2nd International Symposium on

Clustering as a window on the hierarchicalstructure of quantum systems(CLUSHIQ2022, EMMI workshop)

Oct.31-Nov.3, 2022, @Sendai Int. Center

Welcome address & Introduction
Takashi Nakamura
Tokyo Institute of Technology“Clustering as a window on the hierarchical structure of quantum matter”(2018-2022)
Grant-in-Aid for Science Research on Innovative Areas（新学術領域 MEXT Kakenhi 18H05400)

Clusters and Semi-Hierarchy
Conventional HierarchyO Big Gap between
Hierarchies Strongly Bound Simple constituents:
Nucleus=“nucleonic” system

MoleculeAtomeSemi-Hierarchy
COeeee ee

Feshbach Molecule12Ce e eeee

Rydberg AtomNucleus pnnpppnp

n n pnHadron qqeeNqq qαnn

Hadronicα
Molecule α cluster Halo nucleusqqqQuark q q qqq qqαK Smaller Gap between Hierarchies Weakly Bound (Unbound) Mixed constituents:
Halo Nucleus＝”nucleonic”+”dineutron” systemqqq

Penta quark

Heavy q q
QuarkqBaryonSemi-Hierarchy:
Key Aspects to understand thehierarchical structure of matter

Bridging Hierarchies“Clustering as a window on the hierarchical structure of quantum matter”(2018-2022)
Grant-in-Aid for Science Research on Innovative Areas（新学術領域 MEXT Kakenhi 18H05400)
D01 Emergence mechanism of hierarchical structure ofmatter studied by ab-initio calculations (PI: Emiko Hiyama)

C02 Universal physics of quantum
matter at the change of the hierarchy
and the state (PI: Munekazu Horikoshi)
A01 Dynamics to bridge quark and hadron hierarchies
Ultra-cold Atoms(PI: Kenta Shigaki) CERN LHC-ALICE
C01 Ultracold atom study of exoticMolecules
Quark Gluon Plasma
phenomena bridging different
1st Principle
hierarchies(PI: Yoshiro Takahashi)Calculations
Exotic Nuclei
B02 Exotic nuclei for investigating
Exotic Hadrons
hierarchical structure of matter(PI. Takashi Nakamura)
Hyper Nuclei A02 Elucidation of hierarchical structure between quark and hadron
RIKEN-RIBF
phases by means of quark clusters (PI: Hiroaki Ohnishi)
J-PARC, SPring8
B01 Clusters of strange hadrons forinvestigating hierarchical structure ofmatter (PI: Hirokazu Tamura) J-PARC

Semi-Hierarchy: Clustering and Hierarchy of MatterHoyle StateΛ(1405)NExΛ ud sHadron

αα α

3αEx
Feshbach Molecule

1/ka
0+Ex

Ex
Nucleus
12C(gs) Threshold: Clustering near Threshold  Semi-Hierarchy Degree of Freedom：Neutralization of Charge, Spin(S), Isospin(T)Molecule

Closed Quantum System�
N+𝐾𝐾

α cluster0Electron Spin0 S, T0Color Charge

HadronMolecule

ExOpen Quantum System

ExAtomHadron

Quark

Closed or Open?
Closed system

Open system

Unbound States (Continuum)

E=0
Bound States

Bound States
ClassicalQuantum

ClassicalQuantum• Normal particles: Bound and Isolated system Closed quantum system• Particles at the edge: Highly excited states  (Near) Open quantum system
Boundary of Open-Closed regions:  Exotic phenomena?

6Key Questions• What is the Role of “Threshold” in the formation of clusters andsemi-hierarchy?
• How the cluster in a specific hierarchy is mixed with more
fundamental hierarchy?
• Can we understand the cluster from more fundamental hierarchy andinteractions?
• What is the fundamental law behind the seemingly common
phenomena among different hierarchies?
• What is common and what is different inphenomena/particles/interactions in a wide range of hierarchies?

What is the Role of “Threshold” in the formation ofclusters and semi-hierarchy?
QuarkExΛ(1405)
N HadronicMolecule

�N+𝐾𝐾ExΛ u Hadrond s0Color Charge0Color Charge

Quark

deuteron :Exp+n

deuteron
nucleus or hadron?

a nucleus (two-nucleon system, cluster)ora hadron (6q system)?

7

8

Deuteron in the text book

Nuclear Structure, Bohr & Mottelson p269, Vol.1
B. Mottelson

deuteron

H2 Molecule

1926-2022
Nobel prize 1975

 Size ofthe repulsive coreReplusivecore
Replusivecore

Narrow

Widedeep𝐵𝐵~ 𝑉𝑉

Binding
Energyshallow

𝐵𝐵 = 2.22MeV ~0 ≪ 𝑉𝑉
Binding
Energy𝐸𝐸 = −𝐵𝐵~0 ∶Close to pn threshold
𝑇𝑇~ 𝑉𝑉

Kinetic energy

Potential energy

9deuteron :a nucleus (two-nucleon system, cluster) ora hadron (6q system)?

S. Weinberg, PR 137, 672 (1965)
T. Hyodo, IJMPA 28, 1330045 (2013)

Compositeness : Z
deuteron (hadron): elementary

Deuteron (nucleus): composite (cluster)PZ∼1|𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠⟩ =2 1 − 𝑍𝑍
𝑎𝑎 =𝑅𝑅 + ℴ 𝑚𝑚𝜋𝜋−12 − 𝑍𝑍
𝑍𝑍𝑟𝑟𝑒𝑒 = −𝑅𝑅 + ℴ 𝑚𝑚𝜋𝜋−11 − 𝑍𝑍

S-wave scattering length
Effective range

NZ∼0𝑍𝑍|𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒⟩ + 1 − 𝑍𝑍|𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐⟩

Deuteron: Weakly bound:(B=2.22 MeV, 𝑎𝑎 = 5.42fm, 𝑟𝑟𝑒𝑒 = 1.74fm)

Z∼0

Cluster formation (2-body)is dictated by scattering lengthor equivalently closeness to threshold

Note: Weak bound limit:ℏBinding energy
𝐵𝐵 =𝑚𝑚𝑎𝑎2𝑅𝑅2 =ℏ2𝜇𝜇𝐵𝐵= 4.31 𝑓𝑓𝑓𝑓

𝑎𝑎~𝑅𝑅

10Threshold effect in two-body system:  Universality
S-wave 2-body system:
Atom/Molecule (a pair of Fermions)𝑎𝑎𝑠𝑠 ~𝜆𝜆𝜆𝜆 = 𝜆𝜆/2𝜋𝜋Slide: Y. Ohashi
School Mar.2019

S-wave 1n-halo nucleus
11Be

10Be+n1n halo nucleus

n10Be

Sn=0.502 MeV≪ 8MeV11Beℏ𝐸𝐸 = −𝑆𝑆𝑛𝑛 = −2𝜇𝜇𝜆𝜆2𝑒𝑒 −𝑟𝑟/𝜆𝜆𝜆𝜆 = 𝑎𝑎𝑠𝑠𝜓𝜓 𝑟𝑟 = 𝐶𝐶𝑟𝑟
Sn=0.502 MeV  𝑎𝑎𝑠𝑠 = 6.77 fm
c.f. exp. 𝑟𝑟 2 = 5.77(16) fm

11

Two-body cluster  Three-body Cluster?
Hadron
9Li

11Li
9Li+n+nnS2n=0.37MeV

Hoyle State: 3 α cluster
0 S, TnEx
Hoyle State

11Liα α cluster
α α3αExNucleus
12C(gs)3α: ∼66%
Ab-initio calculations: 3α-cluster
state without requiring thethreshold effectT.Otsuka et al., Nature com. 2234 (2022).

Any universality for three-body systems over a wide range of hierarchies?

12Universality in three-body cluster?

Efimov States
P.Naidon, S. Endo, Rep. Prog. Phys. 80, 056001

2n halo ?

2n Halo Nuclei: Efimov States?
Likely Efimov Ground State,
But no Efimov resonances
How about unbound resonance?

13

Excitation Energy

More “Thresholds”

IKEDA Diagram

Near Threshold Clustering
Mass Number (4A)

Feng-Kun Kuo et al.,Rev. Mod. Phys. 90, 015004 (2018)

 N-body Cluster can be understood in terms of “Threshold”?
 Can we understand Cluster in the continuum (Resonance) in terms of “Threshold”?
 Effect of Mixture of other configurations: How is it relevant to “Threshold”?
 Relation of Cluster Formation to the many-body effect (Pauli Principle), density, and interactions?

Interactions between cluster particles
ProtonNeutrondeuteron Interactions:Strong Inside, Weak Outsideαα Can we build and understand thecluster-cluster interaction from
more fundamental interactions?

α12C(0+ )2Hoyle State

Σ+Proton

Elastic Scattering of hyperon on proton at J-PARC

T. Nanamura et al., PTEP 2022, 093D01 (2022).
K. Miwa et al., PRC104, 045204 (2021)., K. Miwa et al., PRL128, 072501 (2022).

14

15

3-body force

Site-occupancy resolved Spectra in Optical LatticeπN∆

π
3N force effectNN

Y.Nakamura, Y.Takahashi et al., PRA99, 033609 (2019).
Fujita-Miyazawa type three-body force may
explain three-atomic states in optical lattice.

Fujita Miyazawa-type 3N force
Prog.Theor.Phys. 17, 360 (1957).

d+p elastic scattering

K. Sekiguchi et al., PRC65, 034003 (2002).
c.f.
3He+p: A.Watanabe et al. PRC103, 044001(2021).
Chiral Effective Field Theory: E.Epelbaum, EPJ A 92, 56 (2020).

16

dineutron : universality in fermion pair?

Pairing correlation in Nucleinn

2n in Free space: S-wave Scattering Length: 𝑎𝑎𝑠𝑠 = −18.9 4 𝑓𝑓𝑓𝑓

A.Gårdestig, J.Phys. G, Nucl. Part Phys. 36, 053001 (2009).

n𝑎𝑎𝑠𝑠 ≫ 𝑟𝑟𝑒𝑒 = 2.80 11 𝑓𝑓𝑓𝑓
PRC36, 691 (1987)

n nn

BCS-like Pairing Correlation(long range, weak coupling)
Known for (normal) nuclei for 60 years

Bohr, Mottelson, Pines, Phys.Rev.110, 936(1958).

A.B.Migdal, Sov.J.Nucl.Phys.238(1973).
 Strong-correlated dineutron(quasi-bound two neutrons)

Dineutron correlation（short-range, strong coupling)
Not yet established(A Few examples suggested in Halo Nuclei)Analogy in atomic systems
Cooper pairs (BCS)

Weak

Crossover

Ultra-cold atom experiments
Bose Gas (BEC)

StrongPairing Interaction (𝑘𝑘𝐹𝐹 𝑎𝑎𝑠𝑠 )−1

Slide: Y. Ohashi
School Mar.2019

Density dependence of nn correlation
Mean field theory for nuclear matter M.Matsuo Phys. Rev. C73, 044309 (2006).
𝜉𝜉𝑟𝑟𝑟𝑟𝑟𝑟 =𝑟𝑟𝑛𝑛𝑛𝑛 2 = � 𝑑𝑑𝑟𝑟⃗ 𝑟𝑟 2 |𝜓𝜓𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (𝑟𝑟)|2

rms distance of the cooper pairnDineutron region𝟏𝟏𝟏𝟏−𝟒𝟒 <𝝆𝝆< 𝟎𝟎. 𝟏𝟏𝝆𝝆𝟎𝟎

mean distancerms Cooper-pair distancennnnn 𝑑𝑑𝑖𝑖𝑖𝑖nn

𝑟𝑟𝑛𝑛𝑛𝑛nnnnnnn

Neutron matter
Dineutron in 11Li (2n-halo nucleus)
TN et al., PRL96, 252502(2006).
Y. Kubota et al., PRL125, 252501 (2020)“dineutron localized near the surface of the core”
Dineutron in 19B (2n-halo nucleus)
K.J. Cook, TN et al., PRL 124, 212503 (2020).
Dineutron in 6He (2n-halo nucleus)
Y.L. Sun, TN et al., PLB814, 136072 (2021).

20

Further Questions on dineutron• Dineutron: Crossover or BEC? (Most likely crossover, M. Matsuo PRC 2006)• Multi-Dineutron?
 4n (tetra-neutron) observed as a resonance in the RIKEN experiment.
M.Duer et al., Nature 606, 678 (2022). 2n-2n?

 28O=24O+2n+2n? Y.Kondo et al.
 Our group will investigate 6n states in 10He

• What is common and what is different between dineutron and atomic
fermion pair?
• What is common and what is different between dineutron and diquark?

Clusters and Semi-Hierarchy

Conventional Hierarchy
O Big Gap betweenHierarchies Strongly Bound Simple constituents:
Nucleus=“nucleonic” system

Molecule
Atome

Semi-Hierarchy
COeeee ee

Feshbach Molecule

12Ce e eeee

Rydberg AtomNucleus pnnpppnp

n n pnHadron qqeeNqq qαnn

Hadronicαα
clusterMolecule
Halo nucleusqqq
Quark q q qqq qqαK

 Smaller Gap between Hierarchies Weakly Bound (Unbound) Mixed constituents:
Halo Nucleus＝”nucleonic”+”dineutron” systemqqqPenta quark

Heavy q q
QuarkqBaryonSemi-Hierarchy:
Key Aspects to understand thehierarchical structure of matter

What is common and what is different?

22

Key Questions• What is the Role of “Threshold” in the formation of clusters andsemi-hierarchy?
• How the cluster in a specific hierarchy is mixed with more
fundamental hierarchy?
• Can we understand the cluster from more fundamental hierarchy andinteractions?
• What is the fundamental law behind the seemingly common
phenomena among different hierarchies?
• What is common and what is different inphenomena/particles/interactions in a wide range of hierarchies?

23

Thank you very much for the support“Clustering as a window on the hierarchical structure of quantum matter”(2018-2022)
Grant-in-Aid for Science Research on Innovative Areas（新学術領域 MEXT Kakenhi 18H05400)

Best three poster presenters will be awarded ANPhA prizes

Enjoy CLUSHIQ2022 Symposium !
All the sciences, and not just the sciences but all the efforts ofintellectual kinds, are an endeavor to see the connections of thehierarchies. Richard P. Feynman, The Character of Physical Law

Kaisen-don (Sashimi-Rice-bowl)

Gyutan (Beaf-tongue)

Statue of Lord DATE-MASAMUNE

Zuiganji-temple in Matsushima

25Backup

Semi-Hierarchy in neutron-rich limit
A=const. N/ZLarger
HadronExN/Z≫ ∞0S

0 S, T

Hadronα clusterE dineutron cluster
Neutron Halo

Hoyle State

N/Z>2n11Li(3p+8n)

EEx
Nucleus

12C(gs)

N/Z~1

Nucleus11B(5p+6n)

Closed Quantum System3αn9Li+2nαα αOpen Quantum System

ExLargerNeutron Matter27

6q state(discrete)p-n continuum

Overlap with 6q state (discrete) Overlap with pn continuum

Itlic texts byT.Nakamura

Slide by T. Hyodo

28

Slide by T. Hyodo

Coulomb Breakup of 19B @RIKEN RIBF
Two-neutron halo nucleus
19B

β∼0.6

Electric Dipole Excitation
19B*

29

K.J. Cook, TN et al., PRL 124, 212503 (2020).
17B

nγ(virtual photon)nHigh-Z Target(Pb)Strong Electric Dipole Transitions (Soft E1 Excitation)

𝑃𝑃(17B)
𝑃𝑃(𝑛𝑛)
𝑃𝑃(𝑛𝑛)

B(E1) = 1.64 ± 0.06 (stat) ± 0.12 (sys) e2fm2
Soft E1 Excitation: Signature of Halo!

n17B
19Br
θ12n

dineutron