Hadronic Atoms in Momentum Space

A momentum space method for hadronic atoms is developed to incorporate relativistic, nonlocal, complex hadron-nucleus interactions. The logarithmic singularity due to the Coulomb interaction has been treated by Lande's subtraction technique. Vacuum polarization, and both nuclear and pion finite-size effects have been included in this momentum space method. Precision eigenvalues and eigenfunctions for the Schroedinger, relativistic Schroedinger, Klein-Gordon (of various types), and Dirac equations have been calculated using a rapid and convenient inverse iteration method. Reliability of this novel approach is confirmed by comparing with parallel coordinate space methods. Several illustrative applications are made to simple pionic, and kaonic cases to demonstrate possible applications. For example, it is found that: (1) to extract the pion size from pionic atom data, energy shifts must be measured to an accuracy of better than 50 eV; (2) to determine the form of Klein-Gordon equations appropriate for kaonic atoms, one needs a precision of better than 20 eV; (3) the finite-range of the ..pi..-N interaction plays a non-negligible role and, therefore, should be carefully included in the pion-nucleus interaction. More extensive applications of these methods are suggested.