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We present a new method for computing the recurrence spectra of n ≈40, m=0 lithium Rydberg atoms in strongparallel exteal electric and magnetic fields. This method is based on an extended closed-orbit theory allowing thecomputation of the scattering of the electron by the ionic core. We pay particular attention to the scaling properties,which are extremely important for understanding the correspondence between classical and quantum mechanics. Thespectra with a constant scaled electric field F=0.01 and a scaled energy e = -0.03 are recorded and compared withthose of hydrogen obtained by the standard closed-orbit theory. The result shows that the additional strong resonancestructures can be interpreted in terms of the core-scattered classical closed orbits.