di-neutron correlation in borromean nucleikouichi.hagino/talks/dcen2011.pdf · cf. similar...
TRANSCRIPT
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Di-neutron correlation in Borromean nucleiK. Hagino (Tohoku University)H. Sagawa (University of Aizu)
1. Introduction: Di-neutron correlation2. Three-body model for 11Li and 6He
- Spatial structure (geometry) of valence neutrons- E1 strength
3. 1-Dimensional 3-body model4. Summary
11Li, 6HeWhat is the spatial structure of valence neutrons?Compact? Or Extended?
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Borromean nuclei and Di-neutron correlationBorromean nuclei: unique three-body systems
for 6He
Yu.Ts. Oganessian, V.I. Zagrebaev, and J.S. Vaagen, PRL82(’99)4996
M.V. Zhukov et al., Phys. Rep. 231(’93)151
for 11Li
G.F. Bertsch, H. Esbensen,Ann. of Phys., 209(’91)327
strong di-neutron correlationin 11Li and 6He
Three-body model calculations:
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Borromean nuclei and Di-neutron correlation
strong di-neutron correlationin 11Li and 6He
Three-body model calculations:
cos θ12
P(θ 1
2)
1.0 -1.0
210Pb
G.F. Bertsch, R.A. Broglia, and C. Riedel,NPA91(‘67)123
F. Catara, A. Insolia, E. Maglione, and A. Vitturi, PRC29(‘84)1091
r (fm
)
R (fm)
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How to probe the strong dineutron correlation?Remaining problem:
•Coulomb excitations?
T. Nakamura et al., PRL96(’06)252502T. Aumann et al., PRC59(‘99)1252
11Li6He
* (indirect) evidence for dineutron correlation
dineutron correlation in the ground state?
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Experimental evidence: T. Nakamura et al., PRL96(’06)252502 Recent Coulomb dissociation data of 11Li
H. Esbensen, K. Hagino, P. Mueller, and H. Sagawa,PRC76(’07)024302
renewed interests in dineutron correlations in weakly bound nuclei
c.f. M. Matsuo et al., PRC71(’05)064326PRC73(’06)044309
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Remaining problems•spatial structure of dineutron (cf. a large pair coherence length?)•dineutron correlation in heavy nuclei?•E1 excitations?•Pair transfer?
9Li
n
nWhat is the spatial structure of the valence neutrons?
To what extent is this picture correct?
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Density-dependent delta-force
coren
nr1
r2
VWS
VWS
G.F. Bertsch and H. Esbensen,Ann. of Phys. 209(’91)327
H. Esbensen, G.F. Bertsch, K. Hencken,Phys. Rev. C56(’99)3054
Three-body model with density-dependent delta force
11Li, 6He
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vnn
n
n continuum states: discretized in a large box
contact interaction v0: free n-n density dependent term: medium many-body effects
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uncorrelated basis
diagonalization of Hamiltonianmatrix(~ 1500 dimensions)
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Two-particle density for the ground state of 11Li and 6He11Li
6He
K.H. and H. Sagawa, PRC72(’05)044321
r
rθ12
strong di-neutron correlation
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Role of pairing correlation
with pairingwithout pairing [1p1/2]2
(z1,x1)=(3.4 fm, 0)
configuration mixing of different parity states11Li
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M. Matsuo, PRC73(’06)044309
Matter Calc.
2n-rms distance
K.Hagino, H. Sagawa, J. Carbonell, and P. Schuck, PRL99(’07)022506
11Lispatially compact
K.H., H. Sagawa, and P. Schuck, J. of Phys. G37(‘10)064040
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2n-rms distance
K.H., H. Sagawa, J. Carbonell, and P. Schuck, PRL99(’07)022506
11Lispatially compact
Size of deuteron in 6Li
K. Itonaga and H. Bando,PTP44(‘70)1232
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PRL32(‘74)173
PRC23(‘81)2371d(d,t)p
6Li(d,tp)4He
kα=0 kα=-30MeV/c
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cf. “di-proton” correlation17Ne = 15O + p + p (S2p = 0.944 MeV)
vpp = density-dep. contact interaction + Coulomb
about 14% contribution
T. Oishi, K. Hagino, and H. Sagawa, PRC82(‘10)024315
similar
17Ne = 15O + p + p 16C = 14C + n + n
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cf. “di-proton” correlation
T. Oishi, K. Hagino, and H. Sagawa, PRC82(‘10)024315
exact treatment for Coulomb
switch off the Coulomb,but renormalize the nuclear force
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T. Oishi, K. Hagino, and H. Sagawa,arXiv:1109.2994 [nucl-th]Phys. Rev. C, in press.
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11Li
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Dipole excitations
Response to the dipole field:
ground stateexcited states
(note) analytic expression for a single-particle potential model
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Dipole excitations
K.H. and H. Sagawa,PRC76(’07)047302
Response to the dipole field:
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K.Hagino and H. Sagawa,PRC76(’07)047302
recoil term
with recoil for the g.s.but without for 1-
continuum calculations
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More direct information on the correlation?
dipole operator
rR r1
r2
9Li
n n
dipole
The relative motion r = r1 – r2 is not affected by the dipole operator.
Probing dineutron correlation with E1 excitation?
11Li
especially with energy (and angular) distribution(s)?
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New 2n correlation experiment (Nakamura et al.)
T. Nakamura et al., unpublished
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Continuum Dipole Response
dipole operatorFSI
unperturbed continuum wf
Dµ
H. Esbensen and G.F. Bertsch, NPA542(‘92)310
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11Li 6He
cf. ground state densityK.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
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11Li 6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
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11Li 6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
similar
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11Li 6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
p3/2 resonance for 5Heat 0.91 MeV
p1/2 resonance for 10Liat 0.54 MeV
s-wave virtual state in 10Li
(scattering length:a =-30 +12
-31 fm) (cf. s-wave scattering length:a = +4.97 +/- 0.12 fm)
distribution for 11Li: consistent with preliminary expt. data (T. Nakamura et al.)
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Analysis with three-body model
continuum response
plane wave final state wf (No FSI):(vnn =0, Vnc=0)
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How to probe the strong dineutron correlation?Remaining problem:
•Coulomb excitations? A problem: an external field is too weak
11Li 6He
p3/2 resonance for 5Heat 0.91 MeV
p1/2 resonance in 10Liat 0.54 MeV
s-wave virtual state in 10Li
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
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How to probe the strong dineutron correlation?Remaining problem:
•Coulomb excitations?•Nuclear breakup?
6He 4He + n + n
M. Assie et al., Eur. Phys. J. A42 (’09) 441
cf. 4-body CDCC for exclusive cross sections?
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How to probe the strong dineutron correlation?Remaining problem:
•Coulomb excitations?•Nuclear breakup?
•Pair transfer?144Sm + 208Pb
no enhancement of P2n for (semi-)magic nuclei
J. Speer et al., PLB259(‘91)422
112Sn + 120Sn
W. von Oertzen et al., Z. Phys. A326(‘87)463
enhancement
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How to probe the strong dineutron correlation?Remaining problem:
•Coulomb excitations?•Nuclear breakup?
•Pair transfer?
Reaction mechanism?- sequential vs simultaneous- Q-value, angular momentum matchings
Role of dineutron correlation (on the surface)?Influence to other reaction processes (e.g., subbarrier fusion)?
have not yet been fully clarified
to be discussed on the next Monday
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example of 2n transfer calculation
M.A. Franey et al.,PRL41(‘78)837
effects of unbound intermediate states?
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A. Chatterjee et al., PRL101(’08)032701
6He + 65Cu
Recent experiments for transfer reaction of neutron-rich nuclei1H(11Li,9Li)3H
I. Tanihata et al., PRL100(‘08)192502
It is timely to construct: a new theory of pair transfer with dineutron correlation.
need a deep understanding of reaction dynamicsa simple and intuitive schematic model
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One-dimensional three-body modelTwo interacting neutrons in a one-dimensional potential well:
density-dependent contact interaction:
•S = 0 state: symmetric for the spatial part of wf
•n, n’: the same parity
x
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Similar one-dimensional model for two-electron systems
He atom (4He + e- + e-)H- atom (p + e- + e-)
double ionization by intense laser fields1D model Experimental Data
correlation effect
J.B. Watson et al., PRL78(‘97)1884
xe-e-
SAE: single active electron approximationNS: non-sequential
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cf. TDH(F) for a one-dimensional system
B. Yoon and J.W. Negele, PRA16(‘77) 1451
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Model Setup for core+2n
Weakly bound s.p. level at -0.15 MeV
occupied by the core nucleus
discretized continuum states
the strength of the pairing interaction g:adjusted so that Egs = -1 MeV
Ecut = 30 MeV, Rbox = 90 fm
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Ground state properties
two-particle density: x1
x2
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Ground state properties
two-particle density:
correlated uncorrelated
largely suppressed
dineutron correlation
x1
x2
four symmetric peaks
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interference
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Nuclear Breakup Process
Time-dependent two-particle Schroedinger equation:
(one-body) external field
Vc = 3 MeV, σt = 2.1 hbar/MeV, x0 = 0
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correlated uncorrelated
two-particle density at t = tini
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correlated uncorrelated
time evolution
large (bc) component
x1
x2
“dineutron emission”
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Pairing: enhances the breakup
Correlated: (cc) process
Uncorrelated: (bc) process
Pcc: 2 neutron breakupPbc: 1 neutron breakup
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Application to 2p radioactivity
di-proton emission (x1 = x2) sequential 2p emission (x2 ~ 0)
T. Maruyama, T. Oishi, K.H., preliminary
t = 0
t > 0
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Summary
Energy distribution of neutrons from the E1 excitations in 11Li and 6He
continuum responsesthe shape of distributions: primarily determined
by n-core dynamics rather than n-nenergy distribution: very different between 11Li and 6He
s-wave virtual state in 11Licf. similar dineutron correlations in the g.s.
Three-body model with density-dependent contact interaction
Ground state of 11Li and 6He
similar di-neutron correlation
One dimensional model for 2n halo nucleisimple, and schematic model. detailed studies of dynamics