Abstract
The Faddeev-Yakubovsky theory is applied to the system of ${(^{4}\mathrm{He})}_{4}$ interacting pairwise through a realistic He-He potential. The $S$-wave two-body $t$ matrix is obtained using the unitary pole expansion method, while the $S$-wave [3+1] and [2+2] subamplitudes are obtained by the Hilbert-Schmidt and the energy-dependent pole expansion (EDPE) methods. The convergences of the latter subamplitudes are tested and the superiority of the EDPE over the Hilbert-Schmidt expansion (HSE) is confirmed. The present results also confirm the results of a previous calculation using the ATMS method (amalgamation of two-body correlations into the multiple-scattering process).
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