Radius perturbation theory and its application to pionic atoms

Radius perturbation theory, starting from a variational principle, is developed for a two particle interaction, consisting of two parts, an external and the internal "core" part. The small parameters of the theory are the ratios of the core radius to the characteristic length parameters of the outer potential, such as the radius, the size of the bound state orbits and so on. The simple formulae for core corrections to scattering amplitudes, wave functions and bound state levels of the external potential are obtained. Comparison of our approximation with exact solutions for pionic atoms and the nucléon-nucléon system, as well as with results obtained in other approximation theories, is given. The present theory includes from the beginning the finite size of the core interaction and therefore its first approximation to the energy shifts of pionic atoms yields much better results than the usual zero range approximation to which our theory reduces in the limit of a zero core size. The present theory is able also to reproduce both the form and the magnitude of the pion wave function reasonably well.