CRITICAL PARAMETERS FOR THE HELIUM-LIKE ATOMS - A PHENOMENOLOGICAL RENORMALIZATION STUDY

A mapping between the quantum few-body problem and its classical mecha nics pseudo-system analog is used to study the critical parameters for the helium isoelectronic sequence. The critical point is the critical value of the nuclear charge Z(c), for which the energy of a bound sta te becomes degenerate with a threshold. A finite-size scaling ansatz i n the form of a phenomenological renormalization equation is used to o btain very accurate results for the critical point of the ground-state energy, lambda(c) = 1/Z(c) = 1 .0976+/-0.0004, as well as for the exc ited 2p(2) P-3 state, lambda(c) = 1.0058+/-0.0017. The results for the critical exponents alpha and nu are also included. (C) 1998 American Institute of Physics.