In order for complex structures such as life to exist, it is necessary for the building blocks of matter - the atoms - to be capable of binding together. For such complex structures as life to exist for the lengths of time necessary for Darwinian evolution to function, atoms and molecules must be very stable indeed. In this Chapter the conditions leading to the stability of the nuclei of atoms are explained. Chapter 10 addresses the stability of atoms themselves, that is the structures formed of nuclei and orbiting electrons. Chapter 11 considers the stability of molecules: the bound states of many atoms.
The discussion of the stability of nuclei uses an approximation for their binding energy known as the liquid drop model. The predictions of the model are tested against the known stability or instability of nuclei in this universe. This covers both fission and weak-force mediated radioactive decays. Having gained confidence that the model is a reasonably indicative guide, the implications of varying the strength of the strong nuclear force (gs) and the electrostatic force (e) are assessed.
As regards fissile instability, the criteria usually adopted are: (a)an increase in total binding energy, or, (b)instability with respect to small shape changes. These are considered but found to be little or no more restrictive than a much simpler criterion, namely that the binding energy be greater than zero. Whichever criterion is employed, instability against fission results from an increase in the relative strength of the electrostatic force compared with the strong-nuclear force. Changing the strength of both these forces equally would not lead to fissile instability. (NB: In this context, 'force' strictly means 'contribution to the binding energy'). The factor by which the ratio of the electrostatic force to strong-nuclear force must be increased to make nuclei unstable is found as a function of atomic number, Z.
In the case of carbon, and assuming no change in the electrostatic energy, fissile instability occurs if gs is reduced by a factor of between 0.54 and 0.72, depending upon the assumed dependence of the binding energy on gs. If the nuclear force is unchanged, nuclear instability occurs in carbon if e is increased by a factor of 3.5. Heavier elements are more sensitive to changes in the strength of the forces, becoming unstable for smaller percentage changes. The sensitivity of nuclear stability to gs is exaggerated by the fact that the binding energy varies as gs^4, or perhaps more sensitively still. Thus, the lower bound for gs of 0.54-0.72 for carbon results from a change in the relative electrostatic:nuclear binding energies of a factor of ~12.
Stability against the weak-force mediated decay modes, beta decay or electron capture, can be expressed in terms of the binding energy difference of nuclei with Z differing by 1. Specifically, beta decay is not possible if B(Z)-B(Z+1) exceeds the mass deficit Mn - Mp - me, whereas electron capture is not possible if B(Z-1)-B(Z) is less than this mass deficit. Decays by positron emission are also subsumed in these criteria. Thus, for example, weak decay modes can be induced by reducing sufficiently the binding energy contributions of both the strong-nuclear force and the electrostatic force in proportion. To induce weak decay instability in carbon, both these binding energy contributions must be reduced by a factor of 0.02. This corresponds to a reduction in gs by a factor of between 0.38 and 0.66, with a simultaneous reduction in e by a factor of between 0.14 and 0.38. The corresponding results are presented in this Chapter for other biologically important elements.
Weak decays induced by non-proportional changes in the force strengths have also been considered. Specifically we assume that their binding energy contributions vary in inverse proportion. This leads to a more restrictive lower bound on gs than the previous cases. For carbon, weak decay modes occur if the nuclear force component of the binding energy is reduced by x0.333, whilst the electrostatic energy is increased byx3.33. This corresponds to a reduction in gs by a factor of between 0.76 and 0.83, with a simultaneous increase in e by a factor of between 1.74 and 2.3. Heavier elements are again found to be more sensitive to changes in the strength of the forces, becoming unstable for smaller percentage changes.
These results suggest that nuclear stability requires a Type C1, single-sided 'coincidence' in gs, and also a Type D1, single-sided 'coincidence' in e. However, the sensitivity of nuclear stability to gs is exaggerated by the fact that the binding energy varies as gs^4, or perhaps more sensitively still. In terms of binding energies, both 'coincidences' would be classed as Type D1, single-sided.
