For isotropic confining Ioffe-Pritchard or TOP potentials, a valence f
ermion trapped with a closed core of other fermions can be described b
y an analytical effective one-particle model with a physical eigenspec
trum. Related constructions exist for Paul and Penning traps. The anal
ytical models arise from quantum-mechanical supersymmetry. (C) 1997 El
sevier Science B.V.