the origin of the peak almost a constant! a peak at …kouichi.hagino/lecture2/...Heavy-ion fusion...
Transcript of the origin of the peak almost a constant! a peak at …kouichi.hagino/lecture2/...Heavy-ion fusion...
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a peak at Fe
(the most stable)
B
the origin of the peak
almost a constant!
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if each nucleon can interact only a-nucleons close by:
A
B/A
B ~ a A/2 B/A ~ a/2 (const.)
rint
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if each nucleon can interact only a-nucleons close by:
A
B/A
B ~ a A/2 B/A ~ a/2 (const.)
rint rint
a small nucleus
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if each nucleon can interact only a-nucleons close by:
B ~ a A/2 B/A ~ a/2 (const.)
rint rint
a small nucleus
A
B/A
a+1
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rint
A
B/A
a+1
rint
nuclear interactionCoulomb interaction
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rintrint
nuclear interactionCoulomb interaction
A
B/A
Coulomb
correction
a peak
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November, 2016
Superheavy elements
20983Bi70
30Zn 279113Nh*
Heavy-ion fusion reaction
the island of stability (安定的島)
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Fusion of medium-heavy systems:
Fusion of heavy and super-heavy systems:
large Coulomb repulsion
→ re-separation
A complication
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Heavy-ion fusion reactions for superheavy elements
Compound
nucleus
reseparation
(quasi-fission)fission evaporation
residue
(rare process)
experimentally
indistinguishable
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CN
ERCN = compound nucleus
ER = evaporation residue
n
experimentally detected
1011 = 100,000,000,000
106 = 1,000,000
99,999,000,000
999,999
1
typical values for Ni + Pb reaction
very rare
event !!
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Element 113 (RIKEN, K. Morita et al.)
K. Morita et al., J. Phys. Soc. Jpn. 81(‘12)103201
only 3 events for 553 days experiment
70Zn (Z=30) + 209Bi (Z=83) 278Nh (Z=113) + n
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Theory: Lagenvin approach
multi-dimensional extension of:
g: friction coefficient
R(t): random force
摩擦乱雑力
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Chemistry of superheavy elements
Are they here in the periodic table?
Does Nh show the same chemical properties
as B, Al, Ga, In, and Tl?
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relativistic effect : important for large Z
E = mc2
Solution of the Dirac equation (relativistic quantum mechanics)
for a hydrogen-like atom:
relativistic effect
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Famous example of relativistic effects: the color of gold
Gold looked like silver if there was no relativistic effects!
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5d
6s
4d
5s
Gold (Au)Silver (Ag)
Non-Rel.Non-Rel.
Rel.
Rel.
3.7 eV 2.4 eV
2.76 eV 1.65 eV
cf. visible spectrum
3.7 eV
reflected (Ag)
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5d
6s
4d
5s
Gold (Au)Silver (Ag)
Non-Rel.Non-Rel.
Rel.
Rel.
3.7 eV 2.4 eV
2.76 eV 1.65 eV
cf. visible spectrum
2.4 eV
reflected (Au)absorbed (Au)
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Gold (Au)Silver (Ag)
Non-Rel.Non-Rel.
Rel.
Rel.
3.7 eV 2.4 eV
Au
blue: absorbed
Ag
no color
absorbed
47th element 79th element
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Chemistry of superheavy elements
How do the relativistic effects alter the periodic table for SHE?
What is the color of superheavy elements?
big open questions
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Kouichi Hagino
Tohoku University, Sendai, Japan
Magic Numbers of Atoms and Nuclei
: quantum mechanics of many-Fermion
systems
1. Identical particles: Fermions and Bosons
2. Simple examples: systems with two identical particles
3. Pauli principle
4. Magic numbers
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Introduction
atom = nucleus
+ many electrons
nucleus = many protons
+ many neutrons
Quantum mechanics for those many Fermion systems?
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Exchange operator: Fermions and Bosons
a two-particle system
1 2
two particles are identical: particle 1 and 2 cannot be distinguished
2 1
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Exchange operator: Fermions and Bosons
where exchange operator
wave functions have to be simultaneous eigen-states of
H and P12
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Exchange operator: Fermions and Bosons
where exchange operator
wave functions have to be simultaneous eigen-states of
H and P12
Eigen-values of P12
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Exchange operator: Fermions and Bosons
Natural Laws: each particle has a definite value of P12
(independent of e.g., experimental setup and temperature)
particles with a half-integer spin: P12 = -1 (“Fermion”)
electrons, protons, neutrons,…..
particles with an integer spin: P12 = +1 (“Boson”)
photons, pi mesons,….
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Simple examples: systems with two identical particles
Assume a spin-independent Hamiltonian for a two-particle system:
→ separable between the space and the spin
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Simple examples: systems with two identical particles
Assume a spin-independent Hamiltonian for a two-particle system:
→ separable between the space and the spin
spin-zero bosons
no spin → symmetrize the spatial part
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Simple examples: systems with two identical particles
spin-1/2 Fermions
Spin part:
symmetric
anti-symmetric
spatial part: anti-symmetric for S = 1
symmetric for S = 0
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Scattering of identical particles
these two processes cannot be
distinguished
add two amplitudes and then
take square
interference
q
p-q
+: for spatially symmetric, and – : for spatially anti-symmetric
detector
(検出器)
干渉
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Experimental data Symmetric at 90 deg.
clear oscillations
D.A. Bromley et al.,
Phys. Rev. 123(‘61)878
cf. Vb ~ 10.3 MeV
16O + 16O elastic scattering
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16O + 16O elastic scattering
16O: spin-zero Boson →
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θlab (deg)
inte
nsi
ty12C + 12C
13C + 13C
Spin 0
Spin half
identical Bosons
→ constructive interference
identical Fermions
→ destructive interferenceS=1
S=0
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Pauli exclusion principle and Slater determinants
Pauli exclusion principle: two identical Fermion cannot take the
same state
Let us assume:
(no interaction between 1 and 2)
separation of variables → a product form of wave function
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Pauli exclusion principle and Slater determinants
Pauli exclusion principle: two identical Fermion cannot take the
same state
separation of variables → a product form of wave function
(Pauli principle)
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x
V(x)Magic numbers
魔法数
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x
V(x)
discrete bound states
The lowest state of many-Fermion systems
= put particles from the bottom of the potential well (Pauli principle)
Magic numbers
魔法数
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Magic numbers
Hydrogen-like potential:
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Magic numbers
Hydrogen-like potential:
1S
2S 2P
3S 3P 3D
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Magic numbers
Hydrogen-like potential:
1S
2S 2P
3S 3P 3D
degeneracy = 2 * (2 l +1)
[2]
(spin x lz)
[2] [6]
[2] [6] [10]
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Magic numbers
Hydrogen-like potential:
1S
2S 2P
3S 3P 3D
degeneracy = 2 * (2 l +1)
[2]
(spin x lz)
[2] [6]
[2] [6] [10]
He
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Magic numbers
Hydrogen-like potential:
1S
2S 2P
3S 3P 3D
degeneracy = 2 * (2 l +1)
[2]
(spin x lz)
[2] [6]
[2] [6] [10]
He
Ne
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Magic numbers
Hydrogen-like potential:
1S
2S 2P
3S 3P3D
degeneracy = 2 * (2 l +1)
[2]
[2] [6]
[2] [6][10]
He
Ne
Vee
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Magic numbers
Hydrogen-like potential:
1S
2S 2P
3S 3P3D
degeneracy = 2 * (2 l +1)
[2]
[2] [6]
[2] [6][10]
He
Ar
Ne
Vee
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Magic numbers
Hydrogen-like potential:
1S
2S 2P
3S 3P3D
degeneracy = 2 * (2 l +1)
[2]
[2] [6]
[2] [6][10]
He
Ar
Ne
Vee
“closed shell”
(magic numbers)
very stable
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Periodic Table of elements
noble gas
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Magic numbers
similar magic numbers also in atomic nuclei
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Magic numbers
Extra binding for N or Z = 2, 8, 20, 28, 50, 82, 126 (magic numbers)
Very stable
42He2,
168O8,
4020Ca20,
4820Ca28,
20882Pb126
B
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Magic numbers
Extra binding for N or Z = 2, 8, 20, 28, 50, 82, 126 (magic numbers)
Very stable
42He2,
168O8,
4020Ca20,
4820Ca28,
20882Pb126
208Pb126206Pb124
204Pb122202Pb120
210Pb128212Pb130
0.9
6
0.9
0
0.8
0
2.6
1 M
eV
0.8
0
0.8
1
the first excited
state of Pb isotopes
N = 126
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1s
1p1d
2s
+ spin-orbit potential
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Atomic magic numbers
electron #: 2, 10, 18, 36, 54, 86
inert gas:He, Ne, Ar, Kr, Xe, Rn
Nuclear magic numbers
proton # or neutron #
2, 8, 20, 28, 50, 82, 126
e.g., 168O8 (double magic)
many oxygen nuclei:
produced during
nucleosynthesis
oxygen: chemically active
several complex chemical
reactions, leading to the
birth of life
Double magic
参考:望月優子 ビデオ「元素誕生の謎にせまる」 http://rarfaxp.riken.go.jp/~motizuki/contents/genso.html
Lucky accident for the origin of lie
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Summary
Nuclear Physics is interesting!
Everything is made from atoms.
Nuclear Physics is important for many things.
Nuclei have very rich nature.
一清、二白、三紅、四緑、五黄
clear lectures(清)?
謝謝!