Effects of core scattering on level statistics in helium atoms in scaled external fields

Abstract

We recorded constant scaled-energy spectra of helium Rydberg atoms in both electric and magnetic fields in a regime where the hydrogen atom behaves regularly. Jonckheere, Grémaud, and Delande ͓Phys. Rev. Lett. 81, 2442 ͑1998͔͒ recently showed that the nearest-neighbor statistics of sufficiently highly excited states follows a ␦-Poisson distribution, which depends on the quantum defect ␦. We find global deviations from this ␦-Poisson model, which we attribute to the size of the effective Planck constant ប eff . Significant deviations at small level spacings indicate that the description of level statistics with the ␦-Poisson model is incomplete. ͓S1050-2947͑99͒50409-5͔PACS number͑s͒: 32.60.ϩi, 03.65. Sq, 05.45.Ϫa, 32.80.Rm Quantum systems showing chaotic behavior in the classical limit, sometimes referred to as quantum chaos, are the subject of detailed theoretical and experimental studies ͓1-5͔. Despite impressive progress in the last decade, a profound understanding of the connection between irregular classical dynamics and quantum mechanics is still lacking. The hydrogen atom in a magnetic field is a prototype system to study this chaotic behavior. The classical dynamics in a constant magnetic field undergoes a smooth transition from regular motion to chaos when the energy is raised up to the ionization limit. Experiments on Rydberg atoms and quantum R-matrix calculations have been used to search for quantum manifestations of chaos. Numerical investigations have revealed a relation between quantum-level statistics and the underlying classical dynamics. Nearest-neighbor spacings ͑NNS's͒ in spectra in the regular regime follow a Poisson distribution, while in the chaotic regime they obey a Wigner distribution ͓6͔. A second connection between energy levels in an absorption spectrum and the classical dynamics of the atom has been provided by closed-orbit theory ͓7͔. According to this theory each electron orbit that starts at and returns to the nucleus shows up as an oscillation in the photoabsorption spectrum.

Investigating interaction-induced chaos using time-dependent density-functional theory

“…It will be interesting to compare the ATDDFT spectrum with that of the scatterer-perturber models in the literature, Refs. [17,18,19,20]. TDDFT treats all electrons quantum mechanically, and provides an ab initio method against which to compare the model potentials.…”

“…[16] for a calculation of level-repulsion in helium). However deviations from Poissonian statistics have been clearly identified in non-hydrogenic Rydberg atoms in either magnetic or electric fields [17,18,19,20]. The hydrogen atom at the corresponding parameter regime is integrable, but scattering off the ionic core in a nonhydrogenic Rydberg atom creates fundamentally different dynamics, with chaotic trajectories depending on the value of the quantum defect.…”

Spectral properties of atoms in fields: A semiclassical analysis

“…The short-range spectral properties of non-hydrogenic Rydberg atoms in external fields were recently found to have an unexpected character [1], the nearest neighbour distribution was neither Poisson nor Wigner-Dyson, but close to a new generic intermediate class known as half-Poisson. These findings have been investigated experimentally for helium atoms in electric fields [2], following much interest in the dynamics of non-hydrogenic atoms in weak fields and the effects of core-induced chaos [3][4][5][6][7]. Concurrently, there has also been much interest in such intermediate Nearest Neighbour distributions [8,9] with broad application in problems such as electronelectron interactions in closed mesoscopic devices [9,10], the metal-insulator transition [11], intruder states in nuclear physics [12], and inclusions in billiards [8].…”

Rydberg Molecules in External Fields: A Semiclassical Analysis

“…Subsequently, the nearest neighbor spacings (NNS) distributions of non-hydrogenic atoms in the 'core-induced chaos' regime were shown in fact [7], to correspond to a distribution which was neither Wigner (chaotic), nor mixed phase-space, but close to a new generic intermediate class known as semi-Poisson [8]. These findings were investigated experimentally for helium atoms in external fields [9].We consider below the form of COT appropriate for simple molecules in external fields. The extension of COT is obtained by merging the standard closedorbit arguments with molecular quantum defect theory (MQDT), the main theoretical approach employed in the studies of Rydberg molecules [10].…”

“…Subsequently, the nearest neighbor spacings (NNS) distributions of non-hydrogenic atoms in the 'core-induced chaos' regime were shown in fact [7], to correspond to a distribution which was neither Wigner (chaotic), nor mixed phase-space, but close to a new generic intermediate class known as semi-Poisson [8]. These findings were investigated experimentally for helium atoms in external fields [9].…”