1. Applications of Heavy-ion accelerators
Korea particle accelerator school (KoPAS 2017) (10-14 July 2017)
Applications of Heavy-ion accelerators
-- Exotic structure of nuclei away from stability -- Satou Yoshiteru RISP/IBS
M.Thoenessen
Rep.Prog.Phys.76
(2013)
A view on physics of unstable nuclei
Neutron halo structure
Evolving shell structures
A spectroscopic study of neutron-rich Carbon isotopes, 17,19C.
Nobel symposium  24 contributions
Articles of world forefront researchers
T.Otsuka
Phys.Scr.T152
(2013)
Nobel Symposium
152: Physics with Radioactive Beams
(24 contributions)

2. abstract
Currently, very neutron-rich nuclei have been a subject of intensive investigations. It is anticipated that various exotic properties are induced by the large excess of neutrons and weak binding of valence neutrons. Nucleon density distribution changes drastically, leading to the emergence of neutron halo. The mean field can change accordingly, which promotes a drastic modification of the shell structure.
A goal of the research involving exotic nuclei is to establish a comprehensive, predictive theory of complex atomic nuclei.
After an overview of the discovery of the nuclei, encompassing the nuclear chart, I touch three topics: (1) neutron halo structure, (2) evolving shell structures, (3) a spectroscopic study of neutron-rich Carbon isotopes, 17,19C, given to illustrate a typical nuclear physics experiment utilizing a forefront accelerator facility.

3. A view on physics of unstable nuclei
O.Tarasov et al., PRC75(2007)
T.Baumann et al., Nature 449(2007)1022.
Disappearance of magicity at N=20
T.Motobayashi et al., PLB346(1995)9.
Disappearance of
magicity at N=8
H.Iwasaki et al., PLB491(2000)8.
Neutron
drip-line
Proton halos
M.Notani et al., PLB542(2002)49.
S.M.Lukyanov et al.,
J.Phys.G28(2002)L41.
H.Sakurai et al., PLB448(1999)180.
With the advent of new radioactive beam facilities capable of producing intense beams of various nuclear species far from stability, an increasingly large amount of spectroscopic information has been accumulated over a wide region of the nuclear chart.
What we see here is the lighter corner of the nuclear chart up to silicon.
Let’s me recall that even in this lighter corner of the chart, new isotopes are being revealed and we do not know the limit of existence, the so called drip-line, beyond the fluorine isotope in the neutron rich side.
Once a new isotope is discovered, we can investigate its properties, such as mass, spin-parity, radioactive half-life, electromagnetic moment, and spectrum of excited states.
By accumulating spectroscopic information we can reveal new phenomena, such as the neutron halo structure and modifications of shell closures.
As one of the spectroscopic tools we are developing an experimental method based on the invariant mass method utilizing nucleon scattering in inverse kinematics.
In this talk I would like to show some the recent results obtained using this method.
New isotopes
Neutron halos
I.Tanihata et al.,
PRL55(1985)2676.
New magic number N=16
A.Ozawa et al., PRL84(2000)5493.
Limits of nuclear existence　
Exotic structures of nuclei away from stability
Nuclear properties relevant to astrophysical phenomena
Test of Standard Model/ fundamental conservation laws
Applications in medicine, electronics, condensed matter, industrial processes
Challenges in nuclear physics
Mass, radius, half-life, electromagnetic moment, and spectrum of excited states

4. Nuclear structure of very-neutron-rich nuclei
Exotic properties are anticipated due to the large excess of neutrons and weak binding of valence neutrons
Nucleon density distribution may change drastically.
⇒　neutron halo, cluster
Mean field can change accordingly.
⇒　modification of shell structure, melting of magicity
Deformability of nuclei is modified accordingly.
Large Fermi energy difference
between neutrons and protons
will modify the effects of Pauli
blocking and enhance the
coupling with continuum states.
Let me focus on the neutron-rich nuclei.
What intriguing properties we may expect for such nuclei ?
Here the situation the neutron-rich nuclei are encountering is depicted and compared with that of the beta stable nuclei.
In normal nuclei, neutrons and protons are filled in a certain amount so that the Fermi energy becomes the same for both of them, no beta decay occurs, it is stable.
By filling neutrons in such a nucleus, the neutron Fermi energy becomes high and the binging energy becomes shallow.
Due to the proton-neutron interaction, which is attractive, the proton Fermi energy becomes low, protons become more deeply bound.
For such neutron-rich nuclei, various exotic properties are anticipated to emerge due to the large excess of neutrons and weak binding of valence neutrons.
(1)Neutron density distribution may change drastically, showing isospin inhomogeneity.
(2)A nucleus tends to be enlarged or diluted, and neutron halo structure and cluster formation emerge.
(3)The mean field can change accordingly, which will promote changes in the shell structure and deformability of nuclei.
(4)Large Fermi energy difference between neutrons and protons will modify the effects of Pauli blocking and enhance the coupling with continuum state.

5. Current status and future potential of nuclide discoveries
M.Thoennessen, Rep. Prog. Phys. 76 (2013)
Over 3000 nuclides of 118 elements are known, while an estimate says a total of 7000 bound nuclei exist. Conservatively, another 1500 nuclides are waiting to be discovered.
Peaks in the # of nuclides discovered are related to the development of new techniques.
The search for new superheavy elements continues to rely on fusion-evaporation reaction. Future choices would be (1) deep inelastic scattering on radioactive targets (e.g., 248Cm) and (2) RI beams + radioactive targets utilized for fusion-evaporation reactions.
Properties of beyond-drip-line nuclei, 21C, 30F, 33Ne, 36Na, and 39Mg, can be studied, which are interesting because they represent the extreme limits for each element.
“for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons”
Enrico Fermi
The Nobel Prize in Physics 1938
Unobservable ~ 2000 ③ ④ ⑤ ② ⑥ ①
① Aston’s positive ray spectrograph
② Light particle induced reactions
③ Fusion evaporation reac.
④ Target&projectile fragmentation
⑤ PF separator (1st gen.), storage ring
⑥ PF separator (2nd gen.),
　　new technical advances
# 253
Unobservable ~ 500
1890
1910
1930
1950
1970
1990
2010
Year

6. Chart of nuclides for elements heavier than nobelium
M.Thoennessen, Rep. Prog. Phys. 76 (2013)
There exists a separation of the more neutron-rich nuclides up to Z=118 produced in ‘hot’ fusion-evaporation reactions from the less neutron-rich nuclides up to Z=113 which were predominantly produced in ‘cold’ fusion-evaporation reactions.
In 2015, four superheavy elements, 113, 115, 117, and 118, verified. Names are given in 2016.
Oganesson (Og)
Tennessine (Ts)
Moscovium (Mc)
Nihonium (Nh)

7. World major RI beam facilities
CERN-ISOLDE
P.Van Duppen and K.Riisager,J.Phys.G:Nucl.
Part.Phys.38(2011)
Louvain
M.Huyse et al.,J.Phys.G:Nucl. Part.Phys.38(2011)
ORNL
J.R.Beene et al., J.Phys.G: Nucl.Part.Phys.38(2011)
TRIUMF-ISAC
G.C.Ball et al.,Phys.Scr.
91(2016)
GANIL
A.Navin et al.,J.Phys.G:Nucl. Part.Phys.38(2011)
RIKEN-RIBF
Y.Yano,NIMB261(2007)1009.
GSI
J.Gerl et al.,Phys.Scr.
91(2016)
MSU
A.Gade,B.M.Sherrill,Phys.Scr.91(2016)
RAON
C.B.Moon, AIP Adv.4 (2014)
Dubna
L.Grigorenko et al.,Nucl.Phys.News,24-4(2014)22.
Lanzou
X.Zhou,Nucl.phys.News,26-2(2016)4.
Legnaro-SPES
G.de Angelis and G.Fiorentini,
Phys. Scr.91(2016)
Focus issue  45 contributions
Physica Scripta91, 2016
Focus issue to celebrate the 40 year anniversary of the 1975 Nobel Prize to Aage Niels Bohr, Ben Roy Mottelson and Leo James Rainwater
(45 contributions)
Projectile fragmentation facility
ISOL (Isotope Separator On-Line) facility

8. Neutron halo structure
Anomalously large matter radius for 11Li from interaction cross section measurement => neutron halo structure
11Li … + 12C at 800 MeV/nucleon x I0 I
Valence
neutrons
𝐼 0 𝐼
core
𝑑𝑃= 𝑁𝜋 𝑅 2 𝐿 2 =𝜎𝑛𝑑𝑧, 𝜎=𝜋 𝑅 2
𝑛= 𝑁 𝐿 2 𝑑𝑧
𝐼= 𝐼 0 exp(−𝜎𝑛𝑧)
This experiment represents the first case in which short lived nuclei (unstable nuclei) produced by high energy heavy ion reactions were used as secondary beams for secondary reaction studies.
Valence neutrons have extended spatial distribution outside of the core where neutrons and protons are equally distributed.
※ First high energy RI beam experiment. ※ A nucleus not saturated in density.
I.Tanihata et al., Phys. Rev. Lett. 55 (1985) 2676.

9. 11Li Neutron halo structure 𝑅≈1.2 𝐴 1 3 (~2.7 fm) Borromean nucleus
Es=0.185
Es=8.000
𝑅≈1.2 𝐴 (~2.7 fm)
11Li
Neutron halo WF
Borromean nucleus
(any sub pairs are unbound)

10. Neutron halo
𝜎 𝑅 ≅𝜋 𝑅 𝑚 2
Outermost loosely bound neutron decoupled from the core: halo neutron
𝑆 𝑛 =500 keV
𝑅 rms Li =3.50±0.09 fm
𝑅 rms 9 Li =2.32±0.02 fm
Rrms (fm)
I.Tanihata et al., Prog. Part. Nucl. Phys. 68 (2013)215.
A regrettable comment.
He missed (overlooked, missed out, passed up) a big fish.
Igal Talmi: Weizmann Institute of Science
He is known for nuclear shell model and his Doctoral thesis advisor is Wolfgang Pauli.
A single s neutron, without Coulomb and centrifugal barriers, with such a small separation energy has a highly extended radial function Be could have been called a “halo nucleus” many years before it was found experimentally. Fifty years of the shell model (2003), Igal Talmi

11. Eikonal approximation for potential scattering
Decompose the scattering wave into the highly oscillating part ( 𝑒 𝑖𝑘𝑧 ) and the remaining slowly oscillating part ( 𝜓 𝒓 ).
➡　Schrödinger eq. is linearized; 𝜓 𝒓 can be obtained. 𝒂
Plane wave
potential
Z direction
Short range potential
High energy
𝜓 𝒓 = 𝑒 𝑖𝑘𝑧 𝜓 𝒓 𝜆= ℏ 𝑝 ≪𝑎, ∆𝑝≪1
𝑣 ℏ 𝑖 𝜕 𝜕𝑧 𝑚 ℏ 𝑖 𝛻 2 𝜓 𝒓 +𝑉 𝑟 𝜓 𝒓 =0
𝜓 𝑥,𝑦,𝑧 =exp 1 𝑖ℏ𝑣 −∞ 𝑧 𝑑 𝑧 ′ 𝑉(𝑥,𝑦,𝑧′) , 𝜓 𝑥,𝑦,𝑧→−∞ =1
𝑓 𝜃 =− 2𝑚 ℏ 𝜋 𝑑 𝒓 ′ 𝑒 −𝑖 𝒌 ′ ∙ 𝒓 ′ 𝑉 𝑟 ′ 𝜓 𝒓 ′
= 𝑖𝑘 2𝜋 𝑑𝒃 𝑒 −𝑖𝒒∙𝒃 1− 𝑒 𝑖𝜒(𝒃)
𝜒 𝒃 =− 1 ℏ𝑣 −∞ +∞ 𝑑𝑧𝑉(𝒃+𝑧 𝒛 ) 𝑘 𝑏
Phase shift function
𝑝=ℏ𝑘
𝑑𝜎 𝑑Ω = 𝑓(𝜃) 2 　
𝜎 el = 𝑑Ω 𝑓(𝜃) 2 = 𝑑𝒃 1− 𝑒 𝑖𝜒(𝒃) 2 　
𝜎 tot = 4𝜋 𝑘 Im𝑓 0 =2 𝑑𝒃 1−Re 𝑒 𝑖𝜒(𝒃) 　

12. Many-body generalization for scattering involving composite nuclei
Glauber theory: A microscopic many-body theory, including multiple scattering　effects to all orders. It does not rely on perturbative expansion.
“Lecture in Theoretical Physics, Vol.1 (1959)”
𝑓 𝛼 𝜃,𝜙 = 𝑖𝑘 2𝜋 𝑑𝒃 𝑒 −𝑖𝒒∙𝒃 Φ 𝛼 1− 𝑒 𝑖 𝑖=1 𝐴 𝜒 𝒃− 𝒔 𝑖 Φ 0
𝜒 𝒃 =− 1 ℏ𝑣 −∞ +∞ 𝑑𝑧𝑉(𝒃+𝑧 𝒛 )
Φ 𝛼 ⋯ Φ 0 refers to integration in terms of the target coordinate
Phase shift function for NN scattering
𝒓 𝑖
𝒔 𝑖
𝑧 𝑖 𝒃 𝒌
𝒃 −𝒔 𝑖
Coordinate variables
Roy J. Glauber
Born: 1925, New York, USA
Nationality: US
Fields: Theoretical physics
Institutions: Harvard university
Doctoral advisor: Julian Schwinger
Known for: Photo detection, Quantum optics
Notable awards: The Nobel Prize in Physics 2005
"for his contribution to the quantum theory of optical coherence"

13. NN Profile function
Relate 𝜒 𝒃 or profile function to NN scattering data.
𝑓 𝜃 = 𝑖𝑘 2𝜋 𝑑𝒃 𝑒 −𝑖𝒒∙𝒃 1− 𝑒 𝑖𝜒(𝒃) = 𝑖𝑘 2𝜋 𝑑𝒃 𝑒 −𝑖𝒒∙𝒃 Γ(𝒃)
Profile function Γ 𝒃 ≡1− 𝑒 𝑖𝜒(𝒃) is related to NN cross sections as follows:
𝜎 tot 𝑁𝑁 = 4𝜋 𝑘 Im𝑓 0 =2 𝑑𝒃ReΓ 𝒃 , 𝜎 el 𝑁𝑁 = 𝑑𝒃 Γ(𝒃) 2
Total and elastic cross sections for pp
collision
Total and elastic cross sections for pn
collision
Total pd pp
Elastic
Elastic
Total pn
Phys. Rev. D86, (2012).

14. Observables 𝜎 el = 𝑑 𝒃 1− Φ 0 | 𝑒 𝑖 𝑖=1 𝐴 𝜒 𝒃− 𝒔 𝑖 | Φ 0 2
Utilized for the analysis of the 11Li + 12C interaction (reaction) cross section data at 800 MeV/nucleon (Tanihata85), which has led to the discovery of “neutron Halo”.
Observables
𝜎 el = 𝑑 𝒃 1− Φ 0 | 𝑒 𝑖 𝑖=1 𝐴 𝜒 𝒃− 𝒔 𝑖 | Φ
𝜎 tot =2 𝑑𝒃 1−Re Φ 0 | 𝑒 𝑖 𝑖=1 𝐴 𝜒 𝒃− 𝒔 𝑖 | Φ 0
𝜎 reac = 𝜎 tot − 𝜎 el = 𝑑𝒃 1− Φ 0 | 𝑒 𝑖 𝑖=1 𝐴 𝜒 𝒃− 𝒔 𝑖 | Φ
𝜎 −1𝑛 ≅ 𝜎 reac 𝐴 − 𝜎 reac 𝐴−1
*) Constructing the nucleus-nucleus scattering amplitude starting from the
elementary nucleon-nucleon (NN) scattering amplitude.
*) Only the ground state wave function is necessary.
Examples are shown later.

15. Evolving shell structures
Intermediate energy Coulomb excitation measurement revealed disappearance of magic numbers
𝐵 𝐸2 =454±78 𝑒 2 fm 4
𝛽=0.512±0.044
𝛽= (4𝜋 3𝑍𝑒 𝑅 2 ) 𝐵(𝐸2)
a:b=3:2
T. Motobayashi et al., Phys. Lett. B346 (1995) 9.
Small E(2+) & large B(E2) value supports the idea of disappearance of the N=20 shell closure in 32Mg.
32Mg(2+)
N=20 isotone
N=28
Breakdown of the N=20 shell closure
Breakdown of the N=20 shell closure
Z=12
Z=10
N=20

16. Magic numbers and their break-down
I.Talmi
Nuclear shell structure ⑧
I.Talmi and I.Unna, PRL4(1960)469. ⑭
12B
13C
11Be N Z
N=7
16N
17O
15C
N=9
Mean potential
0 𝒑 𝟏/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
𝑉 𝑝 1 2 𝑑 5 2 𝑝𝑛
𝑉 𝑝 1 2 𝑠 1 2 𝑝𝑛
2 𝑉 𝑝 1 2 𝑑 5 2 𝑝𝑛 − 𝑉 𝑝 1 2 𝑠 1 2 𝑝𝑛
𝑉 𝑟 = 1 2 𝑚 𝜔 2 𝑟 2 −𝑏 ℓ 2 −𝑎 ℓ∙𝒔
j<(=ℓ-1/2)
j>(=ℓ+1/2)
He has not yet missed (overlooked, missed out, passed up) another big fish.
The Nobel Prize in Physics 1963
"for their discoveries concerning nuclear shell structure"
Maria Goeppert
Mayer
J. Hans
D. Jensen
Magic numbers: 2,8,20,28,50,82,126

17. Tensor force and shell evolution
32Mg
30Ne
42Si
Broken
Broken
11Be
s1/2, p1/2 inversion
15C
d5/2, s1/2 inversion Z
T.Otsuka, Phys. Scr. T152 (2013)
“A question, which occurred to me at the end of the last century, is whether of not there could be new physics in those nuclei. This question […] should be related definitely to nuclear forces which may work in different manners as compared to stable nuclei.”
“In the shell-structure scheme of Mayer and Jensen proposed in 1949, one of the missing element is the first-order contribution of the tensor force.”
Mean potential of Mayer & Jensen
Monopole interaction of Otuka
𝑉 𝑟 = 1 2 𝑚 𝜔 2 𝑟 2 −𝑏 ℓ 2 −𝑎 ℓ∙𝒔
Monopole matrix element of 𝑉
𝑣 𝑚;𝑗,𝑗′ = 𝑘,𝑘′ 𝑗𝑘 𝑗 ′ 𝑘 ′ 𝑉 𝑗𝑘 𝑗 ′ 𝑘′ 𝑘,𝑘′ 1
𝑉 : two-body “residual” int.
𝑗,𝑘, 𝑗 ′ 𝑘′: single-particle orbits
Monopole component of 𝑉
𝑣 𝑚;𝑗,𝑗′ = 𝑣 𝑚;𝑗,𝑗′ 𝑛 𝑗 𝑛 𝑗′
Single-particle energy (SPE) of 𝑗
∆ 𝜖 𝑗 = 𝑣 𝑚;𝑗,𝑗′ 𝑛 𝑗′
𝑛 𝑗 : number operator of orbit 𝑗
𝑣 𝑚;𝑗,𝑗′ becomes a part of the mean potential at the shell closure.
Monopole-based universal int.
𝑉 𝑀𝑈 = 𝑉 𝑐 + 𝑉 𝑇
T.Otsuka et al., PRL104(2010)

18. Two nucleon systems and the tensor force
Tz=-1 pp
Tz=0 pn
Tz=1 nn
S=0, T=1
S=1, T=0 E
The only bound two nucleon
system: deuteron ( 1 2 H )
Relative S wave is assumed
singlet
triplet
Two nucleon system:
Ψ 1,2 =𝜙 𝑟 𝜒 1,2 𝜐 1,2
Two nucleon interaction:
𝑉 1,2 = 𝑉 𝑐 (𝑟) (𝑆=0, 𝑇=1) 3 𝑉 𝑐 𝑟 + 𝑆 12 𝑉 𝑇 𝑟 𝑆=1, 𝑇=0
𝑆 12 =3 𝝈 1 ∙ 𝒓 𝝈 2 ∙ 𝒓 − 𝝈 1 ∙ 𝝈 2
For S=0 with 𝝈 1 =− 𝝈 2 ,
𝑆 12 =− 3 𝑟 𝝈 1 ∙ 𝒓 𝝈 =0
Tensor force acting in the deuteron (S=1):
𝑆 12 𝑉 𝑇 𝑟 =(3 cos 2 𝜃−1) 𝑉 𝑇 𝑟
Tensor force ∝−(3 cos 2 𝜃−1)
spin
isospin
Total wave function must be anti-symmetrized.
Responsible to the bound deuteron r
𝜃=0
𝜃=𝜋/2
−(3 cos 2 𝜃−1) -2 1
attractive
repulsive
negative

19. Tensor force and shell evolution – illustration (1)
T.Otsuka et al., PRL95(2005) ⑭
0 𝒑 𝟏/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
17O
proton
neutron
j>(=ℓ+1/2)
j<(=ℓ-1/2)
j’>(=ℓ’+1/2)
j’<(=ℓ’-1/2)
Tensor force
𝑆 12 𝑉 𝑇 𝑟
0 𝒑 𝟏/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
16N
0 𝒑 𝟏/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
15C
inversion
proton orbit – neutron orbit
Acting force
𝑗 < − 𝑗 > ′ , 𝑗 > − 𝑗 < ′
attractive
𝑗 < − 𝑗 < ′ , 𝑗 > − 𝑗 > ′
repulsive

20. Tensor force and shell evolution – illustration (2)
T.Otsuka et al., PRL104(2010)
Z=12
Z=10
Breakdown of the N=20 shell closure
T.Otsuka et al., PRL95(2005)
30Ne
32Mg
34Si
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
30Ne
0 𝒅 𝟑/𝟐
0 𝒇 𝟕/𝟐 ⑯
proton
neutron
j>(=ℓ+1/2)
j<(=ℓ-1/2)
j’>(=ℓ’+1/2)
j’<(=ℓ’-1/2)
Tensor force
𝑆 12 𝑉 𝑇 𝑟
0 𝒇 𝟕/𝟐
proton
neutron
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
32Mg
0 𝒅 𝟑/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
34Si
0 𝒅 𝟑/𝟐
0 𝒇 𝟕/𝟐
proton orbit – neutron orbit
Acting force
𝑗 < − 𝑗 > ′ , 𝑗 > − 𝑗 < ′
attractive
𝑗 < − 𝑗 < ′ , 𝑗 > − 𝑗 > ′
repulsive ⑳

21. Korea particle accelerator school (KoPAS 2017) (10-14 July 2017)
4. A spectroscopic study of neutron-rich Carbon isotopes, 17,19C Satou Yoshiteru RISP/IBS
Ph.D. Theses:
Hwang Jongwon “Study of 19C by one-neutron knockout reaction with a Carbon target”
[J.W.Hwang et al., Phys. Lett. B769(2017)503.]
Kim Sunji “Spectroscopy of 17C via one-neutron knockout reaction”
[S.Kim et al., in preparation.]
Introduction
Experiment
Results and discussion
Summary

22. Issues:
The cross-shell states in light neutron-rich nuclei are known to be notoriously difficult to describe theoretically, because they involve transitions encompassing two major shells on a proton-neutron asymmetric system.
Obtaining a reliable relevant effective interaction in such cases remains of a special difficulty.
The cross-shell states might have implications to astrophysical radiative neutron captures processes, since they are strongly influenced by the presence of dipole resonances.
This presentation:
An experimental attempt to enlarge the known realm of such dipole states in N-rich C isotopes.
Capability of recently available shell-model calculations on dipole and other states examined.

23. RIKEN SAMURAI Day-1 collaborators
LPC-Caen, ENSICAEN, University de Caen, CNRS/IN2P3
N.L.Achouri, F.Delaunay, J.Gibelin, S.Leblond, M.Marques, N.Orr
Tokyo Institute of Technology
Y.Kondo, T.Nakamura, N.Kobayashi, R.Tanaka, R.Minakata, S.Ogoshi, S.Nishi, D.Kanno, T.Nakashima
RIKEN
H.Baba, P.Doornenbal, N.Fukuda, N.Inabe, T.Isobe, D.Kameda, T.Kubo, J.Lee, H.Otsu, T.Motobayashi, H.Sato, Y.Shimizu, H.Suzuki, H.Takeda, S.Takeuchi, K.Yoneda
Institute fur Kernphysik, Technische Universitat Darmstadt
T.Aumann
Seoul National University
Y.Satou, J.W.Hwang, S.Kim
Tohoku University
T.Kobayashi, K.Muto, K.Takahashi
Rikkyo University
D.Murai
Kyoto University
N.Nakatsuka, T.Murakami
University of York
A.G.Tuff
GANIL
A.Navin
Extreme Matter Institute and Research Division, GSI
Y.Togano
Institute de Physique Nucleaire
M.Vanderbrouck

24. Why study Carbon isotopes
In light elements (Z<8) the number of isotopes is the largest (13); suited for systematic study.
Bound or not?
Where is the ground state? ?
33Ne ?
33F
28O ?
25N
Where is the ground state? ?
Is there a nucleus not touching a drip line ?
Ref.) Thomas Aumann and Haik Simon, Nuclear Physics News, Vol.24, No.2, 2014, p5.

25. Why study Carbon isotopes
In light elements (Z<10) the number of isotopes is the largest (13); suited for systematic study.
They offer a basis to study intricate effects of the nuclear forces.
Quenched N=14 shell gap
Proton core polarization effects

26. ? Quenched N=14 shell gap ⑧ ⑭ 17,19,21O ⑧ ⑭ 15,17,19C proton neutron
M.Stanoiu et al., PRC78(2008) ⑧ ⑭
0 𝑝 3/2
0 𝑝 1/2
0 𝑑 5/2
1 𝑠 1/2
17,19,21O
Deformation ⑧ ⑭
0 𝑝 3/2
0 𝑝 1/2
0 𝑑 5/2
1 𝑠 1/2
15,17,19C ?
An abnormal ground state spin ½+ in 15C.
0 𝒑 𝟏/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
𝑉 𝑝 1 2 𝑑 5 2 𝑝𝑛
𝑉 𝑝 1 2 𝑠 1 2 𝑝𝑛
2 𝑉 𝑝 1 2 𝑑 5 2 𝑝𝑛 − 𝑉 𝑝 1 2 𝑠 1 2 𝑝𝑛
I.Talmi, I.Unna, PR4(1960)469.
T.Otsuka et al., PRL95(2005)
proton
neutron
j>(=ℓ+1/2)
j<(=ℓ-1/2)
j’>(=ℓ’+1/2)
j’<(=ℓ’-1/2)
Tensor force
𝑆 12 𝑉 𝑇 𝑟

27. Proton core polarization effects
Responsible for reduced neutron-neutron matrix elements in the sd shell in Carbon
WBM provides a remedy for in 16,18,20C and 1/2 1 − in 15C.
To what extent WBM is applicable?
※ Only the lowest ℏ𝜔 configurations are considered in SM calc.
H.Ueno et al.,
PRC87(2013)
The extent to which this remedy is applicable and the condition for that will need to be quantified.
Proton excitations to higher shells
Overprediction of E( 𝟐 𝟏 + ) with WBT.
[1] Core polarization effects (should be mitigated in C).
K.Sieja, F.Nowacki, NPA857(2011)9.
[2] Extended radial wave function.
A.Signoracci et al., PRC83(2011)
WBT: E.K Warburton, B.A.Brown, PRC46(1992)923.
WBM: WBP with USD part reduced by 25%.
Proton core polarization effects
0 𝒑 𝟏/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron 0+
T.T.S.Kuo, G.E.Brown, NP85(1966)40.

28. Why study Carbon isotopes
In light elements (Z<10) the number of isotopes is the largest (13); suited for systematic study.
They offer a basis to study intricate effects of the nuclear forces.
Quenched N=14 shell gap
Proton core polarization effects
The region (A<24) represents a frontier of current ab initio calculations including continuum and three-body forces. Advanced shell-model interactions also exist.

29. Shell-model interactions examined
Code (Model space)
Interactions
(OXBASH)
(spsdpf)
WBT: E.K Warburton, B.A.Brown, PRC46(1992)923.
(𝟎−𝟏)ℏ𝝎
WBM: WBP with USD part reduced by 25%.
M.Stanoiu et al., PRC78(2008)
(psd, ℏ𝝎 unrestricted)
B.A.Brown, W.D.M.Rae, Nucl. Data. Sheets 120 (2014) 115.
WBTX: WBT as calculated with NuShellX.
WBMX: WBM as calculated with NuShellX.
YSOX: C.Yuan et al., PRC85(2012)
(𝟎−𝟑)ℏ𝝎
𝒑𝒑 𝑽 𝒑𝒑 SFO
𝒔𝒅 𝑽 𝒔𝒅 SDPF-M
𝒑𝒔𝒅 𝑽 𝒑𝒔𝒅 and 𝒑𝒑 𝑽 𝒔𝒅𝒔𝒅 VMU
VMU strengths adjusted to reproduce N-rich B,C,O masses.
Ab Initio Coupled-Cluster Effective Interaction
CCEI: G.R.Jansen et al., PRL113(2014)
Nonperturbative calculation.
Based on NN and NNN forces from chiral
effective field theory.
No account for the particle continuum.
2p2h excitations
0 𝑝 1/2
1𝑠0𝑑
T.Otsuka et al., PRL104(2010)
No parameters other than those in the initial chiral NN and 3NF.
(Parameters involved are only for those initial nuclear forces.)
𝑯 = 𝒊<𝒋 𝒑 𝒊 − 𝒑 𝒋 𝟐 𝟐𝒎𝑨 + 𝑽 𝑵𝑵 (𝒊,𝒋) + 𝒊<𝒋<𝒌 𝑽 𝟑𝑵𝑭 (𝒊,𝒋,𝒌)

30. Why study Carbon isotopes
In light elements (Z<10) the number of isotopes is the largest (14); suited for systematic study.
They offer a basis to study intricate effects of the nuclear forces.
Quenched N=14 shell gap
Proton core polarization effects
The region (A<~20) represents a frontier of current ab initio calculations including continuum and three-body forces. Advanced shell-model interactions also exist.
Possible implications of properties of light neutron-rich nuclei (including C) to r-process nucleosynthesis in neutrino-driven winds have been suggested. Dipole resonances (L=1) have impact on the neutron capture rates.
M.Terasawa et al., ApJ562(2001) T.Sasaqui et al., ApJ634(2005)1173.
S.Goriely, PLB436(1998)10.

31. Objectives
Clarify sd-shell competition at N=13 (search for 𝟓/𝟐 𝟏 + in 𝟏𝟗 𝐂 )
Confirm 1/2 − (and 3/2 − ) in 17C and furnish new information.
Search for cross-shell 1/2 − states in 19C .
Test theories against new spectroscopy.
enlarged ℏ𝝎 model space
reduced sd neutron-neutron matrix elements
new SM interactions
To demonstrate the equivalence of neutron knockout and 𝛽𝑛 spectroscopy.
Reactions:
Observables: 𝝈 −𝟏𝒏 , 𝒅𝝈 𝒅𝒑 ∥ , 𝒅𝝈 𝒅 𝒑 𝑻 .
12C(18C,17C*→16C+n)
245 MeV/nucleon
12C(19C,18C*→17C+n)
280 MeV/nucleon

32. 17 C 17 B 𝜋 𝜈 1𝑠0𝑑 escape TOF (ns) 𝑝 1/2 𝑝 3/2
Allowed transitions do not involve parity change.
Resulting 𝜈 p-shell hole states can be populated by knockout reactions.
The angular momentum, and thus parity, can be determined by measuring momentum distributions.
1/2 −
𝐵 𝐺𝑇 = 1 2 𝐼 𝑖 𝑓 𝑘 𝜎 𝑘 𝜏 ± 𝑘 𝑖 2
This was the basis for the negative parity assignments of the J=1/2 and 3/2 states.
3/2 −
17 C
17 B
An advantage of the knockout reaction over the beta-delayed neutron emission spectroscopy is that (1) the energetic reaction processes allow large amount of momentum transfers, and that (2) the angular momentum of the knocked-out nucleon, and thus the parity of the final states, can determined experimentally through the measurement and analysis of differential quantities model independently.
1𝑠0𝑑
escape
TOF (ns)
En (MeV)
Ex (MeV)
Width (MeV)
Log ft
𝐽 𝜋
1.86(1)
2.71(2)
0.04(1)
4.8(1)
1/2 −
3.01(1)
3.93(2)
0.16(4)
4.9(1)
3/2 −
4.05(2)
0.06(6)
6.0(1)
5/2 −
𝑝 1/2
𝑝 3/2 𝜋 𝜈

33. One-neutron knockout reaction
P.G.Hansen and J.A.Tostevin, Annu. Rev. Nucl. Part. Sci. 53, 219 (2003).
Exhibit large cross sections ~100 mb.
Knocked-out nucleon is democratically selected from valence orbits.
Momentum distributions of the residue carry information on L, within the approximation the nucleon is suddenly removed.
Projectile
18 C
Target
Target recoil
Knockout
neutron
residue
Experimental scheme
Decay
Residue
(detected)
Decay γ
Neutron
Stripping cross section :
𝑑 𝜎 str 𝑑 3 𝑘 𝑐 = 1 2𝜋 𝑙+1 𝑚 𝑑 2 𝑏 𝑣 1− 𝑆 𝑣 𝑏 𝑣 × 𝑑 3 𝑟 𝑒 −𝑖 𝒌 𝒄 ∙𝒓 𝑆 𝑐 𝑏 𝑐 𝜓 𝑙𝑚 𝒓 2
Inclusive -1n cross section:
𝜎 −1𝑛 = 𝑛𝑙𝑗 𝐴 𝐴−1 𝑁 ∙𝐶 2 𝑆 𝐽 𝜋 ,𝑛𝑙𝑗 ∙ 𝜎 𝑠𝑝 𝑛𝑙𝑗, 𝑆 𝑛 eff
Longitudinal momentum 𝒑 ∥ distribution:
𝑑 𝜎 str 𝑑 𝑘 𝑧 = 1 2𝜋 𝑙+1 𝑚 𝑑 2 𝑏 𝜐 1− 𝑆 𝜐 𝑏 𝜐 ∞ 𝑑 2 𝜌 𝑆 𝑐 𝑏 𝑐 −∞ ∞ 𝑑𝑧 𝑒 −𝑖 𝑘 𝑧 𝑧 𝜓 𝑙𝑚 𝒓 2
Transverse momentum 𝒑 ⊥ distribution:
𝑑 𝜎 str 𝑑 2 𝑘 ⊥ = 1 2𝜋 1 2𝑙+1 0 ∞ 𝑑 2 𝑏 𝜐 1− 𝑆 𝜐 𝑏 𝜐 𝑚,𝑝 −∞ ∞ 𝑑𝑧 𝑑 2 𝜌 exp −𝑖 𝒌 𝑐 ⊥ ∙𝝆 𝑆 𝑐 𝑏 𝑐 𝜓 𝑙𝑚 𝒓 2
Single-particle
wave function
This feature together with the following property [momentum distribution …] makes this one-neutron knockout reaction an ideal tool for probing single-particle properties of unstable nuclei.

34. RIKEN RIBF : Radioactive Isotope Beam Factory
RIBF: Completed in 2007
New-Generation RI-Beam Facility
Primary beam
48Ca, 345 MeV/u, 250 pnA MAX
(~500 pnA, Year 2015)
Production target
20-mm-thick Be
Secondary beam
18C(2300 cps), 245 MeV/u
20C (190 cps), 280 MeV/u
Secondary target
Carbon, 1.8 g/cm3
SAMURAI
RIBF
陽子からウランまでを加速。
インフライトの破砕反応やフィッション（核分裂）を利用して二次不安定核重イオンビームを生成、様々な実験に供用する。
ビームエネルギー（中間エネルギー領域）
旧施設、100 MeV/nucleon 以下。
新施設、300 MeV/nucleon 以下。
RI ビームの利点：
自然界には存在しない短寿命核を生成してビームとして利用できる。
アイソトピカルに完全に分離されている。
SAMURAI Day-1 campaign 2012
Coulomb Breakup of 19B and 22C, Nakamura et al.
Study of 18B,21C, and excited states of 19B, 22C, Orr et al.
Structure of Unbound Oxygen Isotopes 25O,26O, Kondo et al.
Y.Kondo et al., PRL116(2016)
Y.Togano et al., PLB761(2016)412.
J.W.Hwang et al., PLB769(2017)503.

35. SAMURAI spectrometer Neutron 18C beam 16C fragment
Superconducting Analyzer for MUlti-particles from RAdioIsotope beams
T.Kobayashi et al, NIMB317,294(2013).
Invariant mass method
High detection efficiency for decay neutrons. Large 𝜀 𝑛
High coverage of decay phase space due to kinematical focusing.
Large acceptance near Erel~0 MeV due to magnetic separation of neutrons and charged particles.
Good 𝐸 rel resolution suited for spectroscopy.
∆ 𝐸 rel ∝ 𝐸 rel 𝐸 in 𝐴 ∆𝑃 𝑃
12C(18C,17C*→16C+n)
𝑀 inv = 𝐸 𝐶 + 𝐸 𝑛 2 − 𝑷 𝐶 + 𝑷 𝑛 2
𝐸 rel = 𝑀 inv − 𝑀 𝐶 − 𝑀 𝑛
𝐸 𝑥 = 𝐸 rel + 𝑆 𝑛
(3T, 2m dia. Pole, 80 cm gap)
Neutron
𝐸 𝑥 𝑛 𝛾
𝐸 rel
Measurement scheme. 𝑛
16C
𝑆 𝑛
17C
18C beam
16C fragment

36. Coulomb Breakup of 19B and 22C, Nakamura et al.
SAMURAI Day-One, 2012 May
Motobayashi-san is here. Nakamura-san is here, Kondo-san is here, I am unfortunately nowhere.
But two Seoul university students, Kim Sunji and Hwang Jongwon, are here and here.
They are analyzing knockout reaction data of 18C and 20C beams, respectively.
I shown flash reports of their analyses, which are hopefully approaching a final stage.
SAMURAI Day-1 campaign 2012
Coulomb Breakup of 19B and 22C, Nakamura et al.
Study of 18B,21C, and excited states of 19B, 22C, Orr et al.
Structure of Unbound Oxygen Isotopes 25O,26O, Kondo et al.

37. 18C Analysis scheme 18C Analysis Mass resolution, A/△A : 770 in sigma
Intensity : 2300 pps
Energy : 250 MeV/nucleon
Momentum acceptance,
△P/P : ± 3 %
Mass resolution,
A/△A : 770 in sigma
18C
TARGET
DALI2

38. 18C Analysis scheme 17C* 16C Analysis Mass resolution,
Intensity : 2300 pps
Energy : 250 MeV/nucleon
Momentum acceptance,
△P/P : ± 3 %
Mass resolution,
A/△A : 770 in sigma
18C
17C*
TARGET
DALI2
Mass resolution,
A/△A : 250 in sigma
16C Z
16C
A/Z

39. 18C Analysis scheme 17C* 16C Analysis Mass resolution,
Intensity : 2300 pps
Energy : 250 MeV/nucleon
Momentum acceptance,
△P/P : ± 3 %
Mass resolution,
A/△A : 770 in sigma
18C
17C*
TARGET
DALI2
Mass resolution,
A/△A : 250 in sigma
16C
Counts Z
16C
energy [MeV]
A/Z

40. 18C Analysis scheme 17C* 16C Analysis Mass resolution,
Intensity : 2300 pps
Energy : 250 MeV/nucleon
Momentum acceptance,
△P/P : ± 3 %
Mass resolution,
A/△A : 770 in sigma
16C*(2 + )
18C
17C*
TARGET
DALI2
Mass resolution,
A/△A : 250 in sigma
16C
Counts Z
16C
energy [MeV]
A/Z

41. Fragment 18C magnet FDC2 HOD FDC1 target Analysis
(Forward Drift Chamber)
FDC1
18C
target

42. Neutron NEBULA n NEUT ) 30 modules/layer Ⅹ 4 layers
Analysis
Neutron n
Counts
𝜀 𝑛 ~ 32% for 250 MeV neutron
@ 6 MeVee threshold
energy [MeV]
Neutron detector timing resolution in ~ 11 m
: 270 ps for neutron walls
NEBULA
NEUT ) 30 modules/layer Ⅹ 4 layers
VETO ) 12 modules/layer Ⅹ 2 layers

43. γ-ray γ DALI2 140 NaI(Tl) crystals C(18C,17C*→16C*(2 + ) +n)
Analysis
γ-ray γ
Counts
C(18C,17C*→16C*(2 + ) +n)
Efficiency at 1 MeV : ~ 15 %
Eγ [keV]
DALI2
140 NaI(Tl) crystals

44. Results: 12C(18C,17C*→16C+n)@245 MeV/u
Longitudinal momentum
distribution ③ ③
L=1 ④ ④
L=1 ① ②
Momentum distributions were calculated by MOMDIS:
C.A.Bertulani, A.Gade, Comput. Phys. Commun. 175(2006)372.

45. Results: 12C(18C,17C*→16C+n)@245 MeV/u
Transverse momentum
distribution ③ ③
L=1 ④ ④
L=1 ① ②
Momentum distributions were calculated by MOMDIS:
C.A.Bertulani, A.Gade, Comput. Phys. Commun. 175(2006)372.

46. Summary of parameters of observed resonances in 17C*
No.
Erel (MeV)
Ex (MeV)
𝚪 (MeV) L
𝝈 −𝟏𝒏 𝐞𝐱𝐩 (mb)
𝝈 −𝟏𝒏 𝐭𝐡 (mb)
𝑪 𝟐 𝑺 𝐞𝐱𝐩
𝑪 𝟐 𝑺 𝐭𝐡 (b)
𝑬 𝒙 𝐭𝐡 (b) (MeV)
𝑱 𝝅 ①
0.57(4)(a)
3.07(5)
0 (fixed)
---
0.38(7)
3.07
9/2 1 + (c) ②
0.81(5)
1.55(6)
0.37(8)
0.36
0.015
1.60
( 5/2 2 + ) ③
1.92(1)
2.66(2)
0.32(1) 1
15.8(10)
29.0
0.736
1.350
2.53
1/2 1 − (d) ④
3.24(2)
3.98(2)
0.03(6)
2.20(16)
3.58
0.107
0.174
4.18
3/2 1 − (d)
(a) 𝛾-ray coincidence is observed.
(b) From YSOX.
(c) H.G.Bohlen et al., EPJA31(2007)279. Y.Satou et al., PLB660(2008)320.
(d) H.Ueno et al., PRC87(2013) Ex=2.71(2) MeV for 1/2 1 − and 3.93(2) MeV for 3/2 1 − . ③
L=1 ③ ② ④ ① ④
L=1 ②

47. Presently observed states
By an elimination method, 1.55 MeV state  5/2_2+.

48. Results: 12C(20C,19C*→18C+n)@280 MeV/u
Longitudinal
momentum
distribution ① ① ②
MeV/c ① ③ ③ ②
J.W.Hwang et al., PLB769(2017)503.
Momentum distributions were calculated by MOMDIS:
C.A.Bertulani, A.Gade, Comput. Phys. Commun. 175(2006)372.

49. Summary of parameters of observed resonances in 19C*
No.
Erel (MeV)
Ex (MeV)
𝚪 (MeV) L
𝝈 −𝟏𝒏 𝐞𝐱𝐩 (mb)
𝝈 𝒔𝒑 (mb)
𝑪 𝟐 𝑺 𝐞𝐱𝐩
𝑪 𝟐 𝑺 𝐭𝐡 (a)
𝑬 𝒙 𝐭𝐡 (a) (MeV)
𝑱 𝝅 ①
0.036(1)
0.62(9)
< 0.015 2
61(5)
22.9
2.40
3.80
0.240
5/2 1 + ②
0.84(4)
<0.02 1
4(1) ③
2.31(3)
2.89(10)
0.32(1)
15(3)
18.6
0.77
1.38
1.907
1/2 1 −
(a) From WBP. ① ①
L=2 ③ ② ③
L=1 ②
L=1

50. Presently observed states
By an elimination method, 1.55 MeV state  5/2_2+.

51. Quenched N=14 shell gap Discussion-1: ⑧ ⑭ 17,19,21O ⑧ ⑭ 15,17,19C
M.Stanoiu et al., PRC78(2008) ⑧ ⑭
0 𝑝 3/2
0 𝑝 1/2
0 𝑑 5/2
1 𝑠 1/2
17,19,21O
Deformation ⑧ ⑭
0 𝑝 3/2
0 𝑝 1/2
0 𝑑 5/2
1 𝑠 1/2
15,17,19C
This work
An abnormal ground state spin ½+ in 15C.
22O-21N (N=14)
22O-20C (N=14)
I.Talmi, I.Unna, PR4(1960)469.
C.X.Yuan et al., Nucl. Phys. A 883 (2012) 25.
0 𝒑 𝟏/𝟐
0 𝒅 𝟓/𝟐
𝟏 𝒔 𝟏/𝟐
proton
neutron
𝑉 𝑝 1 2 𝑑 5 2 𝑝𝑛
𝑉 𝑝 1 2 𝑠 1 2 𝑝𝑛
N=14 shell gap evolution
Proton-neutron int.
Attractive neutron-neutron int. due to the many-body correlations.
2 𝑉 𝑝 1 2 𝑑 5 2 𝑝𝑛 − 𝑉 𝑝 1 2 𝑠 1 2 𝑝𝑛

52. Spectroscopy of lowest-lying states, 𝟐 𝟏 + in even C and
Discussion-2:
Spectroscopy of lowest-lying states,
𝟐 𝟏 + in even C and
𝟓/𝟐 𝟐 + and 𝟏/𝟐 𝟏 − in odd C,
in comparison to WBT(X), WBM(X) SM.
The effects of enlarged ℏ𝜔 model space by using NuShellX are small (large) for positive (negative) parity states.
WBM gives a deteriorated description of 5/
S.Kim
J.W.Hwang et al.,
PLB769(2017)503.
S.Kim
This work
Y.Satou et al., PLB660(2008)320.
The excitation energy is the energy measured from the lowest-lying state whose Jpi is the same as that for the experimentally known ground state of the relevant nucleus (not measured from the predicted ground state).
Shell-model interactions, WBT and WBM, are used in both NuShell and NuShellX.
Enlarged model space in terms of hbw has little effects on the location of positive parity states, while it has large effects for the negative parity states.
For odd carbon isotopes, we do not observe a good convergence (nor consistency) in the predicted positions for 1/2-.
This indicates the limitation of these interactions in describing cross-shell transitions of very neutron-rich nuclear species, caused either by an inadequate parameterization of the TMBE and/or limited model space in terms of hbw.
※ Excitation energy is from E( 3/2 1 + ) and E( 1/2 1 + ) for 17C and 19C, respectively.

53. Spectroscopy of lowest-lying states, 𝟐 𝟏 + in even C and
Discussion-3:
Spectroscopy of lowest-lying states,
𝟐 𝟏 + in even C and
𝟓/𝟐 𝟐 + and 𝟏/𝟐 𝟏 − in odd C,
in comparison to YSOX, CCEI SM.
YSOX does not solve the overprediction problem of , while CCEI does.
YSOX provides a good description of 5/ and 1/2 1 − .
CCEI works well for 5/ n
Core(2+)
Cross-shell states, the positions of which are, notoriously, not well predicted by former shell-model interactions, turned out to be described by YSOX adequately. This is likely to be due to (1) the successful fine tuning of its cross-shell part which is guided by VMU and (2) the incorporation of a larger hbw model space (up to 3hbw).
(2) Positive parity states are best described by CCEI;
while there are no predictions for negative parity states from CCEI. Present data set for negative parity states would provide a good testing ground for further developments of the CCEI and other theories.
(3) Overprediction of 2+ by YSOX indicates that the absence of core polarization effects involving p1/2 protons in C is not well handled by the calculation with this interaction.
[5/2_2+]
In a weak-coupling model, this state is formed by 2+ excited core plus valence neutron.
(2008, Satou) n
Core(0+)
※ Excitation energy is from E( 3/2 1 + ) and E( 1/2 1 + ) for 17C and 19C, respectively.

54. Summary Knockout reaction as a complement to 𝛽𝑛.?
Knockout reaction as a complement to 𝛽𝑛.
Parity is determined experimentally in KO.
Confirmation/finding of some new states.
𝟏/𝟐 − , 𝟑/𝟐 − , ( 𝟓/𝟐 𝟐 + ), 𝟗/𝟐 𝟏 + in 17C
𝟏/𝟐 − , 𝟓/𝟐 𝟏 + in 19C
quenched 𝑠 1/2 − 𝑑 5/2 shell gap in the N=13 isotone confimred.
New spectroscopy to test SM interactions.
YSOX describes cross shell states in C well.
YSOX overpredicts 𝟐 𝟏 + in 16,18,20C, but CCEI not.
YSOX and CCEI describe 𝟓/𝟐 𝟐 + in 17,19C well.
Light nuclear systems, as C isotopes, continues to pose challenges to our attempt to understand nuclear structures.
As far as the low-lying positive parity states are concerned, CCEI seems to be perfect, but it lacks predictions for negative parity states.
Present data on dipole transitions will provide a good testing ground of this theory.
YSOX works well in predicting energies of cross-shell states.
The over-binding of the ground state from the core polarization is not eliminated in the description of 2+ energies with YSOX.
YSOX, together with CCEI, provides a good description of supposedly core-excited 5/2_2+ states in 17,19C.

55. Narrow momentum distribution of valence neutrons supports the neutron halo structure of 11Li
C target
11Li + C → 9Li + X
0.79 GeV/nucleon 𝜎=
23±5 MeV/c
Es=0.185 MeV -> k ～ 20 MeV/c
Observed narrow component in the momentum distribution of valence neutrons provides a further support of the halo structure of 11Li.
T.Kobayashi et al., Phys. Rev. Lett. 60 (1988) 2599.

56. Electric dipole response in a break-up reaction of a Halo nucleus
11Be
Pb target
10Be γ
neutron
11Be + 208Pb → 10Be + n
Virtual photon number
208Pb
11Be
T.Aumann, Nucl. Phys. A 805 (2008) 198c.

57. Nuclear landscape Proton number Z Proton drip line Neutron drip line
112 Cn
114 Fl
116 Lv
(2012)
(2010)
Proton drip line
Less than 300 stable
113 Uut
115 Uup
117 Uus
118 Uuo ⋮
Isotone
Proton number Z
R-process path
protons
𝑍 𝐴 El ⋯
Neutron drip line
Isotope
Terra incognita
Known nuclei
Neutron drip-line (beyond this the nucleus becomes unstable against particle decay)
Proton drip-line
Also there is a limit in heavier region.
In this respect, it is worth mentioning that new elements, such as Copernicium, Flerovium, and Livermorium, have been officially recognized by IUPAC recently and the periodic table is being updated.
The number of stable nuclei (black boxes) is less than 300 (256).
The number of known nuclei (shaded boxes) is about 3000.
The number of nuclei predicted to exist is less than
Roughly, about half of the nuclei have been confirmed in the laboratory, but other half remain undiscovered. The chart tells us that there is a quite large discovery potential.
< 300 stable nuclei
~3000 known nuclei
<10,000 nuclei predicted to exist
Neutron number N

58. Challenges in radioactive beam physics
Limits of nuclear existence　
Exotic structures of nuclei away from stability
Nuclear properties relevant to astrophysical phenomena
Test of Standard Model/ fundamental conservation laws
Applications in medicine, electronics, condensed matter, industrial processes
R-process path
Neutron number N
Proton number Z
Nuclear landscape
Neutron drip line
Proton drip line
Challenges in physics involving nuclei represented in the chart are
To clarify the limits if existence (as for the neutron rich side, the drip-line is established only up to oxygen).
Exotic structures of nuclei away from stability, which may contain new physics of nuclear many-body systems.
To examine nuclear properties relevant to astrophysical phenomena is also an important issue. Here the estimated path for rapid neutron capture process is show. It is considered half of the elements heavier than iron were created by this process, which is believed to take place at the cite of the supernova explosion. But we see most of the r-process nuclei belong to unknown region, never created in the laboratory.
Testing standard model and fundamental conservation laws using various atoms is also important.
We could find a lot of applications in medicine (like 18F for PET imaging) , electronics, and so on.