Introduction

Abstract

The main object of experiments in the field of β-decay is to obtain information about form factors. Form factors can be expressed in terms of matrix elements if it is assumed that the weak interaction causes the nucleons inside the nucleus to decay like free particles. Precise values for the above quantities, however, can be extracted only if all effects due to the electromagnetic interaction between the β-particles and the nucleus are properly taken into account. Of major importance is the distortion of the wave function of the emitted β-particle by the electrostatic Coulomb field of the nucleus. The most obvious effect of this distortion of the wave function is that it strongly affects the shape of all β-decay spectra and makes it necessary to introduce the so-called Fermi-function. To obtain the distortions of the wave functions, one has to solve the Dirac equation for an unbound electron in the field of a nucleus. For the exact solution of this problem one has to consider the finite size of the nucleus as well as the screening of the nuclear electrostatic field by the orbital electrons. Such a solution can only be obtained numerically.