A mapping between the quantum few-body problem and its classical mechanics 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 state becomes degenerate with a threshold. A finite-size scaling ansatz in the form of a phenomenological renormalization equation is used to obtain 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 excited 2p(2) P-3 state, lambda(c) = 1.0058+/-0.0017. The results for the critical exponents alpha and nu are also included.