Understanding the Process

The next major step in understanding how stars produce energy from nuclear burning, resulted from applying quantum mechanics to the explanation of nuclear radioactivity. This application was made without any reference to what happens in stars. According to classical physics, two particles with the same sign of electrical charge will repel each other, as if they were repulsed by a mutual recognition of 'bad breath'. Classically, the probability that two positively charged particles get very close together is zero. But, some things that cannot happen in classical physics can occur in the real world which is described on a microscopic scale by quantum mechanics.

In 1928, George Gamow, the great Russian-American theoretical physicist, derived a quantum-mechanical formula that gave a non-zero probability of two charged particles overcoming their mutual electrostatic repulsion and coming very close together. This quantum mechanical probability is now universally known as the "Gamow factor.'' It is widely used to explain the measured rates of certain radioactive decays.

In the decade that followed Gamow's epochal work, Atkinson and Houtermans and later Gamow and Teller used the Gamow factor to derive the rate at which nuclear reactions would proceed at the high temperatures believed to exist in the interiors of stars. The Gamow factor was needed in order to estimate how often two nuclei with the same sign of electrical charge would get close enough together to fuse and thereby generate energy according to Einstein's relation between excess mass and energy release.

In 1938, C.F. von Weizsäcker came close to solving the problem of how some stars shine. He discovered a nuclear cycle, now known as the carbon-nitrogen-oxygen (CNO) cycle, in which hydrogen nuclei could be burned using carbon as a catalyst. However, von Weizsäcker did not investigate the rate at which energy would be produced in a star by the CNO cycle nor did he study the crucial dependence upon stellar temperature.

By April 1938, it was almost as if the scientific stage had been intentionally set for the entry of Hans Bethe, the acknowledged master of nuclear physics. Professor Bethe had just completed a classic set of three papers in which he reviewed and analyzed all that was then known about nuclear physics. These works were known among his colleagues as "Bethe's bible.'' Gamow assembled a small conference of physicists and astrophysicists in Washington, D.C. to discuss the state of knowledge, and the unsolved problems, concerning the internal constitution of the stars.

In the course of the next six months or so, Bethe worked out the basic nuclear processes by which hydrogen is burned (fused) into helium in stellar interiors. Hydrogen is the most abundant constituent of the sun and similar stars, and indeed the most abundant element in the universe.

Bethe described the results of his calculations in a paper entitled "Energy Production in Stars,'' which is awesome to read. He authoritatively analyzed the different possibilities for reactions that burn nuclei and selected as most important the two processes that we now believe are responsible for sunshine. One process, the so-called p-p chain, builds helium out of hydrogen and is the dominant energy source in stars like the sun and less massive stars.

The CNO cycle, the second process which was also considered by von Weizsäcker, is most important in stars that are more massive than the sun. Bethe used his results to estimate the central temperature of the sun and obtained a value that is within 20% of what we currently believe is the correct value (16 million degrees Kelvin).² Moreover, he showed that his calculations led to a relation between stellar mass and stellar luminosity that was in satisfactory agreement with the available astronomical observations.

In the first two decades after the end of the second world war, many important details were added to Bethe's theory of nuclear burning in stars. Distinguished physicists and astrophysicists, especially A.G.W. Cameron, W.A. Fowler, F. Hoyle, E.E. Salpeter, M. Schwarzschild, and their experimental colleagues, returned eagerly to the question of how stars like the sun generate energy. From Bethe's work, the answer was known in principle: the sun produces the energy it radiates by burning hydrogen. According to this theory, the solar interior is a sort of controlled thermonuclear bomb on a giant scale.³ The theory leads to the successful calculation of the observed luminosities of stars similar to the sun and provides the basis for our current understanding of how stars shine and evolve over time. The idea that nuclear fusion powers stars is one of the cornerstones of modern astronomy and is used routinely by scientists in interpreting observations of stars and galaxies.

W.A. Fowler, Willy as he was universally known, led a team of colleagues in his Caltech Kellogg Laboratory and inspired physicists throughout the world to measure or calculate the most important details of the p-p chain and the CNO cycle. There was plenty of work to do and the experiments and the calculations were difficult. But, the work got done because understanding the specifics of solar energy generation was so interesting. Most of the efforts of Fowler and his colleagues M. Burbidge, G.R. Burbidge, F. Hoyle, and A.G.W. Cameron) soon shifted to the problem of how the heavy elements, which are needed for life, are produced in stars.

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² According to the modern theory of stellar evolution, the sun is heated to the enormous temperatures at which nuclear fusion can occur by gravitational energy released as the solar mass contracts from an initially large gas cloud. Thus, Kelvin and other nineteenth-century physicists were partially right; the release of gravitational energy ignited nuclear energy generation in the sun.

³ The sensitive dependence of the Gamow factor upon the relative energy of the two charged particles is, we now understand, what provides the temperature "thermostat'' for stars.

 

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