高等原子核理论
Advanced Nuclear Theory
北京大学物理学院 技术物理系 • 裴俊琛
Junchen Pei, School of Physics, Peking University
2014.9, Beijing
Contents
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Background and developments
Earlier Nuclear models
Ab inito and Shell Model
Density Functional Theory
Nuclear forces
Nuclear superfluidity
Symmetries and collective motion
DFT extensions
Reaction Theory
Advanced Nuclear Theory----J.C. Pei
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Challenges in nuclear physics
RNB facilities offer unprecedented opportunities to access unstable nuclei
Progress In Computing Nuclei and Cold Atoms
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RNB facilities around the world
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FRIB
FAIR
RIBF
SPAIRL-II
Argonne, HRIBF, HIRFL-CSR,
Why RNB?
Advanced Nuclear Theory----J.C. Pei
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How to study nuclear physics
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Reaction-observation-nuclear models
Different reaction mechanism
Observations: decays, fragments, emissions  structures
Models: many-body Hamilton and nuclear forces
Advanced Nuclear Theory----J.C. Pei
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Background
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Nuclear theory at different resolutions/precision, with
different degrees of freedom
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Effective nuclear forces associated nuclear many-body
problems
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Multi-Physics overlaps and observables in different aspects
Advanced Nuclear Theory----J.C. Pei
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本科生—研究生
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本科：书本上基础知识学习， 主要是为了考试
研究生：主要目的是研究，学习为了研究和解决问题，
创造新知识，职业训练（独立科研的能力）
导师---学生
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导师： 提供平台， 建议方向，教授方法， 解决难题
学生： 实现物理想法，团队合作，自我提升
导师---学生之间interface： 沟通，信任
不愤不启，不悱不发 《论语》
魔鬼在细节中
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不要Assume你的结果：结果没有好坏， unexpected往往
才是有价值的！
时间在点滴之中
物理 <------格物
理论与实验
观测量直接对比
Pesudo间接对比
实验与预言
不同模型
不同方法
对比
创新
变化
系统性对比发现变化
归纳已知外推未知
创新引起变化
关于物理的思考---裴俊琛 2013 PKU
新的理论，思想
新的Hamiltonian
新的观测量
新的模型方法
新的实验和理论精度
新的参数
核物理的前景
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物质结构不同的层次划分：
宇观，宏观，分子，原子，核，核子，夸克
不同层次的都有自身特点和问题并且不可替代
对交叉的物理问题有贡献：量子多体，核天体，QCD, 甚至生物，金融等
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超级计算机的发展：
petaflop（天河1号2.6-天河2号38）—exaflop
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FRIB (Facility for Rare Isotope Beams)
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应用：能源，信息，医疗……
原子核理论的发展与前沿
The Developments and Frontiers of
Theoretical Nuclear Physics
北京大学物理学院 • 裴俊琛
Junchen Pei, School of Physics, Peking University
2013.9
Outline
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Nuclear structure: macroscopic and microscopic perspectives
Modern nuclear theory and supercomputing
Nuclear theory and multi-disciplinary subjects
Summary and outlook
Advanced Nuclear Theory----J.C. Pei
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Nuclear liquid drop model and fission
Nuclear liquid drop model of Fission: the competition between Coulomb and
surface tension (1939), By Bohr and Wheeler
Fission calculations on the first computer Eniac (1946), By Frankel (1947)
𝐸 = 𝐸𝑣𝑜𝑙𝑢𝑚𝑒 + 𝐸𝑠𝑢𝑟𝑓𝑎𝑐𝑒 + 𝐸𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑦 + 𝐸𝐶𝑜𝑢𝑙𝑜𝑚𝑏
Problems:
Can not explain the asymmetric fission
Z>104 nuclei is unstable against spontaneous fission
Magic numbers are missed (N=2, 8, 20, 28, 50, 82, 126, …..)
Advanced Nuclear Theory----J.C. Pei
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Explanation of liquid drop model
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Fermi Gas model (non-interacting Fermions)
𝜑𝑘 ∝ sin(𝑘𝑥 x) sin(𝑘𝑦 y) sin(𝑘𝑧 z)
a
Boundary condition (quantization)
𝜋
𝑘𝑥(𝑦,𝑧) = 𝑎 𝑛𝑥 (𝑛𝑦 , 𝑛𝑧 ),
Eigen energy： 𝜀 =
𝑛𝑥 , 𝑛𝑦 , 𝑛𝑧 =1,2,3….
ℎ2
2 +n 2 +n 2 )
(n
𝑥
𝑦
𝑧
2
8𝑚𝑎
Can explain the liquid drop model’s volume energy, surface energy, symmetry
energy (due to different proton neutron numbers)
Problem: magic numbers are missed
Solution: we need nuclear interactions beyond Pauli principle
Advanced Nuclear Theory----J.C. Pei
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Magic numbers and shell effects
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Magic numbers: Shell effects in finite Fermi systems
Strong spin-orbit coupling in nuclei
Mayer and Jenson (1949)
3s, 2d, 1g
2p, 1f
2s,1d
1p
Magic numbers in atoms: 2, 10, 18, 32, 54, 86
1s
N=4 [70]
N=3 [40]
N=2 [20]
+𝑳∙𝑺
N=1[8]
N=0 [2]
Magic numbers in nuclei: 2, 8, 20, 28, 50, 82…
General shell effects in quantum dots, droplets, alkali clusters, metal nanowires …
Advanced Nuclear Theory----J.C. Pei
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Macroscopic plus microscopic
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Oscillations in level density (quantum effects), 1967
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E = Eliquid-drop+ Eshell-correction
classical
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quantum
Very successfully for describe nuclear bulk properties: mass, deformation,
second minimum
Advanced Nuclear Theory----J.C. Pei
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Nuclear many-body Hamiltonian
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Generally:
Problem: Can not be solved exactly for N>3
Solution: solving the many-body problem with a finite model space
Solving the equation with different precision with different many-body
techniques: ab inito, configuration interaction, density functional theory
Advanced Nuclear Theory----J.C. Pei
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Solving the Many-body problem
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Start from the independent-particles
(A Hilbert space)
A slater determinant
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Assume correlated many-body wavefunction can be expanded
in the Fock space
Fock space is the combination of various Hillbert spaces with different
quasiparticles
Diagonalization:
Advanced Nuclear Theory----J.C. Pei
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Modern Nuclear Forces
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Phenomenogical terms: Argonne v18
Meson exchange theory: CD-Bonn
chiral perturbative theory: N3LO, three-body forces
Lattice QCD calculations: residual interactions of quark clusters
Effective nuclear forces:
Renormalization: G-matrix, Vlow-k
Advanced Nuclear Theory----J.C. Pei
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Nuclear physics at multi-resolutions
Hadron physics
resolution
Ab inito
CI
Nuclear physics
DFT
Collective models
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Overlaps are important
Advanced Nuclear Theory----J.C. Pei
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Recent developments in nuclear theory
Drip-line of O isotopes
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Ab inito model study of 3-body forces
E
Conclusion: 3-body force is important
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Ab inito model study of nuclear reactions
NCSM+RGM: provide important benchmark for
reactions in astrophysics and NIF
Advanced Nuclear Theory----J.C. Pei
Exceptional long life time of C14
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Recent developments in nuclear theory
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UNEDF project in US
Universial Nuclear Energy Density Functional
involve 19 institutions and 50 researchers
Computer science, applied math, nuclear theorists
Advanced Nuclear Theory----J.C. Pei
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Challenges and opportunities
RIB facilities offer unprecedented opportunities to access unstable nuclei
Advanced Nuclear Theory----J.C. Pei
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Latest nuclear landscape
From J. Erler et al., Nature, 486, 509(2012)
Advanced Nuclear Theory----J.C. Pei
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Drip-line nuclei
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Continuum coupling effects
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Open quantum systems
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Halo structures
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Halos (1990s)
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Deformed Halo (Ne38)?
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Shell structures at drip-lines
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Advanced Nuclear Theory----J.C. Pei
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New collective motion mode
Collective oscillation between core and
the halo/skin
Low energy E1 transition (pygmy resonances)
Advanced Nuclear Theory----J.C. Pei
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Treatment of Continuum
HFB includes generalized quasi-particle correlations; while BCS is a special
quasiparticle transformation only on conjugate states.
HFB G.S.:
BCS G.S.:
Deep bound states in BCS become quasiparticle resonances in
HFB theory due to continuum coupling.
HFB is superior to BCS for describing weakly-bound systems
where continuum coupling becomes essential
Box solution: bound states, continuum and embedded
resonances are treated on an equal footing; L2 discretization
leads to a very large configuration space(expensive)
Advanced Nuclear Theory----J.C. Pei
JP et al. PRC, 2011
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Answers to nuclear astrophysics
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Advanced Nuclear Theory----J.C. Pei
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Neutron stars
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Related to nuclear equation of state
A neutron star of 2.0 sun mass (2010)
Pasta
Advanced Nuclear Theory----J.C. Pei
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Nuclear mass limits
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How to chose the target, bombard, and the collision energy
Hot fusion vs cold fusion?
Advanced Nuclear Theory----J.C. Pei
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Nuclear spin limits
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The highest spin in the universe : 65hbar
Advanced Nuclear Theory----J.C. Pei
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Nuclear Temperature limits
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Fission and neutron evaporation competition at high
temperatures
It becomes symmetric fission at high temperatures
Advanced Nuclear Theory----J.C. Pei
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Radioactive Beams Facilities
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Great opportunities in 5 years
Advanced Nuclear Theory----J.C. Pei
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Supercomputing
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Three legs of nuclear physics: experiments, theory, supercomputing
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Without supercomputing, ab inito, large scale DFT, continuum treatment
are impossible
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New architures: multi-core+GPU (why: moving data is expensive)
From Tianhe-1 to Tianhe-2, 20 times faster
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Advanced Nuclear Theory----J.C. Pei
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Novel DFT infrastructure
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Multi-resolution ADaptive Numerical Scientific Simulation
 CS infrastructure:
Task-oriented: MPI, Global arrays, multi-threaded, futures (asynchronous computation),
loadbalance
API
1. do A
2. do B if A
3. do C
4. do D if A
Task dependencies:
managed by Futures
WorldTaskQueue
ThreadPool
Main
MPI
1.
3.
2.
4.
Advanced Nuclear Theory----J.C. Pei
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Dialogue with other physicists
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Talk with condensed matter, cold atoms on many-body problems,
superfluidity
Talk to astrophysics on the evolution of universe, neutron stars
Talk to high energy physics on testing standard model, AdS/CFT
Advanced Nuclear Theory----J.C. Pei
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Summary and outlook
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The Nucleus is such a unique finite quantum system,
presenting intriguing physics
RIB facilities provide great opportunities and challenges for
nuclear theory
The development of modern nuclear theory is closed related
to the capability of supercomputers
Big collaborations, multi-disciplinary dialogues are very useful
How about the future?
Thanks for your attention!
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