advanced nuclear physicskouichi.hagino/lectures/...advanced nuclear physics nuclear theory group,...
TRANSCRIPT
![Page 1: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/1.jpg)
Advanced Nuclear Physics
Nuclear Theory Group,Tohoku UniversityKouichi Hagino
原子核理論特論
東北大学原子核理論研究室萩野浩一
![Page 2: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/2.jpg)
ContentsNuclei: aggregate of nucleons (protons and neutrons)
Nuclear Many-Body Problems
(Low-energy) Nuclear Physics:
to understand rich nature of atomic nuclei starting from nucleon-nucleon interactions
- size, mass, density, shape- excitations- decays- nuclear reactions
two kinds of particle: protons and neutrons
![Page 3: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/3.jpg)
ContentsNuclei: aggregate of nucleons (protons and neutrons)
Nuclear Many-Body Problems
Liquid drop modelSingle-particle motion and shell structureHartree-Fock approximationBruckner theoryPairing correlations and superfluid NucleiAngular momentum and number projections1-neutron and 2-neutron halo nucleiRandom phase approximation (RPA)Nuclear reactions
microscopic descriptions of atomic nuclei
![Page 4: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/4.jpg)
References
Bohr-Mottelson Ring-Schuck Rowe Frobrich-Lipperheide
![Page 5: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/5.jpg)
Lecture notes:
http://www.nucl.phys.tohoku.ac.jp/~hagino/lecture.html
(Tohoku University → Physics → Nuclear Theory→ Kouichi Hagino → Lectures)
![Page 6: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/6.jpg)
Introduction: atoms and atomic nuclei
~ 50 cm
~ 10-10 m
cellsDNA
~ 10-8 m
atom
Everything is made of atoms.
~ µm = 10-6 m
![Page 7: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/7.jpg)
Introduction: atoms and atomic nuclei
~ 50 cm
~ 10-10 m
cellsDNA
~ 10-8 m
atom
~ 10-15 m
atomic nucleus
![Page 8: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/8.jpg)
electron cloud (-e)
proton (+e)
neutron (no charge)
Neutral atoms: # of protons = # of electronsChemical properties of atoms # of electrons Mp ~ Mn ~ 2000 Me the mass of atom ~ the mass of nucleus
![Page 9: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/9.jpg)
NuclearPhysics
Nucleus as a quantum many body system
charge mass (MeV) spinProton +e 938.256 ½+Neutron 0 939.550 ½+
Basic ingredients:
(note) n p + e- + ν (10.4 min)
1 fm = 10-15 m
![Page 10: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/10.jpg)
protons
neutrons
Nucleons are not stopping inside a nucleus.(they move relatively freely)
Yet, they are not completely independent.A nucleus keeps its shape while nucleons influence among themselves so that a nucleon does not escape.
a self-bound system
![Page 11: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/11.jpg)
protons
neutrons
Nucleons are not stopping inside a nucleus.(they move relatively freely)
Yet, they are not completely independent.A nucleus keeps its shape while nucleons influence among themselves so that a nucleon does not escape.
a self-bound system
What happens if a photon is absorbed into a nucleus? - one nucleon simply starts moving faster?
photon
![Page 12: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/12.jpg)
protons
neutrons
Nucleons are not stopping inside a nucleus.(they move relatively freely)
Yet, they are not completely independent.A nucleus keeps its shape while nucleons influence among themselves so that a nucleon does not escape.
a self-bound system
What happens if a photon is absorbed into a nucleus? - one nucleon simply starts moving faster?
Very coherent motion can happen
Collective motions
![Page 13: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/13.jpg)
protons
neutrons
Nucleons are not stopping inside a nucleus.(they move relatively freely)
Yet, they are not completely independent.A nucleus keeps its shape while nucleons influence among themselves so that a nucleon does not escape.
a self-bound system
What happens if a photon is absorbed into a nucleus? - one nucleon simply starts moving faster?
Very coherent motion can happen
Collective motions
![Page 14: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/14.jpg)
a variety of motions→ very rich!
Very coherent motion can happen
Collective motions
![Page 15: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/15.jpg)
Nuclear Chart: 2D map of atomic nuclei
neutron number
proton number
![Page 16: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/16.jpg)
Periodic table: protons only, no neutrons
![Page 17: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/17.jpg)
Nuclear Chart: 2D map of atomic nuclei
neutron number
proton number isotopes
16O (Z=8, N=8, A=16)17O (Z=8, N=9, A=17)18O (Z=8, N=10, A=18)
A=Z+N
![Page 18: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/18.jpg)
neutron number
proton number
・Stable nuclei in nature: 287 ・Nuclei artificially synthesized :about 3,000・Nuclei predicted:about 7,000 ~ 10,000
Nuclear Physics: Several static and dynamical propertiesof those nuclei
![Page 19: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/19.jpg)
Nuclear Chart: 2D map of atomic nuclei
neutron number
proton number how many neutrons can be attached?
what is the shape of nuclei?is there any exotic structure? what is the heaviest nucleus? how do nuclei decay?….. etc. etc.
![Page 20: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/20.jpg)
Extension of nuclear chart: frontier of nuclear physics
neutron-rich nuclei (RIBF)
halo nuclei
superheavy elements
Nihonium(element 113)
![Page 21: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/21.jpg)
Neutron-rich nuclei (RIBF at RIKEN)
r-process nucleosynthesis
![Page 22: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/22.jpg)
Prediction of island of stability: an important motivation of SHE study
Yuri Oganessianisland of stability around Z=114, N=184W.D. Myers and W.J. Swiatecki (1966), A. Sobiczewski et al. (1966)
modern calculations: Z=114,120, or 126, N=184 e.g., H. Koura et al. (2005)
nuclei in nature
![Page 23: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/23.jpg)
Nuclear Chart: 2D map of atomic nuclei
neutron number
proton number how many neutrons can be attached?
what is the shape of nuclei?is there any exotic structure? what is the heaviest nucleus? how do nuclei decay?….. etc. etc.
![Page 24: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/24.jpg)
a nucleus is not always spherical
Quantum shape dynamics
![Page 25: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/25.jpg)
Density Distribution High energy electron scattering
Born approximation:
(Fourier transform of the density)
Form factor
e-
![Page 26: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/26.jpg)
Born approximation
θV(r)
![Page 27: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/27.jpg)
Born approximation
θV(r)
incident flux:
θ
momentumtransfer
![Page 28: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/28.jpg)
Electron scattering
Form factor
e- e-
* relativistic correction:
![Page 29: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/29.jpg)
Fermi distribution
(fm-3)(fm)
(fm)
Saturationproperty
![Page 30: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/30.jpg)
Momentum Distribution
Fermi gas approximation
kx
ky
kz
Fermi energy: (MeV)
(note: spin-isospin degeneracy)
ρ = 0.17 fm-3 kF ~ 1.36 fm-1
kF
![Page 31: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/31.jpg)
Nuclear Mass
B(binding energy)
![Page 32: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/32.jpg)
![Page 33: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/33.jpg)
1. B(N,Z)/A ~ 8.5 MeV (A > 12) Short range nuclear force
![Page 34: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/34.jpg)
If one nucleon interacts only with surrounding α nucleons
B ~ αA/2 B/A ~ α/2 (const.)
For A < α+1, one nucleon interacts with all the other nucleons
A
B/A
α+1
![Page 35: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/35.jpg)
1. B(N,Z)/A ~ 8.5 MeV (A > 12) Short range nuclear force2. Effect of Coulomb force for heavy nuclei
![Page 36: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/36.jpg)
Nuclear Chart
Stable nuclei:
![Page 37: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/37.jpg)
1. B(N,Z)/A ~ -8.5 MeV (A > 12) Short range nuclear force2. Effect of Coulomb force for heavy nuclei3. Fusion for light nuclei4. Fission for heavy nuclei
![Page 38: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/38.jpg)
(Bethe-Weizacker formula: Liquid-drop model)
Volume energy:
Surface energy:
Semi-empirical mass formula
Coulomb energy:
Symmetry energy:
![Page 39: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/39.jpg)
How well does the Bethe-Weizacker formula reproduce the data?
![Page 40: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/40.jpg)
cf. N,Z = 2, 8, 20, 28, 50, 82, 126: large binding energy“magic numbers”
How well does the Bethe-Weizacker formula reproduce the data?
![Page 41: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/41.jpg)
(note) Atomic magic numbers (Noble gas)He (Z=2), Ne (Z=10), Ar (Z=18), Kr (Z=36), Xe (Z=54), Rn (Z=86)
shell structure
![Page 42: Advanced Nuclear Physicskouichi.hagino/lectures/...Advanced Nuclear Physics Nuclear Theory Group, Tohoku University Kouichi Hagino 原子核理論特論 東北大学 原子核理論研究室](https://reader031.vdocuments.mx/reader031/viewer/2022040921/5e992ece0093ff5d8a1a5705/html5/thumbnails/42.jpg)
level density
uniform non-uniform
Why do closed-shell-nuclei become stable?
smaller total energy(more stable)