Circular Rydberg states in parallel electric and magnetic fields

Circular and nearby Rydberg states in parallel electric and magnetic fields are studied using semiclassical and exact quantum-mechanical methods. A wide range of external field strengths is considered including regimes close to and beyond the classical ionization thresholds. When the tunneling decay rates due to the presence of the electric field are negligible, semiclassical eigenvalues and wave functions represent very good approximations. The combination of the complex-coordinate method with a discrete variable representation and the Lanczos iterative scheme provides an efficient way to calculate exactly the complex eigenvalues corresponding to the resonances emerging from the quasibound circular and nearby Rydberg states. Magnetic fields have in general a stabilizing effect, diminishing the decay rates, although there are cases showing the nonmonotonic (oscillatory) dependences of the imaginary parts of the eigenvalues with increasing magnetic field strength.