  We have obtained new inelastic neutron scattering (INS) data for the
molecular magnet Mn12-acetate which exhibit at least six magnetic peaks in the
energy range 5-35 meV. These are compared with a microscopic Heisenberg model
for the 12 quantum spins localised on the Mn ions, coupled by four inequivalent
magnetic exchange constants. A fit to the magnetic susceptibility under the
constraint that the spin of the ground state be S=10 yields two dominant
exchange constants of very similar value, J1 ~ J2 ~ 65 K (~ 5.5 meV), and two
smaller exchange constants J3 and J4. We compute the low-lying excitations by
exact numerical diagonalisation and demonstrate that the parameters determined
from the ground state and susceptibility fit provide qualitative agreement with
the excitations observed by INS.
