The three-body nuclear interaction in K-40

Abstract

An estimate of the effective three-body nuclear interaction between the nucleons outside closed subshells in K⁴⁰ is made by comparing the low-lying energy levels of Cl³⁸ and K⁴⁰. Use is made of the fact that, in jj coupling, and for an arbitrary two-body interaction, the d_3/2^±1f_7/2 levels of one nucleus may be calculated from those of the other. After making a plausible calculation of the effects due to departures from the pure coupling scheme, we find a residual discrepancy between prediction and experiment which can be reasonably explained by invoking a repulsive three-body interaction. An argument, based on detailed features of the interconfiguration effects, suggests indeed that such a three-body interaction is required; if we assume this to be of short range, its magnitude is such that it contributes between 50 and 250 kev (for different J values) to the energy of the four outside nucleons in K⁴⁰. These magnitudes should, at least, define a reasonable upper limit to the allowable three-body interaction.