Many-Body Interactions in Atomic and Nuclear Systems

When particles interact with each other through the intervening mechanism of a field, the description of their dynamical behavior by means of action-at-a-distance potentials is only of an approximate nature. Two-body, three-body,. . . , m-body potentials may be regarded as successive stages of this approximation; their relative magnitudes are examined systematically for several types of classical and quantized fields, e. g. , electromagnetic, mesotron, etc. It is found that the description of electrons in atomic systems by the customary two-body potentials is an excellent approximation; in nuclei, independent of the details of the field, one finds: three-body potentials (v₍c) (two-body0ex{0ex}potentials), m-body potentials ({v₍c) }^m-2 (two-body0ex{0ex}potentials), where v₍ is the average velocity of the heavy particles in the nucleus. The usual description of nuclei in terms of two-body potentials cannot therefore be considered satisfactory, except in the case of the deuteron.