  Closed orbit theory is generalized to the semiclassical calculation of
cross-correlated recurrence functions for atoms in external fields. The
cross-correlation functions are inverted by a high resolution spectral analyzer
to obtain the semiclassical eigenenergies and transition matrix elements. The
method is demonstrated for dipole transitions of the hydrogen atom in a
magnetic field. This is the first semiclassical calculation of individual
quantum transition strengths from closed orbit theory.
