  Beginning with a Heisenberg spin Hamiltonian for the manganese ions in the
Mn_12 Ac molecule, we find a number of low-energy states of the system. We use
these states to solve the time-dependent Schrodinger equation and find the
magnetization of the molecule in the presence of a slowly varying magnetic
field. We study the effects of the field sweep rate, fourth order anisotropic
spin interactions and a transverse field on the weights of the different states
as well as the magnetization steps which are known to occur in the hysteresis
plots in this system. We find that the fourth order term and a slow field sweep
rate are crucial for obtaining prominent steps in magnetization in the
hysteresis plots.
