The CFHHM (Correlation Function Hyperspherical Harmonic Method) is a method of directly solving the Schroedinger equation of the few-body problem. It has been applied to several atomic physics three-body problems, the prototype of which is the Helium atom. The extension to the four-body problem is in progress. The method is usually contrasted with the variational method in the sense that the latter is formulated to obtain a good value of the energy only, while in CFHHM, other observables are obtained with comparable accuracy. This is possible because the CFHHM wave function is a true (numerical) solution of the Schroedinger equation and therefore has accurate local properties and uniform accuracy over a finite region of the configuration space.

The method is being developed in collaboration with V.B. Mandelzweig of Hebrew University, Jerusalem, and M. Haftel of Naval Research Laboratory, Washington.

The main achievements have been the then best value of the annihilation rate of the positronium negative ion (1993), the confirmation that the Lamb shift discrepancy between theory and experiment for the first excited state of Helium atom is not caused by possible bad convergence of the variational wave functions (1994), and the best values of the sticking probability and fusion rate from the ground state of the muonic deuteron-triton molecule (1995). (See the bibliography.)

The following information is mostly for internal use.

The results of the calculation of the Muonic Helium-4 atom ground state properties by CFHHM using a nonlinear correlation function are presented here. We attempted primarily to obtain a good value of the hyperfine splitting of the ground state where there is discrepancy within the literature. A fast-converging parametrization of the correlation function was found after a considerable effort. We succeeded to make the rsults converge better than the discrepancies in the literature among other methods.

The results of the calculation of the Muonic Helium-3 atom ground state properties by CFHHM using a nonlinear correlation function are presented here.