The coupled, two-variable integral equations that determine the four-body bound state, when the interactions are represented by separable potentials, are derived from the Schrödinger equation instead of the Yakubovsky $t$-matrix equations. The integral equations are solved numerically for simple $s$-wave potentials without resort to separable expansions of their kernels. For rank-one potentials the $\alpha$ particle is severely overbound. Sensitivity to the singlet effective range and the tensor component of the triplet interaction is discussed.

NUCLEAR STRUCTURE ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ bound state; four-body integral equations; separable potentials; singlet effective range.

• Received 12 April 1976

DOI:https://doi.org/10.1103/PhysRevC.14.685