This excited state of the
carbon nucleus is 7.65 million electron volts (MeV) above the energy of the
carbon nucleus in its normal state, the state of lowest energy. Calculations [M. Livio, D. Hollowell, A.
Weiss, and J. W, Truran, Nature 340, 281 (1989)] show that it would be
necessary to increase the energy of the excited state by considerably more than
0.06 MeV in order significantly to reduce the amount of carbon and heavier
elements produced in stars. Since 0.06
MeV is less than one percent of 7.65 MeV, this may look like some sort of fine
tuning is at work. But, as Livio et al.
point out, if we think of this excited state of the carbon nucleus as an
unstable state of a beryllium nucleus and a helium nucleus, then we should
compare 0.06 MeV with the energy of the excited state relative to the total
energy of a beryllium nucleus and a helium nucleus, which is only 0.281 MeV,
rather than with the energy of the normal state. Since 0.06 MeV is 21 percent of 0.281 MeV, this is not a very
impressive example of fine tuning.
Recent calculations [S. H. Hong and S. J. Lee, nucl-th/9903001, to be
published] show that in fact there would be expected to be an unstable state of
a beryllium nucleus and a helium nucleus at about this energy, with no fine
tuning needed.
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