I arrived in the United States at the end of 1940. I immediately went to Washington to work with Professor Gamow. I had practically no astronomical or astrophysical knowledge. Gamow was very interested in studying the supernova star. Exactly, in those years, nuclear physics applications had begun to explain the evolution of stars, the production of energy, the increase in luminosity. Gamow and Teller had already done work on giant stars. Gamow gave me a work by a German from 1935 to read. He said that, if a stellar mass were contracting, the protons would capture the electrons. So, I read that work and immediately went to talk to Gamow: "Look, this work cannot serve as a basis, because it does not take into account that the capture of the electron by the nucleus was accompanied by the emission of a neutrino." When I said that, Gamow put his hand on his head and said: "Oops, I think you hit the critical point. It's exactly the neutrino. This emission of neutrinos is what must produce a collapse process." When the centre of the star reaches a very high density and electrons begin to be captured, the neutrino escape will cool the centre of the star. The energy that escapes, because the neutrino passes through the mass of the star and leaves, can cause the star to collapse.
Then, we immediately wrote a note that appeared in the Physical Review. It was sent in 1940. Here is its Abstract:

It can be considered at present as definitely established that the energy production in stars is caused by various types of thermonuclear reactions taking place in their interior. Since these reaction chains usually contain the processes of p-disintegration accompanied by the emission of high speed neutrinos, and since the neutrinos can pass almost without difficulty through the body of the star, we must assume that a certain part of the total energy produced escapes into interstellar space without being noticed as the actual thermal radiation of the star. Thus, for example, in the case of the carbon-nitrogen cycle in the sun, about 7 percent of the energy produced is lost in the form of neutrino radiation. However, since, in such reaction chains, the energy taken away by neutrinos represents a definite fraction of the total energy liberation, these losses are of but secondary importance for the problem of stellar equilibrium and evolution.

We want to indicate here that the situation becomes entirely different in cases where, as the result of the progressive contraction of the star, the density and temperature in its interior become sufficiently high to permit the penetration of free electrons into different nuclei resulting in the formation of unstable isobars with smaller atomic number.

Then in Physical Review we published, in 1941, the most complete calculation about it. Here is its Abstract:

At the very high temperatures and densities which must exist in the interior of contracting stars during the later stages of their evolution, one must expect a special type of nuclear processes accompanied by the emission of a large number of neutrinos. These neutrinos penetrating almost without difficulty the body of the star, must carry away very large amounts of energy and prevent the central temperature from rising above a certain limit. This must cause a rapid contraction of the stellar body ultimately resulting in a catastrophic collapse. It is shown that energy losses through the neutrinos produced in reactions between free electrons and oxygen nuclei can cause a complete collapse of the star within the time period of half an hour. Although the main energy losses in such collapses are due to neutrino emission which escapes direct observation. the heating of the body of a collapsing star must necessarily lead to the rapid expansion of the outer layers and the tremendous increase of luminosity. It is suggested that stellar collapses of this kind are responsible for the phenomena of novae and supernovae, the difference between the two being probably due to the difference of their masses.

We call this work the Urca effect. There was a lot of speculation about why that name. This is a curious fact, because they give some explanations as if the term Urca were Ultra Rapid Catastrophe, but it is nothing like that. It was actually the name of the Urca Casino. Gamow was a very playful person, he really liked to joke. We had actually gone to play at Cassino da Urca. Then, Gamow said: "In honour of Brazil, let's call it the Urca Effect, because energy disappears as quickly there in the centre of the star as money disappears in the Urca Casino." Then it was called the Urca process.

But the history of science is a funny thing. This work was received with a certain interest, but not excessive, at that time. However, it only had repercussions and began to become very important about 20 years later. Well, it was only after the war that radio telescopes were greatly developed, and with these devices they actually discovered things that would confirm the idea that stars could explode. So, that's when the work began to acquire great interest. Well, the interesting thing is that, after 1960, I became uninterested in Astrophysics; it didn't even move me anymore.

On one occasion they called me saying that Professor Morrison was here in São Paulo and would very much like to talk to me. Morrison then asked me if I knew that the work I had done there with Gamow had become very important. I said, "No, I didn't know." He said: "Really, it is now understood that these explosions in stars play such a fundamental role. Therefore, the neutrino has become a fundamental element in the evolution of the universe, galaxies, stars, etc." Gamow had a very decent attitude. He told several people there that the neutrino idea was mine. So, Morrison wanted to know how, on that occasion, I had the idea of putting the neutrino there. I think this is a strange thing, and even stranger is asking why others hadn't thought of putting in the neutrino. It's one of those inexplicable things. There was a lot of thought, so much so that Gamow himself had given me a job to study electron capture.

Now, how come they didn't understand? At that time there was already - even Fermi had already made the theory - the idea that, in the emission of beta rays, there was the emission of a particle. In fact, the beta ray theory was presenting a difficulty, because there was a certain transition in the nucleus and an electron was emitted. The energy of the electron was not always the same. One moment it would come out with greater energy, another time it would come out with lower energy. Even Born had expressed the idea that there would be no conservation of energy in this process, in the emission of beta rays. So, in a meeting where they were discussing this subject, Pauling said: "No, that could be explained," saying that "not only the electron would be emitted, but that, along with the electron, another neutral particle of low mass would be emitted. So, part of the energy would be carried by the electron and part of the energy would be carried by the other particle." This would explain why the electron does not leave with fixed energy. The total energy would be divided between the two particles, both of which could carry energy. Then the word neutrino came up, that is, it was neutral, but it was small. To be a neutron, it would be large; the small one would be the neutrino. Then, in 1934, Fermi created a theory of emission. So, I just opened the 1935 work and thought: "But where is the neutrino? Why didn't they put the neutrino there?" And I said, "Look Morrison, I think it's not at all extraordinary that I thought about the neutrino. What's more extraordinary is that others didn't think about it. Why didn't others think? It was not an unknown effect, on the contrary. There was no direct proof yet, of course, but it was quite likely that was the mechanism.

Abstract

The evolution of the stars on the main sequence consequent to the gradual burning of the hydrogen in the central regions is examined. It is shown that, as a result of the decrease in the hydrogen content in these regions, the convective core (normally present in a star) eventually gives place to an isothermal core. It is further shown that there is an upper limit ( 10 per cent) to the fraction of the total mass of hydrogen which can thus be exhausted. Some further remarks on what is to be expected beyond this point are also made.

General considerations.

The problem of stellar evolution is intimately connected with that of energy production in the stars. Both Bethe and Weizsacker showed that the source of the energy radiated by the main-sequence stars is the transformation of hydrogen into helium through the so-called "carbon cycle." On the basis of the Bethe-Weizsacker theory, G Gamow outlined a picture of stellar evolution.

The Gamow theory is based on three fundamental assumptions: (a) the stars evolve gradually through a sequence of equilibrium configurations ; (b) the successive equilibrium configurations are homologous; and (c) the nuclear reaction continues to take place until the entire hydrogen in the star is exhausted.

Such a picture of stellar evolution presents certain difficulties. The assumption that the successive equilibrium configurations are homologous cannot be expected to be rigorously valid; for the nuclear reaction reduces the hydrogen content in the neighbourhood of the centre of the star, and therefore the molecular weight in this region becomes increasingly larger than that of the rest of the stellar material, unless we suppose that a diffusion process rapidly mixes the whole of the stellar mass. The only region in which the mixing can be supposed to take place is the Cowling convective core; but stellar configurations in which the ratios of the molecular weights of the convective core and envelope are different are not homologous, contrary to assumption (b).

Another difficulty of the Gamow theory is the uncertainty of the amount of hydrogen that can be burned. It is important to determine this quantity accurately, since its value affects essentially the final luminosity and effective temperature given by the homology formulae. Again it does not appear probable that the entire hydrogen content could be exhausted, since it would imply a thorough mixing of the stellar material, in order that the entire content could reach the centre, where the nuclear reactions principally take place. Sometimes it is assumed that only 14.5 per cent of the entire hydrogen content (which is the fraction of the total mass contained inside the Cowling convective core) participate in the carbon cycle. This hypothesis; though apparently more plausible, should be further amended, for it would be valid only if the turbulence in the convective core mixed the material rapidly enough to avoid the formation of an isothermal region at the centre which would tend to stop convection. However, even if there is no formation of an isothermal core, the fraction of the stellar mass contained in the convective region would be expected to diminish as the molecular weight increases relatively to that of the rest of the stellar material. We shall obtain the precise amount of this diminution; but it is clear that only a small fraction of the stellar hydrogen could be burned if only the hydrogen in the convective core was available for the nuclear reaction. We should not conclude, however, that only that small amount of hydrogen could be burned, since there is the possibility of the formation of an isothermal core after the exhaustion of hydrogen has stopped the convection in the central regions. Such a possibility results, as we shall show, from the existence of equilibrium configurations formed by isothermal cores surrounded by point-source envelopes, the mass of the isothermal cores being larger than that of the limiting convective core of vanishing hydrogen content.

In the isothermal core-radiative envelope models the nuclear reaction takes place at the interface of core and envelope. The fraction of the mass contained in the isothermal core cannot exceed a fixed value, so that the nuclear reaction will finally cease when the mass in the core reaches its maximum value. A possibility which should not be overlooked is that, during the transition to gravitational energy production, larger cores could be formed that would not be equilibrium configurations; however, the lifetime of such configurations is presumably small, so that in a first approximation we can neglect such possibilities. ...
...
So far we have discussed the evolution of a star only during the relatively early stages of the exhaustion of hydrogen in its, central regions. The question now arises as to what can be said concerning the evolution during the later stages, i.e., after the isothermal core has grown to include the maximum possible mass. When this stage has been reached, the liberation of energy from the carbon cycle must cease, and we should expect the star to adjust itself to a contractive model and evolve according to the Helmholtz-Kelvin time scale. But this gravitational contraction cannot proceed indefinitely, for with continued contraction the temperature at the interface between the central regions exhausted of hydrogen and the outer envelope containing hydrogen will steadily increase. And, when the temperature exceeds a certain value, the nuclear reactions will start, and the carbon cycle will again become operative. At first, the energy liberated by the nuclear processes will be small compared to the gravitational liberation. But very soon, because of the high-temperature sensitiveness of the nuclear reactions, the energy liberation from the carbon cycle will exceed the liberation of energy by the gravitational contraction. In other words, the central regions must again tend to become isothermal. However, no equilibrium configuration is possible under these circumstances: for the isothermal core would have to contain a greater fraction of the total mass than is possible under equilibrium conditions. It therefore appears difficult to escape the conclusion that beyond this point the star must evolve through nonequilibrium configurations. It is difficult to visualise what form these nonequilibrium transformations will take; but, whatever their precise nature, they must depend critically on whether the mass of the star is greater or less than the upper limit $M_{3}$ to the mass of degenerate configurations. For masses less than $M_{3}$ the nonequilibrium transformations need not take particularly violent forms, as finite degenerate white-dwarf states exist for these stars. However, when $M > M_{3}$, the star must eject the excess mass first, before it can evolve through a sequence of composite models consisting of degenerate cores and gaseous envelopes toward the completely degenerate state. Our present conclusions tend to confirm a suggestion made by one of us (S. C.) on different occasions that the supernova phenomenon may result from the inability of a star of mass greater than $M_{3}$ to settle down to the final state of complete degeneracy without getting rid of the excess mass.

Meanwhile, a new factor had entered into the situation, because of the possible exhaustion of hydrogen. Because of the increase in energy-generation with temperature, this exhaustion takes place first near the centre. Because it leaves the gas heavier, it prevents mixing with unexhausted gas. Thus Schönberg and Chandrasekhar were led in 1942 to discuss models in which a radiative envelope surrounded either a convective core of higher molecular weight, still generating all the star's energy, or an exhausted isothermal core of higher molecular weight, the energy now being generated in a thin shell at the interface between envelope and core. They found it impossible to construct models in which more than about 10 per cent of the mass was included in the exhausted core. ...

The exhaustion implied that the assumption of uniform composition, regularly made so far, had now to be abandoned. This altered the predicted course of evolution of a star in the Hertzsprung-Russell diagram from that for fully mixed stars, and removed a discrepancy with observation. ...

A fruitful application of inhomogeneities of composition was to the problem of red giants. According to Eddington, there was no problem; the giants obeyed his mass-luminosity law just as well as main-sequence stars. But when it was recognised that there ought to be a radius-luminosity law also, the existence of a problem could not be doubted. Opik in 1939, and Hoyle and Lyttleton soon after, suggested that the solution might be found in an inhomoneity of composition. The matter was investigated by a large number of other workers, notably the Bondis, and Schwarzschild and his co-workers. They were able to show that stars of large radius, consisting of a dense core surrounded by a tenuous envelope, could exist if the molecular weight in the core markedly exceeded that in the envelope ...

The most remarkable result came, however, when Schwarzschild and Sandage in 1952 set to work to find what happened to a star which had burnt so much of its hydrogen that, according to Schönberg and Chandrasekhar, no static model existed. The reason for its non-existence is that the core, having no sources of energy, tends to contract and (according to Lane's law) becomes hotter; this makes the envelope immediately round the core generate too much energy, and the envelope expands. ...

The particle dynamics in the world-manifold is taken as the foundation of the world-geometry in a Hamiltonian formalism with a scalar mass Hamiltonian not involving the value of the mass. The Riemannian metric is obtained from the linear relation between the covariant and contravariant vectors of the mechanical momentum of a particle involved in the formalism. The basic differential equations for the world-lines of the particles allow one to define a new kind of parameter called the duration, with the same dimension as the Einstein gravitational constant. The proper-time parameter is defined in terms of the duration and the mass Hamiltonian, before the introduction of the Riemannian metric. The metric tensor $g(x)$ comes in as a mechanical field related to the inertial properties of the particles, which determines the mass Hamiltonian of the free particles. The symmetry of $g(x)$ is a consequence of the mass Hamiltonian formalism. Our classical Hamiltonian formalism is naturally related to the wave equations of the relativistic quantum mechanics, and leads to a generalisation of those wave equations.