m. matsuo, prc73(’06)044309 matter calc. two-particle density
TRANSCRIPT
![Page 1: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/1.jpg)
![Page 2: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/2.jpg)
M. Matsuo, PRC73(’06)044309
Matter Calc.
![Page 3: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/3.jpg)
Two-particle density
![Page 4: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/4.jpg)
Dipole Excitations
Response to the dipole field:
Smearing:
Experimental proof of di-neutron
![Page 5: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/5.jpg)
Comparison with expt. data (11Li)
Epeak=0.66 MeVB(E1) = 1.31 e2fm2 (E < 3.3 MeV)
T. Nakamura et al., PRL96,252502(2006)
Epeak ~ 0.6 MeVB(E1) = (1.42 +/- 0.18) e2fm2 (E < 3.3 MeV)
T. Aumann et al., PRC59, 1259(1999)
![Page 6: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/6.jpg)
Constraining the size of 11Li by various experiments
R
r
H. Esbensen et al., Phys. Rev. C (2007).
![Page 7: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/7.jpg)
Geometry of Borromean nuclei
11Li
6He
B(E1)
matter radius
(11Li)
(6He)
K.Hagino and H. S.,PRC76(’07)047302
“experimental” mean opening angle
C.A. Bertulani and M.S. Hussein, PRC76(’07)051602
12
![Page 8: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/8.jpg)
11 e n
1
2e
2
Li9
11 Li three-body break-up cross sections
2n
K. Hagino, H.S.,T.Nakamura and S.Shimoura, PRC80,031301(R)(2009)
![Page 9: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/9.jpg)
Dalitz Plot of Triple coincidence experiments
Exp. T. Nakamura et al., to be published
![Page 10: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/10.jpg)
Nakamura-san’s slides
![Page 11: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/11.jpg)
Double differential strength function for 11Li
full calculation(with FSI)
( without FSI)
(with FSI) No Vn-core
(No Vn-core
virtual s-state!virtual s-state!
![Page 12: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/12.jpg)
full calculation No Vn-core
(with FSI)
( without FSI)
![Page 13: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/13.jpg)
Di-proton correlation in aproton-rich Borromean
nucleus 17Ne
Tomohiro OishiA,Kouichi HaginoA, Hiroyuki SagawaB
ATohoku Univ., BUniv. of Aizu
PRC82, 024315(2010)http://arxiv.org/abs/1007.0835
![Page 14: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/14.jpg)
])(exp[1)(
1
4)()(),(
101
210
2
12121
aRr
vvrg
rr
ergrrrrVpp
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
Cljnnlj
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.
![Page 15: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/15.jpg)
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
![Page 16: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/16.jpg)
3.1 Results (1)
(C)ppV excluding
, (fm) 81.7ppa
0.14 )(
)(
Npp
Cpp
V
V
2NNr
22 CNr
Core
22
2
2
C
C12
1-12
3
2A
AE1 , coscos CN
C reZ
B
![Page 17: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/17.jpg)
Corer
2
221 CNrz
z
3.2 Results (2)
1222
1221 sin24),( rrrrr
1222122222
1/2221 sin , cos , ), ; z( rxrzxzrr CN
Ne17C16
“Di-proton correlation”
![Page 18: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/18.jpg)
Summary IApplication of three-body model to Borromean nuclei
11Li
Di-neutron wave function for each R
Concentration of a Cooper pair on the nuclear surface Relation to BCS-BEC crossover phenomenon
E1 response and geometry of Borromean nuclei
n-n coincidence cross sections from 11Li* and 6He* importance of n-core interaction clear evidence of virtual s-state in n-9Li system correlation angle is determined experimentally.
strong pair correlations in di-neutrons
12
![Page 19: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/19.jpg)
Di-neutron correlations in 11Li and 6He
K.Hagino and H. S., PRC72(’05) 044321.K.H.agino and H. S., PRC75(’07)021301(R).K.Hagino, H. S., J. Carbonell, and P. Schuck, PRL99(’07)022506.H. Esbensen, K.Hagino, P. Mueller, and H. S., PRC76(’07)024302.K.Hagino and H. S., PRC76(’07) 047302.
energy and angular n-n coincidence cross sections
Recent publications:Recent publications:Recent publications:Recent publications:
K.Hagino, H.S. ,T. Nakamura and S. Shimoura, PRC80,031301 (R)(2009).
Di-proton correlations in 17Ne
T.Oishi, K. Hagino and HS, PRC82,024315 (2010).
Strong di-proton correlations is found in 17NeTwo body Coulomb interaction decreases 13% of di-proton correlations.
Summary II
![Page 20: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/20.jpg)
Spatial structure of neutron Cooper pair in infinite matter
M. Matsuo, PRC73(’06)044309
BCS
Crossover region
![Page 21: M. Matsuo, PRC73(’06)044309 Matter Calc. Two-particle density](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56649f255503460f94c3c6a5/html5/thumbnails/21.jpg)
BCS-BEC crossover behavior in infinite nuclear matter
Neutron-rich nuclei Weakly bound levelsdilute density around surface (halo/skin)
pairing gap in infinite nuclear matter
M. Matsuo, PRC73(’06)044309