An approximate method for three-body bound atomic systems

Abstract

<p>The Feshbach-Rubinow approximation which is one of the many approximate methods to solve three-body problems was first applied to the triton problem. In this approximation, the three-body problem is reduced to an equivalent two-body problem and the total three-body wavefunction is assumed to depend on a single non-negative variable. The problem then reduces to the solving of a single second order differential equation. When this approximation is made in the atomic three-body problem of the helium atom and helium-like ions, the Schrödinger-like equation that is obtained is analytically solvable, yielding reasonable results for the ground-state energy. Calculations have previously been done with just one variational parameter in the variable on which the wavefunction depends. In this thesis, the definition of the variable has been modified on physical grounds to take better account of screening, and contains two variational parameters. Analytic solutions of the differential equation can again be found, and improved numerical results are obtained. These are compared with the results obtained from the more elaborate K-harmonics approach.</p>