bei48482_FM

462 Chapter Twelve

The Triple-Alpha Reaction

B

ecause no sufficiently stable nuclides with A5 or A8 exist, there is no simple way

in which protons, neutrons, and alpha particles can add together in succession to form the

nuclei of carbon and elements of still higher atomic number. Eventually it became clear that

three alpha particles could react to produce a^126 C nucleus in stars whose interiors are suffi-

ciently hot. However, the cross section (Sec. 12.7) for the process seemed much too small for

the reaction to be significant. Then, in 1953, the British astronomer Fred Hoyle realized that a

resonance associated with the triple-alpha process would greatly enhance its likelihood. Hoyle’s

calculation indicated that the resonance would correspond to an excited state in^126 C of

7.7 MeV. Experiments soon showed that this excited state indeed occurred and increased the

cross section by a factor of 10^7 , thereby removing the biggest obstacle to understanding the

origin of the elements.

Figure 12.28How the rates of

energy generation for the carbon

and proton-proton fusion cycles

vary with the temperature of a

star’s interior. The rates are equal

at about 1.8  107 K. Note that

the power output scale is not

linear.

contraction compresses the core and raises its temperature to the 10^8 K needed for

helium fusion to begin. This involves the combination of three alpha particles to form

a carbon nucleus with the evolution of 7.5 MeV:

4

2 He

4

2 HeS

8

4 Be

4

2 He

8

4 BeS

12

6 C

Because the beryllium isotope^84 Be is unstable and breaks apart into two alpha particles

with a half-life of only 6.7  10 ^17 s, the second reaction must take place immediately

after the first. The sequence is called the triple-alpha reaction.

The smallest stars do not get hot enough (over 10^7 K) to go beyond hydrogen fusion,

and helium fusion is as far as a star with the sun’s mass gets. But in heavier stars, core

temperatures can go even higher, and fusion reactions that involve carbon then be-

come possible. Some examples are

4

2 He

12

6 CS

16

8 O

12

6 C

12

6 CS

24

12 Mg

12

6 C

12

6 CS

20

10 Ne

4

2 He

The heavier the star, the higher the eventual temperature of its core, and the larger the

nuclei that can be formed. (The high temperatures, of course, are needed to overcome

the greater electric repulsion of reacting nuclei with many protons.) In stars more than

Proton-proton cycle

Carbon cycle

Temperature, 107 K

Relative power output

102

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

1

104

106

108

1010

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