Investigation of the halo structure in 17C
• Hokkaido Univ. Naoya Furutachi
Introduction
 Investigation of halo structure is extending to
heavier mass region
－Light halo nuclei
6He、8B、11Li、11Be
、14Be …
－Recently found halo nuclei
22C、 31Ne
－Further investigation of halo structure
C, Ne, Mg, Si isotope
One (two) neutron removal cross section,
Coulomb breakup …
 The most simple picture of halo nucleus:
Spherical inert core + weakly bound 1,2 nucleon
－6He、11Li …
Core excitation is
important
 Halo structures with deformed core
（Core+1,2 nucleon）
 31Ne: One neutron halo
Excitation of 30Ne core (Z=10,N=20)
－Low 2+ excitation energy (0.8 MeV)
of 30Ne
－AMD+RGM
30Ne(2+)⊗1p
3/2: 24%
Spherical,
Inert
Deformed,
Modified from bare
nucleus ?
 22C: Two-neutron halo
Excitation of 20C core (Z=6,N=14)
－breaking of N=14 subshell closure,
low 2+ excitation energy (1.61 MeV),
large B(E2) of 20C

37Mg: 36Mg
core (Z=12,N=24 －open shell ) K.Minomo et al., PRL108(2012)052503
15C
 Halo structure and its core excitations
of odd Carbon isotopes

15C
, 19C: one neutron halo
19C
14C
Small excitation of
14C core
18C
Excitation of
deformed (oblate ?)
18C core
 Core excitation of 19C
－ One neutron removal of 19C, particle-γ coincidence measured
Y.Kondo et al., PRC79 (2009) 014602
 Halo structure and its core excitations
of odd Carbon isotopes

15C
, 19C: one neutron halo
15C
19C
14C
Small excitation of
14C core

15, 17C
－ Coulomb breakup, γ coincidence
18C
Excitation of
deformed (oblate ?)
18C core
 What are neutron configurations of neutron-rich Carbon isotopes ?
Why there is no ground state halo in 17C ?
 Ground state spin-parity
15C: 1/2+, 17C: 3/2+, 19C: 1/2+
17C: no ground state halo
 Nilsson diagram with WS potential designed for 17C
I.Hamamoto, PRC69 (2004) 041306
Naïve expectation:
15C
: single particle 1s1/2 state
→ halo
17C : [220 ½] orbit,
→ no ground state halo
19C : [211 ½] orbit,
large l=0 component
→ halo
15C
?
17C
?
19C
?
 Exotic structure of 17C
Snof 1/2+ state is 0.5 MeV
→ halo structure ?
Small B(M1; 1/2+ →3/2+)
－1/2+ state: [211]1/2 orbital ?
Increase of 1s1/2 component in
This orbital decrease M1 transition
to the ground state
D.Suzuki et al., PLB666 (2004) 041306
HF+BCS calculation
－Shape coexistence
3/2+ : Kπ=3/2+ with prolate deformation
1/2+ : Kπ=1/2+ with oblate deformation
Shape difference of 3/2+ and 1/2+ state reduces M1 transition
H.Sagawa et al., PRC78 (2008) 041304 (R)
 Halo effect and shape coexistence expected in 17C
 Few particles in sd-orbit
is expected to enhance
prolate deformation.
 On the other hand,
oblate deformation of
proton promote oblate
deformation of neutron
Oblate
1/2+
1/2+
Halo 1/2+
1/2+
g.s.
 17C is intriguing nucleus to investigate the halo effect
(l=0 component in valence neutron orbital)
and core excitation (shape difference of core)
To investigate 17C,
Halo structure and shape coexistence should be treated simultaneously
→ MAMD framework has been applied
Framework
 Multiple width Gaussian bases
antisymmetrized molecular dynamics (MAMD)
AMD wave function
Improved nucleon wave function
α=2 for |N-Z| neutron wave function
α=1 for N=Z nucleon wave function
Variational function
Hamiltonian
；Volkov No.2+G3RS force
Energy variation
(V0=900 MeV)
GCM
Generator coordinate; proton and neutron radii
Proton radius: Description of core excitation
Neutron radius: Description of halo
 Effectiveness of MAMD
 Comparison with ordinal AMD results
－ AMD results : Values in parenthesis
B.E. [MeV]
15
C 1/2+ Cal. 107.1 (103.5)
Exp.
106.5
15
C 5/2+ Cal. 105.3 (103.6)
Exp.
105.76
17
C 1/2+ Cal. 109.5 (104.6)
Exp.
111.26
17
C 3/2+
109.2 (105.5)
Exp.
111.47
Rn [fm]
2.87 (2.62)
2.56 (2.52)
2.83 (2.67)
2.76 (2.65)
 Two-dimensional energy surface of 15C
 Energy surface as functions
of proton and neutron radii
Density distribution
 Color plot : Valence 1n
 Contour line : 14C core
15C 1/2+
Oblate
Oblate ～ Spherical ～ Prolate
•
•
Proton and neutron radii are correlated
 Constant neutron skin thickness is favored
Valence one neutron has non-negligible effect on 14C core
 Different neutron configuration have different dependence
on proton radius and deformation shape (oblate ～ triaxial)
 Neutron configurations of 15C
 Energy surface as function of deformation parameter β
prolate
Oblate～prolate
Spherical
15C
βn～0.3(prolate)
βn～0 (1s1/2)
～
Density distribution
 Color plot : Valence 1n
 Contour line : 14C core
βn～0.5(prolate)
～
 Neutron configurations of 17C
triaxial
β～0
Prolate
βn～0.4(prolate)
βn～0.2(triaxial)
Last 1n
Last 1n
0d5/2
～
17C
Density distribution
 Color plot : Valence 1n
 Contour line : 16C core
Large rn(prolate)
Last
Last 1n
1n
～
Second 1n
Second 1n
Second 1n
 Energy levels of 17C
3/2+
1/2+
5/2+
3/2+
5/2+
Exp.
5/2+
1/2+
3/2+
3/2+
1/2+
5/2+
Cal.
 Compressed energy levels of 3/2+, 1/2+, 5/2+
states are consistent with the experiment
 M1 transitions of 17C
5/2+
3/2+
11
6.3
1/2+
Cal.
Unit: 10-2 μn2
Exp.
D.Suzuki et al., PLB666 (2004) 041306
 B(M1; 1/2+→3/2+) is small compared to 21Ne
 B(M1; 5/2+→ 3/2+) reproduced
 M1 transitions of 17C
 If the shape of 3/2+ and 1/2+ states are different (prolate and oblate),
M1 transition between these states is strongly suppressed
H.Sagawa et al., PRC78 (2008) 041304 (R)
 Present calculation
3/2+
βn～0.4(prolate)
Last 1n
1/2+
βn～0.2(triaxial)
Large rn(prolate)
Last 1n
Last
Last 1n
1n
+
Second 1n
Second 1n
Second 1n
 Valence neutron configuration is different between
1/2+ and 3/2+ states, but change in core shape is small
→ Finite value of B(M1; 1/2+ → 3/2+)
 Inclusion of halo-like state decrease B(M1; 1/2+ → 3/2+)
Summary
 Structure of 17C was investigated focusing on the exotic
M1 transition between ground and first excited state
 MAMD framework applied
 Halo structure of 15C was described
 Drastically improved from usual AMD
 Structure of 17C was discussed
 Compressed energy levels of 1/2+, 3/2+, 5/2+ states are consistent
with experiment
 Suppression of B(M1; 3/2+→1/2+) is considered to be due to
cooperative effect of change of core shape and halo effect.