Using symplectic integrator schemes, we calculate the classical trajectory of a Rydberg electron in external electric and magnetic fields. We also solve the equation of motion obtained by taking the mean values over one revolution of the electron in the undisturbed motion. The resulting secular motion is periodic. When only an electric field F is applied, as long as the modulation period in the orbital angular momentum l is longer than the revolution period, the motion agrees with the secular one and the duration for which l is much larger than its low initial value is stretched. The residence time (RT), namely, the probability of finding the electron at the distance r, is hence smaller than that at F = 0. In crossed electric and magnetic fields, the secular motion predicts that an additional time stretching due to a magnetic field occurs up to the critical value of magnetic field strength, Bc = 3 √3nF (n is the principal action). In the actual simulations, the RT near the core is smaller than that at B = 0 even beyond Bc, regardless of the magnitude of the non-Coulombic interaction C2/r2. Slow modulations in l are generated by transitions to secular motions that maintain high l, in addition to the fast modulation originating from the secular motion. When the magnetic field is so strong as to induce chaotic motion (∼4000 G for the energy of -5 cm-1), the RT is one order of magnitude as large as those in weak field cases around 40 G. In the intermediate region (> a few hundred Gauss), without a non-Coulombic interaction, the RT monotonically increases as B increases. In the presence of C2/r2, transitions from low l states to high l states occur: the RT decreases. The motions in high l states can be explained by the well-known model in which an electron bound to the core by a harmonic force moves in a magnetic field.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry