Nucleosynthesis
(Adapted with modifications from Benjamin Weaver,
http://ultraman.ssl.berkeley.edu/nucleosynthesis.html)
One of the fundamental problems of astrophysics is the problem of the origin
of chemical elements. It has been postulated for quite some time that elements such as hydrogen, helium, and some lithium
would have been formed just moments after the Big Bang (Alpher, Bethe
& Gamow 1948). With all cosmological theories that depend upon an
initiating event, the only time hydrogen atoms form is during this initial event. Prior to that, nothing exists! Such
a premise is totally outside the bounds of experimental physical science. It represents a complete dead end from
the standpoint of a scientific theory.
In the present author's view, hydrogen is regenerated over and over again
without ever losing or creating any new matter through a cosmological hydrogen cycle. When accreting matter
gets large enough to form black holes, these in turn create the conditions that allow all captured, higher Z elements
to be broken down to quarks and then reassembled back into hydrogen atoms.
But this leaves the problem of the other elements, rather important ones
like carbon, oxygen, iron, and gold. As it turns out, elements can be fabricated in a variety of astrophysical sites. Most
of these sites have been identified, isotope by isotope. The principal modes of nucleosynthesis, along with isotopic abundances,
for naturally-occurring isotopes have been tabulated (Anders & Grevesse
1989). This list of isotopes is available (see below).
The heaviest elements, and indeed, nearly all isotopes heavier than 76Ge,
are formed in one of two processes. These elements are not effectively produced by charged nuclear reactions. Further charged
nuclear interactions, i.e. thermonuclear fusion, become far more difficult due to the strong repulsion of heavy nuclei,
and beyond 56Fe, fusion reactions do not release energy. However, nuclei can capture neutrons, provided some source
of free neutrons is available.The existence of these two processes was first recognized by Burbidge, Burbidge, Fowler, and
Hoyle (Burbidge et al. 1957)
and independently by Cameron (Cameron 1957).
However, the identification of the astrophysical site of these processes took considerably longer. The two processes are named
by the timescale over which they operate: the slow or s-process and the rapid or r-process.
S-Process
Let us imagine that through some other means, we have some supply of seed nuclei such as 56Fe. Let us futher imagine
that we have such a source of free neutrons, and that it is very diffuse, so that the average rate at which a nucleus captures
neutrons is much slower than the average rate of beta decay. It has been estimated (Pagel
1997) that, on average, hundreds to thousands of years may pass between
successive neutron captures. The s-process is indeed slow. In this situation, a seed nucleus will slowly capture neutrons,
for example 56Fe -> 57Fe -> 58Fe -> 59Fe, followed by 59Fe
-> 59Co (beta decay). This process continues, building up nuclei by climbing the line of stability, until 208Pb
and 209Bi are reached. Beyond this point, no nuclei are stable enough to allow neutron capture to operate. Thus
we come to our first critical point: actinides cannot be synthesized by the s-process.
The s-process imposes certain features on the "spectrum" of heavy element
abundances. For certain neutron numbers--N = 28, 50, 82, 126--neutron capture cross-sections are much smaller than
neighboring neutron numbers. This means that once one of these "magic" numbers is reached, it becomes significantly less likely
for the nucleus to capture more neutrons. These numbers are a quantum mechanical effect of closed shells, in precisely the
same way that closed electron shells produce high chemical stability--the noble gasses. If the s-process operates in some
environment for some finite length of time and then shuts off, we expect a fair number of nuclei to be "stuck" at these "magic"
numbers. Elements which correspond to these "magic" numbers of neutrons will thus be especially abundant. We see these in
the Solar System as abundance peaks around 88Sr, 138Ba, and 208Pb.
Detailed calculations based on the observed abundances of s-process elements
leads to specific details--temperature, duration, neutron density--about the astrophysical environment in which the s-process
must take place. Such an environment is present in the Asymptotic Giant Branch (AGB) stars. These are old, mostly burnt-out
stars with a degenerate carbon-oxygen core. They are supported by helium burning in a shell around this core. In this shell
certain reactions release neutrons:
22Ne + 4He -> 25Mg + n
13C
+ 4He -> 16O + n
Once s-process
elements are formed, the AGB star conveniently convects these to the surface, where they may be released either in a stellar
wind or in a subsequent supernova explosion.
R-Process
The s-process, while an elegant theory of nucleosynthesis, cannot explain
some basic features of element abundances. As we have already noted, the s-process cannot produce actinides, which definitely
are present in significant abundance in the Solar System. In addition, each abundance peak we noted in the explanation of
the s-process is accompanied by another abundance peak, shifted toward lower neutron number. Finally, there are some
isotopes, such as the most abundant isotope of osmium, 192Os, which cannot be synthesized in abundance by the s-process,
because 191Os is beta-unstable with a half-life of only about 15 days.
To obtain the r-process, we can start by simply reversing the situation of
the s-process. In the r-process, neutron capture is very rapid, with the time between captures much shorter than the average
beta-decay half-lives. Since beta-decay half-lives far from the line of stability can be on the order of seconds, the r-process
must very rapid indeed. Under these conditions, nuclei will absorb neutrons until neutrons are as easily knocked loose by
thermal photons as they are absorbed. In the literature this is known as the (n,
) <-> (,n) equilibrium. Again, the"magic" neutron numbers operate, serving as bottlenecks to nuclei climbing the r-process path.
However, this time the "magic" nuclei are of an exotic, highly neutron-rich type. For example, 130Cd is an isotope
with the N = 82 "magic" number, but the heaviest stable isotope of cadmium is 116Cd with 14 fewer neutrons.
Now if the neutron source only lasts for a short time, highly unstable nuclei will be left on the r-process path, with many
stuck at the "magic" bottlenecks. These beta-decay back to the line of stability. In our example, 130Cd would eventually
decay to 130Te, the most abundant isotope of tellurium. Since beta-decay reduces the number of neutrons, abundance
peaks show up at lower neutron number than the s-process peaks.
The r-process is fast enough to break past the region of alpha-instability
beyond 208Pb. The stable actinides may be produced directly from a neutron-rich precursor, or from alpha-decay
of even heavier elements. For the purposes of cosmic ray research, the stable actinides may be considered any with a half-life
in excess of 106 years. Those are:
| Species |
t½ [years] |
| 232Th |
1.405 · 1010 |
| 235U |
7.038 · 108 |
| 236U |
2.342 · 107 |
| 237Np |
2.14 · 106 |
| 238U |
4.468 · 109 |
| 244Pu |
8.26 · 107 |
| 247Cm |
1.56 · 107 |
A number of astrophysical sites for the r-process have been proposed over
the years, but so far the best candidated is the hot neutrino-driven wind blown off the surface of a newly-formed neutron
star.
Light Elements
Most of the elements lighter than iron and nickel can be built up from successive
rounds of thermonuclear fusion burning in the cores of stars. There are, however, some unusual processes that operate to produce
certain of the light elements. For example, in the early Universe and in thermonuclear reactions involving helium, the isotopes
6Li, 9Be, 10B, and 11B are bypassed entirely. To be sure, these elements are extremely
rare in the Solar system, yet neither are they entirely absent. All of these are thought to be formed when energetic cosmic
rays strike target nuclei such as 12C in the Interstellar Medium, resulting in partial fragmentation--"spallation"--
of the target nucleus. 11B can also be produced when the intense flux of neutrinos from a supernova induce spallation
on 12C. This is also thought to be the origin of 19F.
Perhaps the most dramatic nucleosynthesis is the formation of the iron-group
elements. When iron and nickel form in the core of a massive star, no more energy may be released by fusing these into heavier
elements. For a rather short time, iron-group elements are in statistical equilibrium with individual nucleons, thus this
type of nucleosynthesis is referred to as Nuclear Statistical Equilibrium (NSE) or the e-process. If the total number of neutrons
is very nearly equal to the number of protons and under the right temperature conditions, the isotope 56Ni will
be favored, and will be released by a subsequent supernova. The decay of 56Ni -> 56Co -> 56Fe,
provides the power which makes a supernova visible. Furthermore, the iron-group elements thus released provide seeds for further
nucleosynthesis in a subsequent generation of stars.
References
Alpher, R. A., Bethe, H. A., and Gamow, G., Phys. Rev. 73, 803
(1948).
Anders, E. and Grevesse, N., Geochimica et Cosmochimica Acta 53,
197 (1989).
Burbidge, E. M., Burbidge, G. R., Fowler, W. A. & Hoyle, F., Rev. Mod.
Phys. 29, 547 (1957).
Cameron, A. G. W., Atomic Energy of Canada Ltd., CRL-41; Pub. Astr. Soc.
Pacific 69, 201 (1957).
Pagel, B. E. J., Nucleosynthesis and Chemical Evolution of Galaxies (Cambridge
University Press, Cambridge, 1997).
Isotopic Abundances from Anders & Grevesse
[E. Anders and N. Grevesse,
Geochim. et Cosmochim. Acta, 53 (1989) 197.]
________________________________________________________________________
Z
A Atom% Process* Abundance (#/1e06 Si)** Common Isotope Name
________________________________________________________________________
1
1 99.9966 U 2.79e10 Hydrogen-1 (proton)
1
2 0.0034 U 9.49e05 Deuterium
2
3 0.0142 U,h? 3.86e05 Helium-3
2
4 99.9858 U,h 2.72e09 Helium-4
3
6 7.5 X 4.28
3 7
92.5 U,x,h 5.282e01
4 9 100.0 X
0.73
5 10 19.9 X 4.22
5
11 80.1 X 1.698e01
6 12 98.90
He 9.99e06 Carbon-12
6
13 1.10 H,N 1.11e05 Carbon-13
7
14 99.634 H 3.12e06
Nitrogen-14
7 15 0.366 H,N 1.15e04 Nitrogen-15
8
16 99.762 He 2.37e07
Oxygen-16
8 17 0.038 N,H 9.04e03
8 18
0.200 He,N 4.76e04
9 19 100.0 N
8.43e02
10 20 92.99 C 3.20e06
10 21
0.226 C,Ex 7.77e03
10 22 6.79 He,N
2.34e05
11 23 100.0 C,Ne,Ex 5.74e04
12 24 78.99 N,Ex
8.48e05
12 25 10.00 Ne,Ex,C 1.07e05
12 26 11.01 Ne,Ex,C
1.18e05
13 27 100.0 Ne,Ex 8.49e04
14 28 92.23
O,Ex 9.223e05
14 29 4.67 Ne,Ex 4.67e04
14
30 3.10 Ne,Ex 3.10e04
15 31 100.0 Ne,Ex
1.04e04
16 32 95.02 O,Ex 4.89e05
16 33 0.75
Ex 3.86e03
16 34 4.21 O,Ex
2.17e04
16 36 0.02 Ex,Ne,S 1.03e02
17 35 75.77
Ex 2.860e03
17 37 24.23 Ex,C,S 9.13e02
18
36 84.2 Ex 8.50e04
18 38 15.8
O,Ex 1.60e04
18 40 0.0 S,Ne 2.6e01
19
39 93.2581 Ex 3.516e03
19 40 0.01167 S,Ex,Ne 0.440
19
41 6.7302 Ex 2.537e02
20 40 96.941 Ex
5.92e04
20 42 0.647 Ex,O 3.95e02
20 43 0.135
Ex,C,S 8.25e01
20 44 2.086 Ex,S 1.275e03
20
46 0.004 Ex,C,Ne 2.4
20 48 0.187 E,Ex
1.14e02
21 45 100.0 Ex,Ne,E 3.42e01
22 46 8.0
Ex 1.92e02
22 47 7.3 Ex
1.75e02
22 48 73.8 Ex 1.771e03
22 49
5.5 Ex 1.32e02
22 50 5.4
E 1.30e02
23 50 0.250 Ex,E
0.732
23 51 99.750 Ex 2.92e02
24 50 4.345
Ex 5.87e02
24 52 83.789 Ex
1.131e04
24 53 9.501 Ex 1.283e03
24 54
2.365 E 3.19e02
25 55 100.0 Ex,E
9.550e03
26 54 5.8 Ex 5.22e04
26
56 91.72 Ex,E 8.25e05
26 57 2.2
E,Ex 1.98e04
26 58 0.28 He,E,C 2.52e03
27
59 100.0 E,C 2.250e03
28 58 68.27 E,Ex
3.37e04
28 60 26.10 E 1.29e04
28 61
1.13 E,Ex,C 5.57e02
28 62 3.59 E,Ex,O 1.770e03
28
64 0.91 Ex 4.49e02
29 63 69.17
Ex,C 3.61e02
29 65 30.83 Ex 1.61e02
30
64 48.63 Ex,E 6.13e02
30 66 27.90 E
3.52e02
30 67 4.10 E,S 5.17e01
30 68 18.75
E,S 2.36e02
30 70 0.62 E,S
7.8
31 69 60.108 S,e,r 2.27e01
31 71 39.892 S,e,r
1.51e01
32 70 20.5 S,e 2.44e01
32 72 27.4
S,e,r 3.26e01
32 73 7.8 e,s,r 9.28
32
74 36.5 e,s,r 4.34e01
32 76 7.8
E 9.28
33 75 100.0 R,s
6.56
34 74 0.88 P 0.55
34 76
9.0 S,p 5.6
34 77 7.6 R,s
4.7
34 78 23.6 R,s 1.47e01
34 80 49.7
R,s 3.09e01
34 82 9.2 R
5.7
35 79 50.69 R,s 5.98
35 81 49.31
R,s 5.82
36 78 0.339 P
0.153
36 80 2.22 S,p 0.999
36 82 11.45
S 5.15
36 83 11.47 R,s
5.16
36 84 57.11 R,S 2.570e01
36 86 17.42
S,r 7.84
37 85 72.165 R,s 5.12
37
87 27.835 S 1.97
38 84 0.56
P 0.132
38 86 9.86 S
2.32
38 87 7.00 S 1.64
38 88
82.58 S,r 1.941e01
39 89 100.0 S
4.64
40 90 51.45 S 5.87
40 91 11.22
S 1.28
40 92 17.15 S
1.96
40 94 17.38 S 1.98
40 96
2.80 R 0.32
41 93 100.0 S
0.698
42 92 14.84 P 0.378
42 94
9.25 P 0.236
42 95 15.92 R,s
0.406
42 96 16.68 S 0.425
42 97
9.55 R,s 0.244
42 98 24.13 R,s
0.615
42 100 9.63 R 0.246
44 96
5.52 P 0.103
44 98 1.88
P 0.0350
44 99 12.7 R,s
0.236
44 100 12.6 S 0.234
44 101 17.0
R,s 0.316
44 102 31.6 R,S 0.588
44
104 18.7 R 0.348
45 103 100.0
R,s 0.344
46 102 1.020 P
0.0142
46 104 11.14 S 0.155
46 105 22.33
R,s 0.310
46 106 27.33 R,S 0.380
46
108 26.46 R,S 0.368
46 110 11.72 R
0.163
47 107 51.839 R,s 0.252
47 109 48.161 R,s
0.234
48 106 1.25 P 0.0201
48 108
0.89 P 0.0143
48 110 12.49 S
0.201
48 111 12.80 R,S 0.206
48 112 24.13
S,R 0.388
48 113 12.22 R,S 0.197
48
114 28.73 S,R 0.463
48 116 7.49 R
0.121
49 113 4.3 p,s,r 0.0079
49 115 95.7
R,S 0.176
50 112 0.973 P
0.0372
50 114 0.659 P,s 0.0252
50 115 0.339
p,s,r 0.0129
50 116 14.538 S,r 0.555
50 117
7.672 R,S 0.293
50 118 24.217 S,r
0.925
50 119 8.587 S,R 0.328
50 120 32.596 S,R
1.245
50 122 4.632 R 0.177
50 124 5.787
R 0.221
51 121 57.362 R,s 0.177
51
123 42.638 R 0.132
52 120 0.09
P 0.0043
52 122 2.57 S
0.124
52 123 0.89 S 0.0428
52 124
4.76 S 0.229
52 125 7.10 R,s
0.342
52 126 18.89 R,S 0.909
52 128 31.73
R 1.526
52 130 33.97 R
1.634
53 127 100.0 R 0.90
54 124 0.121
P 0.00571
54 126 0.108 P
0.00509
54 128 2.19 S 0.103
54 129 27.34
R 1.28
54 130 4.35 S
0.205
54 131 21.69 R 1.02
54 132 26.50
R,s 1.24
54 134 9.76 R
0.459
54 136 7.94 R 0.373
55 133 100.0
R,s 0.372
56 130 0.106 P
0.00476
56 132 0.101 P 0.00453
56 134
2.417 S 0.109
56 135 6.592 R,s
0.296
56 136 7.854 S 0.353
56 137 11.23
S,r 0.504
56 138 71.70 S
3.22
57 138 0.089 P 0.000397
57 139 99.911
S,r 0.446
58 136 0.19 P
0.00216
58 138 0.25 P 0.00284
58 140 88.48
S,r 1.005
58 142 11.08 R
0.126
59 141 100.0 R,S 0.167
60 142 27.13
S 0.225
60 143 12.18 R,S
0.101
60 144 23.80 S,R 0.197
60 145 8.30
R,s 0.0687
60 146 17.19 R,S 0.142
60
148 5.76 R 0.0477
60 150 5.64
R 0.0467
62 144 3.1 P
0.00800
62 147 15.0 R,s 0.0387
62 148 11.3
S 0.0292
62 149 13.8 R,S
0.0356
62 150 7.4 S 0.0191
62 152
26.7 R,S 0.0689
62 154 22.7 R
0.0586
63 151 47.8 R,s 0.0465
63 153 52.2
R,s 0.0508
64 152 0.20 P,s 0.00066
64
154 2.18 S 0.00719
64 155 14.80
R,s 0.0488
64 156 20.47 R,s 0.0676
64
157 15.65 R,s 0.0516
64 158 24.84 R,s
0.0820
64 160 21.86 R 0.0721
65 159 100.0
R 0.0603
66 156 0.056 P
0.000221
66 158 0.096 P 0.000378
66 160
2.34 S 0.00922
66 161 18.91 R
0.0745
66 162 25.51 R,s 0.101
66 163 24.90
R 0.0982
66 164 28.19 R,S
0.111
67 165 100.0 R 0.0889
68 162 0.14
P 0.000351
68 164 1.61 P,S
0.00404
68 166 33.6 R,s 0.0843
68 167 22.95
R 0.0576
68 168 26.8 R,S
0.0672
68 170 14.9 R 0.0374
69 169 100.0
R,s 0.0378
70 168 0.13 P
0.000322
70 170 3.05 S 0.00756
70 171
14.3 R,s 0.0354
70 172 21.9 R,S
0.0543
70 173 16.12 R,s 0.0400
70 174 31.8
S,R 0.0788
70 176 12.7 R
0.0315
71 175 97.41 R,s 0.0357
71 176 2.59
S 0.000951
72 174 0.162 P
0.000249
72 176 5.206 S 0.00802
72 177 18.606
R,s 0.0287
72 178 27.297 R,S 0.0420
72
179 13.629 R,s 0.0210
72 180 35.100 S,R
0.0541
73 180 0.012 p,s,r 2.48e-06
73 181 99.988 R,S
0.0207
74 180 0.13 P 0.000173
74 182 26.3
R,s 0.0350
74 183 14.3 R,s 0.0190
74
184 30.67 R,s 0.0408
74 186 28.6 R
0.0380
75 185 37.40 R,s 0.0193
75 187 62.60
R 0.0324
76 184 0.018 P
0.000122
76 186 1.58 S 0.0107
76 187
1.6 S 0.0108
76 188 13.3
R,s 0.0898
76 189 16.1 R
0.109
76 190 26.4 R 0.178
76 192 41.0
R 0.277
77 191 37.3 R
0.247
77 193 62.7 R 0.414
78 190
0.0127 P 0.000170
78 192 0.78 S
0.0105
78 194 32.9 R 0.441
78 195 33.8
R 0.453
78 196 25.2 R
0.338
78 198 7.19 R 0.0963
79 197 100.0
R 0.187
80 196 0.1534 P
0.00052
80 198 9.968 S 0.0339
80 199 16.873
R,S 0.0574
80 200 23.096 S,r 0.0785
80
201 13.181 S,r 0.0448
80 202 29.863 S,r
0.1015
80 204 6.865 R 0.0233
81 203 29.524
R,S 0.0543
81 205 70.476 S,R 0.1297
82
204 1.94 S 0.0611
82 206 19.12
R,S 0.602
82 207 20.62 R,S 0.650
82
208 58.31 R,s 1.837
83 209 100.0 R,s
0.144
90 232 100.0 RA 0.0335
92 235 0.7200
RA 6.48e-05
92 238 99.2745 RA 0.00893
________________________________________________________________________
*Processes
[Processes
are listed in the table in order of importance with minor
processes (10%-30% of nuclei for r-process and s-process) shown
in lower
case]
U = cosmological nucleosynthesis (BBN)
H = hydrogen burning
N = hot or explosive hydrogen burning
He
= helium burning
C = carbon burning
O = oxygen burning
Ne = neon burning
Ex = explosive nucleosynthesis
E =
nuclear statistical equilibrium (NSE)
S = s-process
R = r-process
RA = r-process producing actinides
P = p-process
X
= cosmic-ray spallation
________________________________________________________________________
**Abundances
[Abundances
relative to Si at the origin of the Solar System,
4.55e09 yr ago.]
18 40
(2.6 +/- 1.4)e01
19 40 5.48
37 87
2.11
38 87 1.51
57 138
0.000409
58 138 0.00283
60 143
0.100
62 147 0.0399
71 176
0.001035
72 176 0.00793
75 187
0.0351
76 187 0.00807
82 206
0.593
82 207 0.644
82 208
1.828
90 232 0.0420
92 235
0.00573
92 238 0.0181
