We show that the distribution of quantum numbers of Rydberg states does not
only depend on the field strength and wavelength of the laser which the atom is
exposed to, but that it also changes significantly with the duration of the
laser pulse. We provide an intuitive explanation for the underlying mechanism
and derive a scaling law for the position of the peak in the quantum number
distribution on the pulse duration. The new analytic description for the
electron's movement in the superposed laser and Coulomb field (applied in the
study of quantum numbers) is then used to explain the decrease of the Rydberg
yield with longer pulse durations. This description stands in contrast to the
concepts that explained the decrease so far and also reveals that
approximations which neglect Coulomb effects during propagation are not
sufficient in cases such as this.Comment: 8 pages, 8 figure