A complete derivation of a new two-variable integrodifferential equation valid for threeand many-boson systems is given here for the first time, and it is shown to be exact if all correlations higher than those of two-body type can be neglected. Its equivalence to the Faddeev equation for three bodies and its applicability to many-body systems are discussed in detail. Three-body forces are included. It is shown that the threeand four-body binding energies obtained by means of this equation are in good agreement with those obtained from the most sophisticated variational, Faddeev, and Faddeev-Yakubovsky calculations. This indicates that our new two-variable integrodifferential equation should also be useful for larger systems, in particular since unlike other methods it does not suffer from the disadvantage of rapidly increasing complexity with A. We also show that a simple adiabatic method for the solution of this equation {and hence also for the Faddeev equation) is quite sufficient, due to the closeness of the upper and lower bounds obtained in this way. Finally we apply the adiabatic method to nuclear three-body scattering and even include the effect of breakup for spin-dependent forces. It is found that asymptotic behavior is reached for a value of the hyperradius of the order of 3S fm.where

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Results obtained by solving Alt-Grassberger-Sandhas ͑AGS͒-type integral equations for the photodisintegration of 4 He, employing the Malfliet-Tjon potential, are compared with the latest experimental data. Good agreement between theory and experiment is found in electric dipole approximation for the total cross section, but the differential cross sections differ at higher energies. This discrepancy is reduced, but not fully removed by taking into account the electric quadrupole contributions. In order to get some feeling for the sensitivity to the underlying potential, we also show calculations based on the Yamaguchi potential. They differ from the Malfliet-Tjon results in a way which resembles the trends known from triton photodisintegration. ͓S0556-

The inverse problem for quantal potential scattering at fixed energy is solved exactly for a scattering function which has the form of a product of a complex rational function of angular momentum times the scattering function of a given reference potential. Schematic numerical studies indicate the viability of the method in realistic applications.

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The position of the two-particle resonance poles is shown to be the dominant factor in a number of interesting phenomena appearing in the energy spectra of bound three-and four-particle systems with separable two-particle interactions. The validity of the boundstate pole dominance assumption in few-particle systems is shown to depend on the location of the two-particle resonance poles. These results generalize the ground state collapse obtained earlier for the Tabakin rank-one separable interactions in the triton. However, our results also indicate that the collapse does not necessarily occur for more general nonlocal interactions.

The inverse problem for quantal potential scattering at fixed energy is solved for a class of scattering functions which represent nonrational modifications of the rational functions of angular momentum considered in the "Bargmann" method of previous work.The new scheme has a wider range of applicability. This is demonstrated by means of numerical examples.