820
0.675
(2s1/2 )
3 2

0.344
0
15
15
Op
16
Fixed to reproduce
averaged resonance
energies
F
0
O  2p
12

 0.944
17
Ne
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.
 
 
~
 g.s. (r1, r2 )   nn 'lj nn 'lj (r1, r2 )
n n ' l , j
 
nn 'lj (r1, r2 ) 
~
1
j, m; j,m | 0,0
0+ configuration
for g.s.
2( nn'
m




 nljm (r1 )n'lj m (r2 )  n'ljm (r1 )nlj m (r2 )

calculation

 1)
Determined by Hdiagonalization

 
mean - square N - N distance : rN2  N   g .s. | (r1  r2 ) 2 | g .s.
 
mean - square 2N - Core distance : r22N C   g .s. | (r1  r2 ) 2 / 4 | g .s.
A
2A
1
2
r2 
r

rN2  N
2 N C
2
A 2
A
A2
2( A  2)
( A  2)
 
  2
density :  (r1 , r2 )   g .s. (r1 , r2 )   (r1, r2 ,12 ) , (rˆ1  zˆ )
 r2  r2

V pp(C )
(N )
V pp
  0.14
re - adjust ed
cont act,
wit hout Vpp( C )
r22N C
Core
rN2  N
 r2  r2
A 2

A
r2
A 2
A

2A
1
2
r

rN2 N
2 N C
2
( A  2)
2( A  2)
 (r1  r2  r ,12 )  4r 2 2r 2 sin 12
17

 (r1  r22N C
1/2
zˆ ; z2 , x2 ) ,
16
C
Ne
z2  r2 cos 12 , x2  r2 sin 12
Core

r2
z1 
zˆ
r22N C
“Diproton correlation”
rN2  N
r22N C
Core
Minnesota
Contact
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.
p
[ O  p  p]
15
n

nljm (ri )  Rnlj (ri )ljm (rˆi ,  ) ,
ljm (rˆi ,  ) 
 l , ml ;1 2 , ms | j, m Ylml (rˆi )  ms
ms ,ml
Woods-Saxon
+ Coulomb potential for p-Core

V pC (r )  VWS (r )  VClmb (r )
  1 d
2
 V0 f (r )  r0  Vls (   s )
f (r )  VClmb (r )
r dr
1
 r
1 ZC e2 1 

f (r ) 

V
(
r
)

3


1  exp[(r  RCore ) aCore ] Clmb
4 0 RCore 2 
 RCore

1 ZC e2

4 0 r



2


 ( r  RCore )


(r  RCore )
Put infinite wall at r=Rbox: Rnlj (r  Rbox )  0
 Continuum states are discretized.
Resonances of 16F at 0.675 MeV (s1/2) and at 1.129
MeV (d5/2) are reproduced.
 
VNN (r1, r 2 )
 
 

e2
1
Vpp (r1 , r2 )   (r1  r2 ) g (r1 ) 
 
4 0 r1  r2


v



g (r1 )  v0 

1  exp[(r1  R ) a ] 



We need cutoff:EC to determine
v0 (pairing in vacuum).
2
2ann
EC m

2
v0  2
, kC 
m   2kC ann
2
Explicit Coulomb
interaction
Density-dependent
contact interaction
ann  18.5 (fm)
n 'lj  EC ,
 nlj


(1)
( 2)
Other parameters are fixed to obtain g.s.energy
of 17Ne:-0.944 MeV.
S.Hilaire et al., Phys.Lett.B531(2002)
Pairing gap of protons and neutrons
protons
neutrons
Table of Nuclides , http://atom.kaeri.re.kr/ton/nuc6.html
S2p  BE( Ne) - BE( O)  0.944 [MeV]
17
15
S2n  BE(16 C) - BE(14 C)  5.47 [MeV]
VNC (r ) for
16
F and
15
C