Sec$on 5.
核融合反応
5.1 恒星の中心温度5.2 核融合反応

太陽
太陽の明るさ= 4 x 1026 J/s (= W) = 4 x 1033 erg/s(C) JAXA/ISAS

日本の一年の消費電力 = 2 x 1019 J = 2 x 1026 erg
日本が107 年 = 1000万年かけて使うエネルギーを1秒で放射

太陽はなぜこんなに明るいの？？
=> 物理を使って理解しよう

太陽はなぜ明るく輝くのか？
A. 化学反応

B. 原子核反応

https://www.britannica.com/science/chemical-reaction(例) C＋ O2 -> CO2(例) H + H + H + H -> He

原子や分子がくっつく原子核が変わる= 原子核は変わらない= 新しい元素ができる
太陽を約100億年輝かせることができる

星の中では核融合反応が起きているらしい=> 本当？
星の中はどうなっているの？

核融合

The energy levels of the compound nucleus play a crucial rolesection, see Fig. 6.2. Let Emin be the minimum energy required to r
state of C to infinity, analogous to the ionization energy of an atom
spond to bound states in an atom; these can only decay by γ-emissi
These6‘stationary’ energy levels have long lifetimes τ and corre
according to Heisenberg’s uncertainty relation

クーロン障壁 E ~ (Z1Z2e2)/r ~ 10 eV (MeV)!~ 103 eV (keV) <= 107 K
ガスの典型的なエネルギー E ~ ΓkT= .
τ=> トンネル効果

ECMeVV(r)E’量子力学energy温度が高いほど核融合が起こりやすい

keVE0rc

rnE min−V0r

Figure 6.2. Schematic depiction of thetential, shown as a thick line. The potension at distances r > rn , and by nuclea
particle with kinetic energy E at infinity
rc . The horizontal lines for 0 < r < rn innucleus formed during the reaction. Th
quasi-stationary levels with E > 0 are btimes. If the incoming particles have en
they can find a resonance in the compou~10-13 cm (1 fm)
Textbook by Pols

imes that of a typical reaction involving only strongTheinteractions.
Therate cannot
bnet result
ofreactionhydrogenburning
ured in the laboratory and is only known原子核物理
from theory.
1 another4 proton to +from 3 He.
After some deuterium is produced, it rapidly reacts with4 H → He + 2 e + 2 ν .
quently three diﬀerent branches are possible to complete the chain towards 4 He:

水素燃焼 (pp chain)

You may verify using Sec. 6.1.1 th
1 H + 1 H → 2 H + e+ + νnucleus two protons have to be con
2 H + 1 H → 3 He + γ
interactions (p → n + e+ + ν), whic✟❍✟❍❍
not to include the neutrino energi✟❍❍✙✟✟❥
theenergy
thatisusedtoheat
the3 He + 3 He → 4 He + 2 1 H
3 He + 4 He → 7 Be + γ(includingthe γ-rays resulting fro❍✟✟❍✟❍energies
oftheresultingnuclei.
T❍
✟
pp1
✙✟
❥
❍
smallerthan26.734
MeV
anddep7−771
8Be + e → Li + ν

7 Li + 1 H → 4 He + 4 He

pp2

Be + H → B + γ

8 B → 8 Be + e+ + ν

8 Be → 4 He + 4 He

pp3

The pp1 branch requires two 3 He nuclei, so the first two reactions in the chain have to takeTextbook
by Pols
wice. The alternative pp2 and pp3 branches
requireonly one 3 He nucleus and an already existi

原子核物理The CNO cycle

水素燃焼 (CNO cycle)

If some C, N, and O is already present in the gas out of which a star forms, and if the temperatu
is suﬃciently high, hydrogen fusion can take place via the so-called CNO cycle. This is a cyclicsequence of reactions that typically starts with a proton capture by a 12 C nucleus, as follows:❄12 C + 1 H → 13 N + γ

13 N → 13 C + e+ + ν

13 C + 1 H → 14 N + γ✲ 14N + 1 H → 15 O + γ

15 O → 15 N + e+ + ν

15 N + 1 H → 12 C + 4 He→ 16 O + γ

16 O + 1 H → 17 F + γ

17 F → 17 O + e+ + ν

17 O + 1 H → 14 N + 4 He
1

(6.4For example, if we denote by rpD the rate of 2 H + 1 H, one has rpD = rpp , etc. Note that describing the p-p reaction
Textbook by Prialnik
Textbook by Pols
‘slow’ and the 2 H + 1 H as ‘fast’ refers to the diﬀerence in cross-section factors ⟨συ⟩ and not to the number of reactions p

脱線：地上の核融合

imes that of a typical reaction involving only strongTheinteractions.
Therate cannotbnet result
ofreactionhydrogenburning
ured in the laboratory and is only known from theory.
1 another4 proton to +from 3 He.
After some deuterium is produced, it rapidly reacts with
4 H → He + 2 e + 2 ν .
quently three diﬀerent branches are possible to complete the chain towards 4 He:

太陽の核融合You may verify using Sec. 6.1.1 th
1 H + 1 H → 2 H + e+ + ν
非常にゆっくり進むnucleus
two protons have to be con
2 H + 1 H → 3 He + γ
interactions (p → n + e+ + ν), whic✟❍✟❍❍
not to include the neutrino energi✟❍❍✙✟✟❥
theenergy
thatisusedtoheat
the3 He + 3 He → 4 He + 2 1 H
3 He + 4 He → 7 Be + γ(including
the γ-rays resulting fro❍
✟
✟
❍
✟
❍
energies
oftheresultingnuclei.
T❍
✟
pp1
✙✟
❥
❍
smallerthan26.734
MeVanddep
7−771
8Be + e → Li + ν

7 Li + 1 H → 4 He + 4 He

pp2Be + H → B + γ

8 B → 8 Be + e+ + ν

8 Be → 4 He + 4 He

pp3The pp1 branch requires two 3 He nuclei, so the first two reactions in the chain have to takeTextbookby Pols
wice. The alternative pp2 and pp3 branches
requireonly one 3 He nucleus and an already existi

地上の核融合

4D + T ! He + n<latexit sha1_base64="kigrvtkrzbN/vAfiDo4wIn9mvps=">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</latexit>

重水素 三重水素(pn)
(pnn)

ヘリウム

中性子

地球に存在

6
<latexit sha1_base64="ThU2IUu/tufx+jep24v7XOLVvII=">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</latexit>

4

Li + n ! He + T

地球に存在

まとめ

• 恒星の内部• 力学と熱力学で大まかに理解できる• 太陽の中心温度は約10 K (1000万度)• 核融合反応• 原子核のクーロンポテンシャル
7>> 粒子の運動エネルギー• トンネル効果が必要 (量子力学)

熱力学

統計力学

3セメ

5,6セメ

力学

電磁気学

1,2セメ

2,3セメ

宇宙物理学
天体物理学
流体力学

原子核物理学

4セメ

7セメ

量子力学

相対論

4,5セメ

4,7セメ