1.共鳴反応hagino/lectures/nuclth19/...nuclear fusion reactions compound nucleus two positive...
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![Page 1: 1.共鳴反応hagino/lectures/nuclth19/...Nuclear fusion reactions compound nucleus two positive charges repel each other nuclear attractive intraction 複合核 核融合反応:複合核生成反応](https://reader035.vdocument.in/reader035/viewer/2022071102/5fdba6a21d7d456bb3737f89/html5/thumbnails/1.jpg)
原子核反応
今日の内容1.共鳴反応2.核融合反応
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1.共鳴反応
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酸素原子核 (Z=8)
安定同位体:16O (99.757%), 17O (0.038%), 18O (0.205%)
24O の発見:A.G. Artukh et al., PL32B (1970) 43
40Ar の破砕M. Langevin et al.,
PL150B (‘85) 71
25O は不検出
48Ca の破砕D. Guillemaud-Mueller et al.,
PRC41 (‘90) 937
26O は不検出
40Ar の破砕H. Sakurai et al.,
PLB448 (‘99) 180
28O は不検出
酸素の中性子ドリップ線は 24O で確定。25,26,28O は非束縛。
酸素同位体のドリップ線
N=2Z+2
13O 14O 15O 16O 17O 18O 19O 20O 21O 22O 23O 24O
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25O はどのように見えるのか?
269F17から1つ陽子を抜いて
258O17 を
生成→ 1中性子を放出して崩壊
25O → 24O + n
Y. Kondo et al., PRL116 (‘16) 102503
1s1/2
1p3/2
1p1/2
1d5/2
2s1/2
1d3/2
中性子1粒子状態
1d3/2 の「準束縛」状態と解釈することができる
22O 23O 24O 25O 26O
ピーク
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準束縛状態とは?
実際のポテンシャル
束縛状態は E < 0 の領域のみ
d3/2
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準束縛状態とは?
実際のポテンシャル
束縛状態は E < 0 の領域のみ
このようにポテンシャルを変更すると
E > 0 でも束縛状態ができる
= 準束縛(準安定)状態
d3/2
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準束縛状態とは?
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準束縛状態とは?
実際には有限の寿命で障壁をトンネルし崩壊
束縛状態=無限の寿命
「準束縛(準安定)状態」
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準束縛状態とは?
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ガモフ状態
トンネル効果で波動関数が沁み出し、外向きの波として崩壊
エネルギーを複素数にしなければならない:
共鳴エネルギー
共鳴幅
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ガモフ状態
トンネル効果で波動関数が沁み出し、外向きの波として崩壊
が準安定状態の寿命
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まず実際の現象から
陽子非束縛核 169F7
1710Neから1つ陽子を抜いて
169Fを生成 → 崩壊スペクトル
R.J. Charity,
Eur. Phys. J. Plus 131 (‘16) 63
15O + p 弾性散乱の断面積
qcm = 180 deg.
I. Stefan et al., PRC90(‘14) 014307
共鳴エネルギーで弾性散乱の断面積が増大(共鳴散乱)
共鳴状態と弾性散乱(共鳴散乱)
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次に散乱理論共鳴状態と弾性散乱(共鳴散乱)
自由粒子の運動:
解:
遠方での振る舞い:
r
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次に散乱理論共鳴状態と弾性散乱(共鳴散乱)
自由粒子の運動:
解:
遠方での振る舞い:
r
ポテンシャル中の運動:
解:
遠方での振る舞い:
r
* 吸収がなければ |Sl(E)| = 1
V(r)
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次に散乱理論共鳴状態と弾性散乱(共鳴散乱)
自由粒子の運動:
解:
遠方での振る舞い:
r
ポテンシャル中の運動:
解:
遠方での振る舞い:
位相のずれ (phase shift)
* 吸収がなければ |Sl(E)| = 1
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共鳴があると位相のずれはどう振る舞う?
25O → 24O + n
1s1/2
1p3/2
1p1/2
1d5/2
2s1/2
1d3/2
WS ポテンシャルによる n-24O 散乱
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共鳴があると位相のずれはどう振る舞う?
25O → 24O + n
1s1/2
1p3/2
1p1/2
1d5/2
2s1/2
1d3/2
WS ポテンシャルによる n-24O 散乱
Eに対してゆるやかな振る舞いcf. レビンソンの定理
共鳴エネルギーで急に立ち上がる
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共鳴があると位相のずれはどう振る舞う?
Eに対してゆるやかな振る舞い
共鳴エネルギーで急に位相のずれが立ち上がる
共鳴がない場合 共鳴がある場合
弾性散乱の全断面積: →共鳴だと大
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それでは波動関数は?
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それでは波動関数は?
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それでは波動関数は?
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それでは波動関数は?
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それでは波動関数は?
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それでは波動関数は?
on-resonance:
波動関数は障壁の内側で大きな振幅
off-resonance:
障壁の内側では振幅が小さい
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それでは波動関数は?
on-resonance:
波動関数は障壁の内側で大きな振幅
障壁内部の存在確率
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V0 = -50 MeV
R0 = 1.27 * 2001/3 fm
a = 0.67 fm
m = 200 mN / 201
l = 5
もう少し極端な例:
on-resonance
(Ec = 1.72 MeV)
off-resonance
(Ec = 1.2 MeV)
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on-resonance
(Ec = 1.72 MeV)
off-resonance
(Ec = 1.2 MeV)
off-resonance では-波動関数は障壁の外側で大きな振幅
- トンネル効果による障壁内部にしみ込む
on-resonance では-波動関数は障壁内部で束縛状態のように振る舞う
- 障壁にトラップされた波動関数がトンネル効果により障壁の外側にしみ出る
ガモフ状態と同じ振る舞い
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2.核融合反応
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Nuclear fusion reactions
compound
nucleus
two positive charges
repel each other nuclear attractive
intraction 複合核
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核融合反応: 複合核生成反応
Niels Bohr (1936)
原子核による中性子の吸収→ 複合核
Wikipedia
N. Bohr,
Nature 137 (‘36) 351
cf. フェルミの実験 (1935)
MeV スケールの原子核にeV スケールの幅の多数の共鳴状態
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核融合反応: 複合核生成反応
Niels Bohr (1936)
原子核による中性子の吸収→ 複合核
Wikipedia
N. Bohr,
Nature 137 (‘36) 351
PT
P+T
複合核
重イオン反応で複合核をつくる=重イオン核融合反応
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cf. N. Bohr ‘36
PT
P+T
複合核
恒星のエネルギー源 (Bethe ‘39)
元素合成 超重元素の合成
核融合・核分裂: 強い相互作用をする量子多体系の大振幅集団運動
微視的理解:核物理における究極の未解決問題の一つ
核融合反応: 複合核生成反応
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核融合反応: 複合核生成反応
PT
P+T
ACN = AP + AT
蒸発Evaporation
核分裂Fission
Evaporation + Fission
n,p,a放出g 崩壊
cf. 超重核
融合
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蒸発
核分裂
n,p,a放出g 崩壊
融合
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蒸発残留核の測定
ビーム
標的核
蒸発残留核:前方角度へ
n (及び p)の放出
a の放出
J.R. Leigh et al., PRC52(‘95)3151
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蒸発残留核の測定
ビーム
標的核
蒸発残留核:前方角度へビーム粒子も前方角度へ
-20
-10
01
02
0
Evaporation
residues elastics
20°
10°
0°
-
10°
-
20° intensity
beam-like 粒子:蒸発残留核の 104~1012倍の強度
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蒸発残留核の測定
target Si detectors
Velocity filterER
beam
Si detector
velocity filter 等を用いてうまく蒸発残留核と beam-like 粒子をわける
gas filled region
Stopper for
elasticsdetectors
beam
target
ANUで使われている超伝導ソレノイド
M. Dodriguez et al.,
NIM A614(‘10)119
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J.R. Leigh et al., PRC52(‘95)3151
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核分裂片の測定Fission fragmentdetector 1
Fission fragmentdetector 2
Beam
Monitor detectors(out of plane)
Target
Fissionfragment 1
Fission fragment 2
ANUで使われている検出器
D.J. Hinde et al., NPA592(‘95)271
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クーロン障壁
2つの力:1.クーロン力長距離斥力
2.核力短距離引力
ポテンシャル障壁(クーロン障壁)
クーロン障壁P
Tr
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Double Folding Potential
Phenomenological potential
(微視的ポテンシャルの直接項に相当)
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クーロン障壁
2つの力:1.クーロン力長距離斥力
2.核力短距離引力
ポテンシャル障壁(クーロン障壁)
クーロン障壁P
Tr
クーロン障壁近傍のエネルギーにおける核融合反応
→ 多粒子系の量子トンネル現象
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nuclear fusion in stars
extrapolation of data
LOGARITMIC
SCALE
direct measurements
E0 Ecoul
Coulomb barrier
(E)
non-resonant
resonance
extrapolation
needed !
figure: M. Aliotta
トンネル
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Tunnel probability:
x
V(x)
a-a
V0
x
V(x)
Quantum Tunneling Phenomena
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For a parabolic barrier……
x
Vb
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Energy derivative
of penetrability
(note) Classical limit
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potential model
ポテンシャル模型: V(r) + 吸収
cf. 初期の実験:
R.G. Stokstad et al., PRL41(‘78) 465
核融合反応断面積の大きな増大
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ポテンシャル模型:
E > Vb では大体データを再現
E < Vb では核融合断面積を過小に評価
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154Sm : a typical deformed nucleus 154Sm
0+2+
4+
6+
8+
00.082
0.267
0.544
0.903
(MeV)
154Sm
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deformation of 154Sm
154Sm : a typical deformed nucleus 154Sm
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154Sm 16O
q
154Sm
Effects of nuclear deformation
154Sm : a typical deformed nucleus
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Fusion: strong interplay between
nuclear structure and reaction
Effects of nuclear deformation
154Sm : a typical deformed nucleus
deformation
coupling assisted
tunneling
* Sub-barrier enhancement also for non-deformed targets:
couplings to low-lying collective excitations →
154Sm 16O
q
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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
excitation energy excitation operator
0+ 0+
0+ 0+
2+ 0+
coupling
if written down more explicitly:
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coupling
0+ 0+
0+ 0+
2+ 0+
entrance channel
excited channel
Coupled-channels method: a quantal scattering theory with excitations
excitation energy excitation operator
full order treatment of excitation/de-excitation dynamics during reaction
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i) Inter-nuclear potential
a fit to experimental data at above barrier energies
ii) Intrinsic degrees of freedom
in most of cases, (macroscopic) collective model
(rigid rotor / harmonic oscillator)
Inputs for C.C. calculations
0+
2+
0+,2+,4+
0
e
2e
simple harmonic oscillator