  Chains of first-order SUSY transformations for the spin equation are studied
in detail. It is shown that the transformation chains are related with a
olynomial pseudo-supersymmetry of the system. Simple determinant formulas for
the final Hamiltonian of a chain and for solutions of the spin equation are
derived. Applications are intended for a two-level atom in an electromagnetic
field with a possible time-dependence of the field frequency. For a specific
form of this dependence, the time oscillations of the probability to populate
the excited level disappear. Under certain conditions this probability becomes
a function tending monotonously to a constant value which can exceed 1/2.
