4.4. Tuning Levels of Heavier Nuclei

The most celebrated nuclear tunings, first noticed by Salpeter and Hoyle, involve the resonant levels of carbon and oxygen nuclei. The excited resonance level of ¹²C* at 7.65 MeV lies just 0.3MeV above the 7.3667 MeV energy of ⁸Be + ⁴He, allowing rapid enough reactions for carbon to form before the unstable ⁸Be decays. On the other hand the level of ¹⁶O at 7.1187 MeV lies just below that of ¹²C + ⁴He at 7.1616 MeV; if it were higher by just 0.043 MeV, reactions to oxygen would quickly destroy the carbon. The way these interlocking levels depend on m_d, m_u, m_e is too hard to compute from first principles in detail, but Jeltema and Sher (1999) have recently estimated the effect on the nuclear potential of adjusting the Higgs parameter v, tracing its effect on the first reaction above through the work of Oberhummer et al. (1994) and Livio et al. (1989). In this way they estimate a lower bound v / v₀ > 0.9. Oberhummer et al. (1999) have recently computed the dependence of these levels in a simple cluster model for the nuclei, and conclude that the strength of the nuclear force needs to be tuned to the 1% level. This can be interpreted to mean that the products would be radically altered if m_u + m_d changed by even a few percent of m_u + m_d, on the order of 0.05 MeV.