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Nucleosynthesis (Continued)
Origin of The Heavier Elements

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 t [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

Copyrighted (C) by Joseph H. Guth, 2002.  All rights reserved.  No copying or reproduction in any form may be made without the express written consent of the author.