We study a three-dimensional quantum-mechanical supersymmetric model, characterized by a potential with central, spin-spin, and tensor terms, which describes the interaction of two spin-(1/2) particles, each one endowed with an extra internal charge. A particular realization of this model reproduces the long-range behavior of the nucleon-nucleon interaction for each isospin channel. We discuss the complete set of commuting operators for the system paying special attention to the fermionic number operator which is peculiar to supersymmetric systems. We also consider the effect of the supersymmetry generators upon such a set. In terms of the radial functions, we explicitly write down the full set of first-order coupled differential equations which define any N=1 supersymmetric system. They reflect the fact that the supersymmetry generators act as raising and lowering operators among the different channels of the interaction. Using this information we analyze the scattering regime of the model and obtain the constraints that supersymmetry imposes upon the mixing angles and phase shifts of the system. These predictions are illustrated by independently solving the example of a spherical-well superpotential. Finally we discuss the problem of spontaneous supersymmetry breaking in our model.

• Received 15 April 1985

DOI:https://doi.org/10.1103/PhysRevD.32.2174