An astrophysical application: alpha-capture reactions

Stars are ideal places for manufacturing elements such as carbon and oxygen, which are the basic constituents of planets and people. All those elements that have been formed, though, very much depend on some remarkable coincidences in the laws of physics, sometimes also called the ‘antropic’ principle.

About 75 % of a star is hydrogen, about 25 % is helium and a mere 1 % or so consists of heavier elements: this proportion is an important clue that all heavier elements (C, 0, . . .) have been manufactured inside of the stars. This process of nuclear synthesis is quite well understood (see Fowler 1984), though a number of key difficulties remained for some time. It was known how the present abundances of hydrogen and helium and some other light elements such as deuterium and lithium were created in the early phase of the universe formation, starting from the ‘standard’ model. Even early studies in 1950 by Gamow indicated the difficulties of forming heavier elements by synthesis inside stars. But how do stars perform this ‘trick’?

We know that the nucleus 4He is extremely stable (228 MeV of binding energy) and so, nuclei which form an a-like composition show an increased stability compared with nearby nuclei. Carbon (3 a particles) and oxygen (4a particles) are particularly stable elements in that respect. Once these elements are formed in the right quantities, heavier element formation looks quite straightforward using the subsequent interaction with a-particles (in stars or in the laboratory).

A problem showed up, however, at the very first stages. Two ‘He nuclei can form*Be if they have the correct kinetic energy (Q = -0.094 MeV). The nucleus ‘Be, though, is extremely unstable, breaking apart again into two ‘He nuclei, within a lifetime of only z lO-” s. So, how then can 12C be formed which even needs an extra ‘He nucleus to merge with *Be to form a ’*C nucleus.

In 1952, Salpeter suggested that 12Cmight be formed in a rapid two-step process (see figure le.1) with two 4He nuclei, colliding to form a *Be nucleus which was then hit by a third ‘He nucleus in the very short time before desintegration took place. Hoyle, though, puzzled out that, even though the above process looked highly exotic and unprobable, the presence of a resonance level in I2C might make the process feasible. This coincidence, proved later by Fowler, allows indeed the formation of 12C and thus of all heavier elements. When two nuclei collide and stick together, the new nucleus that is formed carries the combined mass (minus the mass defect caused by the strong interaction forces) plus the combined, relative kinetic energy of motion. It now occurs that in the reaction

‘Be + ‘He + T4He -+ I2C*,

a resonance in I2C* is formed at 7.654 MeV excitation energy and a COM kinetic energy of 0.287 MeV is needed to come into ‘resonance’ with the excited state in 12C. The temperature inside the stars is such that in He-burning, the thermal motion can supply this small energy excess.

The combined mass M’(*Be)c2+ M’(‘He)c’ = 7.367 MeV, just about 4% less than the ’*C* excited state of 7.654 MeV. It is this coincidence which has allowed “C formation and that of heavier elements (figure le.2) (Gribben and Rees 1990 and Livio et a1 1989).