Statistics and Correlation Properties of Diamagnetic High Rydberg Hydrogen Atom

The spectra of Rydberg hydrogen atom in magnetic fields have beencalculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 (2006) 3380]. Based on these calculations we have donesome statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in thispaper. For both cases, in range of lower energy, the energy level statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.