The equivalence of effective two-body and two-body plus three-body forces for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system is investigated. Sussex matrix elements are modified to bind the $A=3\mathrm{}$ and $A=4\mathrm{}$ systems in both a two-body as well as three-body approach. Both approaches predict reasonably accurate binding energies and rms radii for the ground states of light systems although these methods do not accurately predict the first excited state in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system.

NUCLEAR STRUCTURE Three-body forces in the $A=3\mathrm{}$ and $A=4\mathrm{}$ systems.

• Received 18 March 1977

DOI:https://doi.org/10.1103/PhysRevC.16.2420