Carbon Nuclear Resonance Theory:

Chemists have identified over hundred chemical elements and arranged them into different rows and columns, well known as the Mendeleev Periodic Table. Of all those elements, Hydrogen (₁H¹) and Helium (₂He⁴) constitute more than 90% of the known matter. Other common elements include the Carbon, Iron etc, while gold, lanthanum are comparatively rare in the universe. For long time, the origin of these elements was a mystery. But the advancements in science and technology paved way for the scientists to guess their origin.

It has been found that Hydrogen and helium were formed, during the first few minutes after the big bang. Now, as these gases cooled, their rapid motion slowed down. So the gravity acted on them and aggregated them into dense cloud. When the temperature attained a critical value, required for fusion to occur, the hydrogen undergoes Nuclear Fusion, thus forming the first stars.

The stars derive most of their energy by the conversion of hydrogen into helium. Four protons undergo fusion to form a helium ion, which is well understood by the following reaction.

4₁H^{1 ---------------------->} ₂He⁴ + 2 ₊₁e⁰ + Energy

As long as there is enough hydrogen, this process goes on. When the star’s supply of hydrogen runs low, it faces an energy crisis. Small and medium sized stars turn into white dwarfs. But this is not the case in the stars of large mass. They can take the nuclear fusion to the next face, as they possess higher internal temperature. So what is the next step after fusion of hydrogen into helium? The direct way ahead would be to add another proton to the existing helium to form the next element, Lithium. However, this reaction won’t work because, a lithium atom consisting of two neutrons and three protons is highly unstable. Perfectly stable lithium consists of either three or four neutrons. So the next way would be to add two helium ions to from Beryllium with 4 neutrons. This is not good either, as the beryllium would disintegrate as soon as it is formed. A Stable nuclei (or atom) of beryllium consists of five neutrons. So the star is confronted with series of nuclear bottleneck.

After Beryllium, carbon is the next heaviest element. A stable element of compound consists of six protons and six neutrons. Have the stars jumped directly to carbon, skipping the formation of lithium and beryllium? Looking in this angle, the possible outcomes could be that three nuclei of helium (₂He⁴), coming at the same moment and combining to form Carbon-6 (₆C⁶). The arithmetic works out correctly (3*2*2 = 6 + 6). But there are certain challenges. Since three protons are involved, the temperature required is high. Also the probability for three helium nuclei to come together is very low. So we could finalize that two helium nuclei had combined initially and the resulting beryllium had somehow stayed long enough for third helium to hit.

A widely unknown English astronomer, Fred Hoyle, took interest in this enigma. He proposed a theory, applying Quantum Mechanics to the nuclear process. This process is explained below.

The rate at which the nuclear reactions proceed depends on the energy of the participating particles. Mostly the variation in the rate is a gentle rise or fall in efficiency, but occasionally there is a sharp spike in this rate. Physicists call this abrupt amplification as ‘resonance’. Applying Quantum mechanics, we could ascribe a wave character to a particle. Waves famously display resonance and quantum waves are not an exception to that.

Hoyle claimed that the carbon formed would be in the excited state, with energy slightly higher that the combined energies of three helium nuclei. He felt that the Helium-Beryllium system would have resonated at this mass-energy, with the small deficit provided by the kinetic energy inside the hot core of the star. This would have the effect of greatly prolonging the stability if the unstable beryllium formed. This would have provided decent time for the third helium to combine with them.

This was only a theory. It needs to be verified experimentally. Hoyle visited a group of nuclear physicists, who were working for the purpose of the Manhattan atomic bomb project, with his prediction. They decided to conduct an experiment to verify his prediction. After making necessary modifications to their existing project, the experiment was carried on and they found that Hoyle was indeed right. A resonance occurred, and just at the right energy as Hoyle calculated theoretically. This experiment confirms that the resonance will prolong the lifetime of unstable Beryllium nuclei to something about a hundred billion- billionths of a second, long enough for a triple helium fusion to occur. After the formation of carbon, the bottleneck in broken and the rest is plain sailing.

Acknowledgement : The Goldilocks Enigma by Paul Davies