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 6 He as a 4 He core plus a concentric neutron shell comprising a holomorphic pair of neutrons, and the 8 He 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 4 He core from the center of mass. The calculations for the charge and matter radii of 4,6,8 He agree closely with observed values. Similar QGT calculation of the sizes of the self-conjugate A=4n nuclei { 4 He, 8 Be, 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, 32 S, 36 Ar, 40 Ca} also agree well with experiment.
OverviewWe will show that the matter and charge radii of the helium isotopes can be calculated ab initio purely from the geometry of