6 Oct. 2011 DCEN2011 1
A new framework to investigate dineutron correlation in neutron-rich nuclei
Kyoto University, Department of Physics,
Fumiharu Kobayashi
Yoshiko Kanada-En’yo
F.K. and Y. Kanada-En’yo, PTP 126 (2011), 457
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Outline
Introduction
Framework : The dineutron condensate (DC) wave
function
Result : Dineutron formation in simplified systems
Summary, Outlook
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Dineutron correlationA dineutron is a compact spin-singlet pair of two neutrons.
Dineutron correlation is enhanced in the low-density region of the nuclear
matter.
Some neutron-rich nuclei have low-density structure, such as neutron-halo and -skin.
Is the strong dineutron correlation formed in neutron-rich nuclei?
Does the dineutron condensate state exist?
core
n
ndineutron
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Dineutron in finite nuclei
In finite nuclei,
what is the universal properties of the dineutron at the nuclear surface?
To answer this question, it is necessary to investigate dineutron correlation in various nuclei systematically.
We constructed a new model, the “dineutron condensate (DC) wave function”
Today’s talk : one-dineutron formation at the nuclear surface is investigated.
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Framework (one-dineutron case)
With AMD+DC w.f., we describe the nuclear states which includes dineutron correlation.
AMD+DC =
AMD
+
DC
AMD+DC wave function ( = superposition of AMD w.f. and DC w.f. )
core (AMD)
states NOT including a dineutron explicitly
states including a dineutron explicitly
A A-2
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1-DC wave function
spatial part
( Not a dineutron condensate state )
Assuming that the A-nucleon system is composed of (A-2)-nucleon core and one dineutron
core (AMD)
dineutron
relative part c.o.m. part
size of dineutron
spread of dineutron
(s-wave)
(S-wave)
β
n
dineutron
core
n
bn
rrG A-2
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2α+2n DC w.f.
2α dineutron
relative part
β
bn
α α
d
size of dineutron
spread of dineutron
c.o.m. part
describing the system decomposed of a dineutron around the 2 core
We have analyzed dineutron energy
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Energy surface ( bn)
The dineutron can extend far from the core keeping a compact size.
: dineutron energy
When the dineutron is distributed near the nuclear surface, its energy has a “valley and barrier” structure.
α α
d
bn
β
bn
: si
ze o
f din
eutr
on (fm) (MeV)
(fm) : spread of dineutron
(1.9, 1.5)
d = 2fm
bn : size of dineutron
E :
din
eutr
on e
nerg
y
β = 5 : far from the core
β = 3 : near the core
(MeV)
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(MeV)
bn : size of dineutron (fm)
E :
din
eutr
on
energ
yValley and barrier in dineutron energy
s-wave neutrons in the core
angular correlated two-neutron in the higher wave
strong Pauli effect
weak Pauli effect
Near the nuclear surface, uncorrelated two-neutron has higher energy due to the Pauli principle and a compact dineutron is favorable.
uncorrelated two-neutron in the s-wave
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t+2n
Energy surface of core+2n systems
+2n
2+2n
: spread of dineutron
bn
: si
ze o
f din
eutr
on
(fm)
(fm) (MeV)
As the core becomes lighter, the “valley and barrier” structure disappears. It originates in a decrease of the potential from the core.
barrier
valley
The potential from the core is essential to
dineutron formation.
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dineutron dineutron
2-DC wave function
core
Distributing two same size dineutrons in the S-wave around the core
size of dineutron
spread of dineutron
same parameters
β
n
dineutron
core
n
bn
r1rG1 bn
r2
rG2
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Energy surface of +2n+2n system +2n+2
n
+2n
: spread of dineutron
bn
: si
ze o
f din
eutr
on
(fm)
(fm) (MeV)
In the two-dineutron case, the compact dineutron is unfavored at the nuclear surface, compared to the one-dineutron case.
under the analysis
: two-dineutron energy
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Summary
We have proposed a new approach to investigate dineutron correlation in nuclei, the dineutron condensate (DC) wave function.
When two neutrons are distributed near the nuclear surface, their energy structure has a “valley and barrier”, so that they favor a somewhat compact size.
The potential from the core might be important for correlation between two valence neutrons.
We have applied the AMD+DC method to 10Be and investigated the dineutron components in 10Be(0+
1).
dineutron formation
poster session in YKIS
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Outlook
Application of the AMD+DC method to the various neutron-rich nuclei
where dineutron correlation is expected to be enhanced, and analysis of the dineutron components in them ( for instance, 6He, 11Li and 12,14Be ).
Analysis two-dineutron condensate state in 7H and 8He in detail, and investigation of the behavior of two dineutrons.
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kmax-dineutron DC w.f.
core (AMD) kmax-dineutrons
spatial part
B
n
n
dineutron
core
Yk
Assuming that the A-nucleon system is composed of (A-2kmax)-nucleon core and one kmax-dineutron
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core (AMD)
dineutron
spatial partB
n
ndineutron
core
Y
fixiing B = Bx = By = Bz
1-DC w.f.Assuming that the A-nucleon system is composed of (A-2)-nucleon core and one dineutron
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relative and c.o.m. w.f. of the dineutron
n
n β
core
2bn
coordinate transformation Y-integral
relative part c.o.m. part
size of dineutron
spread of dineutron
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2-DC wave functionDistributing two same size dineutron in the S-wave around the core Approximately replacing one of the Y-integral to the d-sum
dineutrondineutron
same parameters
core (AMD)
B
n
ndineutron
Y1
Y2
core
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Hamiltonian
: Volkov No.2 M=0.60, B=H=0.125
: LS part of G3RS vLS = 1600 MeV