Superalgebras for the Penning trap

The Hamiltonian describing a single fermion in a Penning trap is shown to be supersymmetric in certain cases. The supersymmetries of interest occur when the ratio of the cyclotron frequency to the axial frequency is 3/2 and the particle has anomalous magnetic moment 4/3 or 2/3. At these supersymmetric points, the spectrum shows uniformly spaced crossed levels. The associated superalgebras are su(2\1) and su(1\1). The phase space for this problem has an osp(2\6) structure and contains all the degeneracy superalgebras. (C) 2001 American Institute of Physics.