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 $\ensuremath{\cong}(\frac{{v}_{n}}{c})\ifmmode\times\else\texttimes\fi{}(\mathrm{t}\mathrm{w}\mathrm{o}\ensuremath{-}\mathrm{b}\mathrm{o}\mathrm{d}\mathrm{y}\phantom{\rule{0ex}{0ex}}\mathrm{p}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}\mathrm{s})\ensuremath{\cdots}$, $m$-body potentials $\ensuremath{\cong}{(\frac{{v}_{n}}{c})}^{m\ensuremath{-}2}\ifmmode\times\else\texttimes\fi{}(\mathrm{t}\mathrm{w}\mathrm{o}\ensuremath{-}\mathrm{b}\mathrm{o}\mathrm{d}\mathrm{y}\phantom{\rule{0ex}{0ex}}\mathrm{p}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}\mathrm{s})$, where ${v}_{n}$ 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.