Electronic Structure Critical Parameters For the Lithium Isoelectronic Series

The finite-size scaling method is used to calculate the critical parameters for the lithium isoelectronic series. The critical nuclear charge, which is the minimum charge necessary to bind three electrons, for the ground state was found to be $Z_c\simeq 2$. Results show that the analytical behavior of the energy as a function of the nuclear charge for lithium is completely different from that of helium. Analogy with standard phase transitions show that for helium, the transition from a bound state to a continuum is “first order,” while lithium exhibits a “second order phase transition.”