Science in Christian Perspective
GAMOW'S THEORY OF ELEMENT BUILDING
Delbert N. Eggenberger
Illinois Institute of Technology
From: JASA, 2, (September1950): 23-26.
2V. M. Goldschmidt, Geochemischo
Verteilungsgesotz der Elemente und der Atom-Arten, IX (Oslo,
3C. von Weizsacher, Phyz. Zeit. 38, 176 (1937)
4C. von Weizsacher, ibid. (1938)
This theory results in a relation in which the logarithm of abundance drops linearly with nuclear binding e4atgy and with atomic weight. Calculated abundances fit data quite well up to about atomic weight seventy. Beyond that, calculated values are too low, the error at atomic number 90 being a factor of 10100. Chandrasechkar and Heinrich4 suggested that heavy elements were formed at an earlier state of higher temperature and density, were frozen, and the lighter elements formed at lower temperatures. Gamow5 , however, points out that at the temperature of 1010o K and density of 106g/cm3 necessary for this typo of reaction to form nuclei, transformations are primarily by absorption and evaporation of free neutrons and would occur for heavy as well as for light elements. Klein, Beskow, and Treffenberg6 recalculated von Weizsachor's work using newer data and introduced high energy level studios which partially accounted for the discrepancy at high nuclear weights, van Albada7 considered electrostatic effects at high densities but the discrepancy,at high weight was not accounted for. Hoyl's suggested that 0, B, and A stars had an interior temperature sufficient for such nuclear reactions to occur and identified the sudden freezing of the distribution with a supernova burst. ter Haar9 assumes reactions to be taking place in stars because the initial expansion of material, was too rapid to permit equilibrium to be established. Gamow5 points out that early expansion was so rapid that the 106 g/cm3 density necessary for equilibrium reactions was reduced by an order of magnitude in about one second. In a few minutes all transformations would have been halted, yet beta decay of neutrons requires approximately an hour. Therefore, equilibrium in the early stages was impossible.
Because of the failure of equilibrium methods to predict satisfactorily the -distribution of heavier elements, Gamow5 in 1946 suggested the possibility of a non-equilibrium process of nuclear construction, In 1948, Alpher, Bethe, and Gamow10 identified this non-equilibrium process with that of neutron-capture. The formulation of this theory into mathematical terms and quantitative explanations has been done by Alpher, Gamow, and Herman12,12,13 . Extensions into astronomical processes were also carried out by these authorsl4, 15, 16, 17, 18.
Non-equilibrium cosmogony begins with the sudden appearance of a mass of energy at a temperature of the order of 1010o K. At this point the mass was almost pure radiation. As cooling took place, conversion into material mass in the form of neutrons occurred. when the temperature dropped to 109o K, which was reached in a span of several minutes, and the density of radiation to a value of about 1 g/cm3
4 Chandrasekhar and L. Heinrich, Astro S J. 95, 288 (1942)
5G. Gamow, P s. Rev. 70, 572 (19467) - EWS
611aein, Beskow, and Treffenberg, Arkiv. f. Mat., Astron. och Fysik 33B, 1 (1946); Beskow and Treffenberg, ibid. 34A.9 13 ( 947)_ 7G.
7 G. B. van Albada, Bull. of the Astron. Inst. of Netherlands 10, 161 (1946)
8F. Hoyle, Monthly Notices 106 343 (1947)
9 D. ter Haar, Am. J. Phys. 17, 282 (1949)
10 R. Alpher, H. Bejhe, and G. Gamow, Phys. Rev. 73,803 (1948)
11R.Alphor, Phys. Rev.. 74, 1577 (1948).
12R. Alphor, and R. Herman, Phys. Rev. 74, 1737 (1948)
13R. Alpher, R. Herman, and G. Gamow, Phys. Rev. 75, 332 (1949)
14G. Gamow, Phys.. Rev. 74, 505 (1948)
15R.Alpher, and R. Herman, Phys, Rev. 75, 1333 (1949)
16R. Alper, and R. Herman, Phys. Rev. 75, 1089 (1949).
17G. Gamow, Nature 162, 680 (1948)
18 R. Alpher and R. Herman, Phys, Rev. 75, 1089 (1949)
the first reaction began to take place, namely, that of capture of a neutron by a
proton to form deuterium. The proton made its appearance by beta-radiation from a
neutron. This process of beta radiation from a neutron occurs not only at extremely
high temperatures but also at much lower temperatures when neutrons are overabundant in a nucleus.
In general, the lower-weight nuclei have small neutron-capture cross sections and relatively small proportions are hit by neutrons to be transformed into higher weight nuclei. The result is that each element is much scarcer than the one next lower in weight. At atomic weights around 100, these cross sections increase at such a rate with increase in atomic weight that relatively large portions of existing nuclei are transformed into higher ones. By assigning suitable conditions it is possible to work out a theoretical distribution that fits the actual quite accurately over the range of known elements.
Calculations show this process to have occurred in a span of time 103 to 104 seconds long, by which time radioactivity of the neutron brought the process to negligible importance. During this period, and for a considerable time afterward, radiation mass was predominant and radiation pressure caused a very rapid expansion. In fact, it was not until a time of 107 years had elapsed that one-half of it had been transformed into matter. This process was probably similar to the formation of mesons today in the form of cosmic rays. At the time matter constituted one-half the total mass, the cosmogonical processes were influenced primarily by material mass. It was then possible for gravitational effects to operate in accordance with Jeans'
law19. At a critical density and temperature, a mass of gas of a given diameter, or larger, began to break away from the surrounding gas and contracted into an astronomical body. This step could well be started by a statistical fluctuation in density
within the bidy of gas. Details of this process have been worked out by Spitzer20 and Whipple21. It is quite possible that dark nebulae represents such a process occurring at present, That this time of equality of radiation and matter density was the time of-condensation into galaxies is suggested by the fact that when that point was reached, the universe went over into free expansion, and condensation would have become increasingly difficult after that16.
Several additional facts support the theory of neutron-capture. The abundance of several heavier elements are somewhat greater than would be expected from a smooth abundance curve. Gamowl4 has pointed out that these particular isotopes have complete neutron shells in the nucleus and have an abnormally low neutron-capture cross section. There would be a tendency for isotopes to-collect at these points, thus accounting for their abnormal abundances. On the other hand., the light elements lithium, beryllium and boron have abnormally low abundances. From. proton-capture cross section data (see for example, Bethe's article22) it is seen that these elements have unusually high cross sections in relation to the small size of the nuclei. Therefore it is to be expected that these elements would tend to be transformed by protons into higher elements. This process could occur for some time after termination of the neutron-capture construction period23. That the abnormally low abundances of the latter elements is observed not only terrestrially but throughout stellar media as well seems to recommend this theory over that of equilibrium methods using stars as the original generators of elements. In this connection it should be mentioned that the neutron density was too 1mv for any capture to materially affect element distribution at resonance temperatures. This moans the process was ended at a still very high temperatures.
19 J. Jeans, Astronomy and Cosmogony, 1928
20 L. Spitzer, Jr., Astrophys'. J. 95, 329 (1942)
21 P. Whipple, Astrophys. J. 104, 1 (1946)
22 H. Botha, Phys. Rev. 55, 434 (1939)
23 R. Alphar, R. Herman, and G. Gamow, Phys. Rev. 74, 1198 (1948)