Phase transitions critical nuclear charges

From the present calculations, the expectation value of the operator r 2 may provide a direct physical picture about the thermodynamic stability and dissociation of Hj-like molecules. As shown in Fig. 16, there is a vertical jump of the mean value ru at Xc. We note that there are similarities and differences between helium-like atoms and Hj-like molecules. In Section V.A of heliumlike systems, based on an infinite mass assumption, we show that the electron at the critical point leaves the atom with zero kinetic energy in a first-order phase transition. This limit corresponds to the ionization of an electron as the nuclear charge varies. For the Hj-like molecules, the two protons move in an electronic potential with a mass-polarization term. They move apart as X approaches its critical point and the system approaches its dissociation limit through a first-order phase transition. 

---