n. itagaki yukawa institute for theoretical physics, kyoto university
DESCRIPTION
Exotic cluster structure in light nuclei. N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University. weakly interacting states of strongly bound subsystems. Excitation energy. decay threshold to clusters. single-particle motion of of protons and neutrons. - PowerPoint PPT PresentationTRANSCRIPT
single-particle motion of of protons and neutrons
weakly interacting states of strongly bound subsystems
decay threshold to clusters
Exc
itatio
n en
ergy
Nuclear structure
3α thresholdEx = 7.4 MeV
0+2
Ex =7.65 MeV
0+
2+
Γγ
Γγ
Γα
Synthesis of 12Cfrom three alpha particles
The necessity of dilute 3alpha-cluster state has been pointed out from astrophysical side, and experimentally confirmed afterwards
Linear-chain structure of three clusters in 16C and 20C
J.A. Maruhn, N. Loebl, N. Itagaki, and M. Kimura, Nucl. Phys. A 833 1-17 (2010)
Cluster study with mean-field models
Stability of 3 alpha linear chainwith respect to the bending motion
Dotted -- 16C Geometric shape is stabilizedby adding neutrons
Solid -- 20C
mean-field, shell structure (single-particle motion)
weakly interacting state of clusters
decay threshold to clusters
Exc
itatio
n en
ergycluster structure with geometric shapes
How can we stabilize geometric shapes like linear chain configurations?
• Adding valence neutrons
• Orthogonalizing to other low-lying states
(14C could be possible by Suhara)
• Rotating the system
single-particle motion ofprotons and neutrons
weakly interacting state of clusters
decay threshold to clusters
Exc
itatio
n en
ergycluster structure with geometric shapes
Gas-like state of three alpha’s around 40Ca?
Hoyle state around the 40Ca core?
Tz. Kokalova et al. Eur. Phys. J A23 (2005)
28Si+24Mg 52Fe
Discussion for the gas-like state of alpha’smoves on to the next step – to heavier regions
Virtual THSR wave function
N.Itagaki, M. Kimura, M. Ito, C. Kurokawa, and W. von Oertzen, Phys. Rev. C 75 037303 (2007)
Gaussian center parameters are randomly generated
by the weight function of
0+ states of 5α system
16O-α model16O-α + 5α gas
N. Itagaki, Tz. Kokalova, M. Ito, M. Kimura, and W. von Oertzen, Phys. Rev. C 77 037301 1-4 (2008).
Two advantages of this treatment
• Coupling with normal cluster states can be easily calculated
• Adding core nucleus is easily done
24Mg = 16O+2alpha’s
7th state, candidate for the resonance stateLarge E0 transition strength
0+ EnergyE0
T. Ichikawa, N. Itagaki, T. Kawabata, Tz. Kokalova, and W von OertzenPhys. Rev. C 83, 061301(R) (2011).
28Si =16O+3alpha’s
T. Ichikawa, N. Itagaki, Y. Kanada-En'yo, Tz. Kokalova, and W. von Oertzen, Phys. Rev. C 82 031303(R) (2012)
How about Fermion case?
• Calculation for a 3t state in 9Li, where the coupling effect with the alpha+t+n+n configuration, is performed
• Not gas-like and more compact?
mean-field, shell structure
Threshold rule:gas like structure clusters
cluster-threshold
Exc
itatio
n en
ergycluster structure with geometric shape
Competition betweenthe cluster and shell structures
α-cluster model
• 4He is strongly bound (B.E. 28.3 MeV) Close shell configuration of the lowest shell This can be a subunit of the nuclear system
We assume each 4He as (0s)4
spatially localized at some position
Non-central interactions do not contribute
• How we can express the cluster-shell competition in a simple way?
The spin-orbit interaction is the driving force to break the clusters
We introduce a general and simple model to describe this transition
The spin-orbit interaction: (r x p) • s
r Gaussian center parameter Ri
p imaginary part of Ri
For the nucleons in the quasi cluster: Ri Ri + i Λ (e_spin x Ri)
exp[-ν( r – Ri )2]
In the cluster model,4 nucleons share the same Ri value in each alpha cluster
(r x p) • s = (s x r) • p
Slater determinant
spatial part of the single particle wave function
Single particle wave function of nucleons in quasi cluster (spin-up):
Quasi cluster is along xSpin direction is along zMomentum is along y
the cross term can be Taylor expanded as:
for the spin-up nucleon (complex conjugate for spin-down)
the single particle wave function in the quasi cluster becomes
0+ states of 16C
Λ = 0.8 Λ = 0.8 and 0.0
3α cluster state is importantin the excited states
H. Masui and N.Itagaki, Phys. Rev. C 75 054309 (2007).
We need to introduce an operator and calculate the expectation value
of α breaking
What is the operator related to the α breaking?
one-body spin-orbit operator for the proton part
Breaking all the clusters
Introducing one quasi cluster
Rotating both the spin and spatialparts of the quasi cluster by 120 degree(rotation does not change the j value)
Rotating both the spin and spatialparts of the quasi cluster by 240 degree(rotation does not change the j value)
Energy sufaces
0+ energy
Minimum pointR = 0.9 fm, Λ = 0.2- 89.6 MeV
LS force
Tadahiro Suhara, Naoyuki Itagaki, Jozsef Cseh, and Marek Ploszajczak arXiv nucl-th 1302.5833
Comparison with β-γ constraint AMD
986.0)0.2fm,9.0(2
AMDSMSO R
overlap
SMSO AMD
energy - 89.6 [MeV] - 90.1 [MeV]
# of freedom 2 ( R, Λ ) 6A ( 3×2×A )xyz 複素数 粒子数
Summary• Nuclear structure changes as a function of excitation energy • Geometric configurations are stabilized by adding neutrons
or giving large angular momentum• Studies of gas-like structure of alpha-clusters are extended
to heavier nuclei• Cluster-shell competition and role of non-central
interactions in neutron-rich nuclei can be studied. We can transform Brink’s wave function to jj-coupling shell model by introducing two parameters