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Beta‐decay half‐lives for the free neutron, for 6He and 8He, and for 8Li are calculated ab initio from geometrical thermodynamics arguments, independently of any quantum mechanics. Half‐lives for the decay of 8Be to two alphas and for the disintegration of the tetraneutron are also calculated. The calculated values are close to those experimentally observed. [ABSTRACT FROM AUTHOR]

The nuclear matter and charge radii of the helium isotopes (A=4,6,8) are calculated by quantitative geometrical thermodynamics (QGT) taking as input the symmetry of the alpha‐particle, the very weak binding (and hence halo nature) of the heavier helium isotopes, and a characteristic length scale given by the proton size. The results follow by considering each isotope in its ground state, with QGT representing each system as a maximum entropy configuration that conforms to the Holographic Principle. This allows key geometric parameters to be determined from the number of degrees of freedom available. QGT treats 6He as a 4He core plus a concentric neutron shell comprising a holomorphic pair of neutrons, and the 8He neutron halo is treated as a holomorphic pair of holomorphic pairs. Considering that the information content of each system allows a correlation angle of 2π/3 between the holomorphic entities to be inferred, then the charge radii of the three isotopes can be calculated from the displacement of the 4He core from the center of mass. The calculations for the charge and matter radii of 4,6,8He agree closely with observed values. Similar QGT calculation of the sizes of the self‐conjugate A=4n nuclei {4He,8Be,12C,16O,20Ne,24Mg,28Si,32S,36Ar,40Ca} also agree well with experiment. [ABSTRACT FROM AUTHOR]

This work proves that stability of C60 is a geometrical property of the thermodynamics of the system: a significant methodological advance since a detailed treatment of the energetics may be avoidable. This approach may be fruitful, not only for fullerenes but also for general problems of molecular stability and in other applications of conformational chemistry. For the non‐chiral C60, C384, and the weakly‐chiral C28, C76 and C380 (of these, C380 and C384 are classed as "unspirallable"), Schlegel projections are used to show that these fullerenes can all be represented by pairs of spirals counter‐propagating in anti‐parallel (C2) symmetry. For C60, the high symmetry is used to construct an analytical approximation for the spherical double‐spirals, shown mathematically to be Maximum Entropy (MaxEnt) using the formalism of Quantitative Geometrical Thermodynamics (QGT). Therefore C60 is necessarily stable. This MaxEnt stability criterion is general, depending only on the geometry and not the kinematics of the system. The sense and degree of chirality for C76 and C380 is also quantified using a Shannon entropy‐based fragmentation metric. [ABSTRACT FROM AUTHOR]