Abstract
A scalar model nonlinear field theory is constructed from an action principle so that the inherent "limit cycle solutions" of the theory correspond to the eigensolutions of the conventional Hartree equation for helium. The properties of the "limit cycle transition" solutions are discussed and offer an alternative method, for solving the nonlinear Hartree eigenvalue equation, which has the distinct advantage of not requiring the spherical averaging approximation inherent in the conventional "self-consistent field" calculations. The elements which control the speed of convergence of a limit cycle transition solution into a limit cycle solution are analyzed; a method of speeding up the process in order to make it competitive, in terms of computer time, with the conventional self-consistent field calculation is discussed.
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