Perspectives on nuclear reaction theory and …kouichi.hagino/talks/KEK2019.pdfPerspectives on...
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Perspectives on nuclear reaction theoryand superheavy elements
1. Nuclear Reactions: overview2. Heavy-ion fusion reactions3. Fusion for superheavy elements4. Summary
Kouichi HaginoTohoku University, Sendai, Japan
KEK, 2019.7.9
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Introduction: low-energy nuclear physics
behaviors of atomic nuclei as a quantum many-body systems
understanding based on strong interaction
static properties: nuclear structure
ground state properties(mass, size, shape,….)
excitations nuclear matter
dynamics: nuclear reactions
an interplay between these
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elastic scattering inel. scattering fusion
Quantum Many-body Dynamics (nuclear reactions)
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elastic scattering inel. scattering fusion
Quantum Many-body Dynamics (nuclear reactions)
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Coulomb barrier1. Coulomb interaction
long rangerepulsion
2. Nuclear interactionshort rangeattraction
Potential barrier(Coulomb barrier)
Coulomb barrierP
Tr
the barrier height → defines the energy scale of a system
Fusion reactions at energies around the Coulomb barrier
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Niels Bohr (1936)
Neutron capture of nuclei → compound nucleus
Wikipedia
N. Bohr, Nature 137 (‘36) 351
cf. Experiment of Enrico Fermi (1935) many very narrow (=long life-time) resonances (width ~ eV)
Fusion reactions: compound nucleus formation
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Niels Bohr (1936)
Neutron capture of nuclei → compound nucleus
Wikipedia
N. Bohr, Nature 137 (‘36) 351
Fusion reactions: compound nucleus formation
PT P+T
compound nucleus
forming a compound nucleus with heavy-ion reactions = H.I. fusion
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cf. Bohr ‘36
PT P+T
Fusion reactions: compound nucleus formation
compound nucleus
energy production in stars (Bethe ‘39)
nucleosynthesis superheavy elements
Fusion and fission: large amplitude motions of quantum many-body systems with strong interaction
microscopic understanding: an ultimate goal of nuclear physics
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Reaction dynamicsstrong interplay between reaction and structure
cf. high E reactions: much simpler reaction mechanisms
Low-energy heavy-ion fusion reactions and quantum tunneling
cf. ・rich intrinsic motions Many-particle tunneling
- several surface vibrations
- several nuclear shapes
several modes and adiabaticities
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Reaction dynamicsstrong interplay between reaction and structure
cf. high E reactions: much simpler reaction mechanisms
cf. ・rich intrinsic motions Many-particle tunneling
- several surface vibrations
- several nuclear shapes
・E: variable cf. α decays: fixed energy“environment” can be changed relatively freely
- several types of nucleon transfers
H.I. fusion reaction = an ideal playground to study quantum tunneling with many degrees of freedom
Low-energy heavy-ion fusion reactions and quantum tunneling
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potential model: inert nuclei (no structure)Discovery of large sub-barrier enhancement of σfus (~80’s)
potential model
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deformation of 154Sm
154Sm : a typical deformed nucleus 154Sm
K. H. and N. Takigawa, Prog. Theo. Phys.128 (‘12)1061.
Discovery of large sub-barrier enhancement of σfus (~80’s)
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154Sm 16O
θ
154SmEffects of nuclear deformation
154Sm : a typical deformed nucleus
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154SmEffects of nuclear deformation
154Sm : a typical deformed nucleus
154Sm 16O
θ
Fusion: strong interplay betweennuclear structure and reaction
deformation
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enhancement of fusion cross sections: a general phenomenon
strong correlation with nuclear spectrum→ coupling assisted
tunneling
potential model
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Coupled-channels method: a quantal scattering theory with excitations
many-body problem
still very challenging
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TDHF simulation
ab-initio, but no tunneling
TDHF = Time Dependent Hartree-Fock(a single Slater determinant)
S. Ebata, T. Nakatsukasa, JPC Conf. Proc. 6 (‘15) 020056
C. Simenel, EPJA48 (’12) 152
16O + 208Pb
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coupling
0+ 0+
0+ 0+
2+ 0+
Coupled-channels method: a quantal scattering theory with excitations
many-body problem
still very challenging
two-body problem, but with excitations(coupled-channels approach)
scattering theory with excitations
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0+ 0+
0+ 0+
2+ 0+
Coupled-channels method:a quantal scattering theory with excitations
dynamics of excitations/de-excitations during reaction
coupling
Non-perturbative (full order) Non-adiabatic (excitation energy)
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Coupled-channels method:a quantal scattering theory with excitations
dynamics of excitations/de-excitations during reaction Non-perturbative (full order) Non-adiabatic (excitation energy)
in the past, the linear coupling approximation in a Hamiltonian :
full order treatment
K.H., N. Rowley, and A.T. Kruppa,Comp. Phys. Comm. 123(‘99) 143.
a standard method
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modellings of coupled-channels calculations
0+
2+
0+,2+,4+
0
ε
2ε
harmonic oscillations
• K.H., N. Rowley, A.T. Kruppa, CPC123 (‘99) 143• M. Zamrun, K.H., S. Mitsuoka, H. Ikezoe, PRC77 (’08) 034604• T. Ichikawa, K.H., A. Iwamoto, PRL103 (‘09) 202701• S. Yusa, K.H., and N. Rowley, PRC88 (‘13) 044620• J.M. Yao and K.H., PRC94 (‘16) 11303(R) etc.
review:K. Hagino and N. Takigawa, Prog. Theo. Phys.128 (‘12)1061.
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0+
2+
0+,2+,4+
0
ε
2ε
simple harmonic oscillator
Coupled-channels + microscopic nuclear structure
calculations(GCM, Shell Model, IBM…..)
relativistic MF + GCM
58Ni
anharmonicityin phonon spectra
Further development: semi-microscopic modelling K.H. and J.M. Yao, PRC91(‘15) 064606
Mean-field
quantumfluctuation
deformation
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0+
3-
(3-)2
2+
2+ x 3-
Relativistic Mean-Field + Quantum fluctuation + coupled-channels
J.M. Yao and K.H.,PRC94 (‘16) 11303(R)
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From phenomenological approach to microscopic approach
C.C. with collective model
C.C. with inputs from microscopic nuclear structure calculations
C.C. with inputs based on TDHF
TDHF simulations
ab initio, but no tunneling
Macroscopic (phenomenological)
Microscopic TDHF = Time Dependent Hartree-Fock
S. Ebata, T. Nakatsukasa, JPC Conf. Proc. 6 (‘15)
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“Beyond mean-field” approximations Time-dependent GCM?
From phenomenological approach to microscopic approach
TDHF simulations ab initio, but no tunneling
C. Simenel, EPJA48 (’12) 152
16O + 208Pb
cf. Stochastic mean-field methodB. Yilmaz et al., PRC90 (‘14) 054617
dynamics with a superposition of many “TDHF trajectories (Slater determinants)”
an open problemK.H., N. Hasegawa, and Y. Tanimura, a work in progress
a single Slater determinant (SD) to multi-SD
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Yuri Oganessiana prediction of island of stability(Swiatecki et al., 1966)
neutron number
prot
on n
umbe
r
nuclei existed in nature
aroundZ=114N=184
Future perspectives: fusion for superheavy elements
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the element 113: Nh
November, 2016
Fusion reactions for SHE
20983Bi70
30Zn 279113Nh*
Heavy-ion fusion reaction
Wikipedia
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112113114115116117118119
165 170 175 180 185
the island of stability?
120Superheavy elements synthesized so far
Future directions of SHE
Towards the island of stability
Towards Z=119 and 120 isotopes
neutron-rich beams: indispensable → reaction dynamics?
Towards Z=119 and 120 isotopesHot fusion reactions with 48Ca, 50
22Ti, 5123V, 54
24Cr etc. Towards the island of stability
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Z1*Z2 = 2000
Z1*Z2 = 1296
fusion hindrance
C.-C. Sahm et al., Z. Phys. A319(‘84)113
fusion hindrance
N
Fusion reactions in the SHE region (ZP*ZT > 1600~1800)
superheavy nuclei
syntheses with heavy-ion fusion reactions
theoretical issues:understanding the reactiondynamics
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Z1*Z2 = 2000
Z1*Z2 = 1296
fusion hindrance
C.-C. Sahm et al., Z. Phys. A319(‘84)113
fusion hindrance
N
Fusion reactions in the SHE region (ZP*ZT > 1600~1800)
modern interpretation of hindrance
quasi-fissioncompoundnucleus
strong Coulomb repulsion→re-separation before the
compound nucleus
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Fusion reactions in the SHE region (ZP*ZT > 1600~1800)
modern interpretation of hindrance
quasi-fissioncompoundnucleus
strong Coulomb repulsion→re-separation before the
compound nucleus
→ large theoretical uncertaintiesSHE formation: a very rare event
theoretical challenge:to reduce theoretical uncertaintitiesand make a reliable prediction
No data for PCNData: only for PER
CN=compound nucleusER = evaporation residues
evaporationresidues
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nuclear spectrum
E*
These states: are excited in a complicated way.
nuclear intrinsic d.o.f. : act as environment
“intrinsic environment”
Nuclear friction and heavy-ion fusion reactions
→ friction
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fusion re-separation
thermal diffusionLangevin approach(Brownian motion)
Langevin approach
(deformation)
V(ε
)
heat-up
Multi-dimensional space・internuclear separation・deformation ・mass asymmetry of the two fragments
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K.H., PRC98 (‘18) 014607
sssd sinj
Vfiss(s)
capture barrier:
Analysis with an extended fusion-by-diffusion approach
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New hybrid model: TDHF + Langevin approachK. Sekizawa and K.H., PRC99 (2019) 051602(R)
a special role of 48Ca?
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fusion re-separation
thermal diffusionLangevin approach
(deformation)
V(ε
)
thermali-zation
how to thermalize?
Quantum friction theory
c.f. tunneling with quantumfriction
M. Tokieda and K.H., PRC95 (‘17) 054604
non-Markov effect? quantum correction for
diffusion over the barrier?
issues from the theoretical physics point of view
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Quantum friction
a quantization: Kanai model E. Kanai, PTP 3 (1948) 440
time-dep. wave packet approach
∆E=5 MeV
M. Tokieda and K.H., PRC95 (‘17) 054604
classical eq. of motion
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fusion
Fusion reactions and non-equilibrium statistical mechanics:Langevin dynamics under a temperature gradient
← coordinate dependenttemperature
a math model for molecular motors
松尾美希、物性研究 73 (‘99) 557
Superheavy elements
SHE formation reactions as a general problem of non-eq. stat. mechanics?
temperature gradient→ one-way dynamics
V(ε
)
re-separation
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112113114
165 170 175 180
neutron-rich beams: indispensable→reaction dynamics?
Fusion of unstable nuclei
K.-S. Choi, K. Hagino et al., Phys. Lett. B780 (’18) 455
the island of stability
good understandings of the structure of neutron-rich nuclei is also important
need further improvements
K.H. and H. Sagawa, PRC72(‘05)044321
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reactions of neutron-rich nuclei
fusion transfer
development of microscopicnuclear reaction theory
nuclear ractions in neutron stars
fusion of neutron-rich nuclei 24O + 24O, 28Ne + 28Ne etc.
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Physics of SHE with n-rich nuclei as important ingredient
reactions of neutron-rich nuclei
fusion transfer
development of microscopicnuclear reaction theory
nuclear ractions in neutron stars
structure of neutron-richnuclei
nucleon correlations collective motions fission
from few-body to many-body
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physics chemistry astronomySHE: quantum many-body systems with a strong Coulomb field
origin of elements r-process kilonova
interdisciplinary SHE science
reaction dynamics quantum friction neutron-rich nuclei
Summary
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full order treatment
K.H., N. Rowley, and A.T. Kruppa,Comp. Phys. Comm. 123(‘99) 143.
diagonalize