Science in Christian Perspective

 

 



 GAMOW'S THEORY OF ELEMENT BUILDING
Delbert N. Eggenberger
Illinois Institute of Technology

From: JASA, 2, (September1950): 23-26.


The phenomenon of universal expansion from a common point, as formulated by the astronomer Hubble in 1926, from data on the red shift of stellar spectra, resulted in renewed interest in the mode of formation of astronomical bodies from a primeval mass. The implication of a definite starting time was an important entity from which cosmogonical science and philosophy could launch a new attack. Physicists became interested in the possibility of the construction of elements from a mass of primary building blocks, a suggestion along this line having been made by Sterne1 as early as 1933. The two problems, that of the origin of elements and of the origin of astronomical bodies, have often been studied together. To one school of thought the two are somewhat linked, However, as this paper is to cover only the former, the latter will be brought in only incidentally.

Basically, the problem consists in finding a process which, when solved, would give the present relative abundance distribution of the elements. The abundance drops rapidly with increase in atomic weight up to about weight one hundred. From that point on the abundances are practically constant2. A few elements vary considerably from the general abundance curve, to which reference will be made later.

Early attempts at the solution of the cosmogonical problem were based upon equilibrium studies of nuclear transformations at high temperature and density. The first rather complete cosmogony based upon these methods was developed by von Weizsacher in 1938 3. He assumed his starting material, the origin of which was beyond the scope of his cosmogony, to be the elements in thermal equilibrium with respect to nuclear transformations at high temperature and density. A change in physical conditions then froze the distributions Later investigators extended the theory by assuming hydrogen to be the starting material.

 The outline of this cosmogony is as follows. A mass of hydrogen at an extremely high temperature and density partially condensed into heavier elements in definite proportions for a given set of conditions. One might think of the condensation as being a result of loss in free energy of surface tension effects balanced against, gain in free energy as a result of coalescence of two like-charged particles. It turns out that for elements having atomic weights below about silver in the atomic series, the surface energy is predominant and neutrons and protons tend to combine into larger groups while for elements having heavier nuclei than silver., the predominant electrostatic effect tends to break up the group. In either case, energy is is released. The latter effect is responsible for atomic energy as we knew it to day. The former principle rarely occurs terrestrially because of the extreme improbability of two nuclei coming so close together that they coalesce at ordinary temperature and pressure. A rapid change in physical conditions, including a drop in temperature, then caused that distribution to freeze.

IT, E. Sterne, Monthly Notices 93, 726 (1933)

2V. M. Goldschmidt, Geochemischo Verteilungsgesotz der Elemente und der Atom-Arten, IX (Oslo, Norway, 1938.
 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)


A few difficulties also appear, as pointed out by Alpher.11 The elements containing 5, 8,and 11 nucleons are particularly resistant to neutron transformation. It was suggested deuterium  capture might bridge the gap. Also, it might be questioned how the very-short-lived radioactive elements are bridged# It is possible that these elements did not become radioactive until one or more beta-decays of neutrons took place, So it appears that neutron-capture offers a quite feasible explanation of the origin of the elements, granted a proper initial mass of energy. However, we naturally hestitate to put a stamp of finality to the process at this time.

A question comes up regarding Gamow's suggestion of the possibility17 that this primordial mass of radiation and neutrons was the result of collapse of a previous universe, In other words, the universe may go through cycles of oscillation, collapsing to a primordial mats and expanding to great distances, finally to collapse again. Present data indicates, however, that expansion rates are such that the state of expansion is permanent. There appears to be no intention of the cosmic material to collect again. Therefore, it appears that the mass of radiation and neutrons at the beginning of the present-expansion was a distinct creation at that time.

A further question is anticipated. On what basis is it stated that element formation began several minutes after the initial appearance of energy? If the integral of the formation-rate curve is assumed to start at zero time, a singularity results -- it goes to infinity. Therefore, by adjusting the definite integral to the element formation period with both limits as positive finite-times., the curve approaches infinity at a time a few minutes earlier than the point of initial formation of deuterium10 . This point is assumed to be the earliest limit of creation.

To the Genesiac exegete, present theories are refreshing in the implication of the sudden appearance of mass a finite length of time back. This could well be the creation of Genesis l:l. The statement of this brief and general verse hardly requires limitation to an interpretation of creation of things in their present forms. Whether or not this theory is the correct interpretation of the Bible verse is, of course, impossible to determine. However, that now developments are compatible with Biblical cosmogony gives us further assurance that our faith in His Word is not misplaced.