Phenomenological Many-Body Exchange Forces

Phenomenological many-body exchange potentials are defined in group-theoretical analogy with the usual 2-body exchange potentials of Heisenberg, Bartlett, and Majorana. The uniform model of Wigner is then extended to include many-body Wigner and Majorana forces. The theory predicts a symmetry energy between neighboring isobars of even-odd nuclei which depends upon whether the isobar of highest T_ζ is OE or EO, where OE signifies that the odd number of particles is greater than the even number, and EO signifies the reverse. A comparison is made with such energy differences in T_ζ=3/2 and 1/2 isobars, taken from β-decay data in the range 15A59. This leads to a rough estimate of the magnitude and sign of the contribution from 3-body potentials. On this basis, the contribution from 3-body potentials is not negligible in comparison with that from 2-body potentials.