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Chinese Physics B

An effective quantum defect theory for the diamagnetic spectrum of a barium Rydberg atom

Bo Li, Hongping Liu

Published Jan 1, 2013• 3 citations
Publisher

Abstract

A theoretical calculation is carried out to investigate the spectrum of a barium Rydberg atom in an external magnetic field. Using an effective approach incorporating quantum defect into the centrifugal term in the Hamiltonian, we reexamine the reported spectrum of the barium Rydberg atom in a magnetic field of 2.89 T [ J. Phys. B 28 L537 (1995) ]. Our calculation employs B -spline basis expansion and complex coordinate rotation techniques. For single photon absorption from the ground 6s 2 to 6s n p Rydberg states, the spectrum is not influenced by quantum defects of channels n s and n d. The calculation is in agreement with the experimental observations until the energy reaches E = −60 cm −1 . Beyond this energy, closer to the threshold, the calculated and experimental results do not agree with each other. Possible reasons for their discrepancies are discussed. Our study affirms an energy range where the diamagnetic spectrum of the barium atom can be explained thoroughly using a hydrogen model potential.

DOI
10.1088/1674-1056/22/1/013203

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A theoretical calculation is carried out to investigate the spectrum of a barium Rydberg atom in an external magnetic field. Using an effective approach incorporating quantum defect into the centrifugal term in the Hamiltonian, we reexamine the reported spectrum of the barium Rydberg atom in a magnetic field of 2.89 T [ J. Phys. B 28 L537 (1995) ]. Our calculation employs B -spline basis expansion and complex coordinate rotation techniques. For single photon absorption from the ground 6s 2 to 6s n p Rydberg states, the spectrum is not influenced by quantum defects of channels n s and n d. The calculation is in agreement with the experimental observations until the energy reaches E = −60 cm −1 . Beyond this energy, closer to the threshold, the calculated and experimental results do not agree with each other. Possible reasons for their discrepancies are discussed. Our study affirms an energy range where the diamagnetic spectrum of the barium atom can be explained thoroughly using a hydrogen model potential.
We report diamagnetic spectra of sodium atoms observed in a strong magnetic field up to 3 T and compare them with theoretical calculations based on the formulation of an exact quantum-defect theory. We focus on one-photon absorption processes from the ground 3s3s3s state to the excited npnpnp Rydberg states whose magnetic quantum numbers are determined by the polarization of the laser field. The calculations employ BBB-spline basis expansion and the complex spatial coordinate rotation technique, and their results agree well with the observed ones when atomic core effects are appropriately taken into account. When graphed against magnetic field, level anticrossings and core-induced interaction of the npnpnp states provide clear signatures for studying the effects of quantum defect on the diamagnetic spectra.
We study the core effect of nonhydrogenic alkaline-earth-metal barium in its diamagnetic spectrum by one photon transition from the ground state 6s26{s}^{2}6s2 1S0{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}1S0​ experimentally and theoretically. The non-Coulombic potential of the ion core introduces an extra energy shift compared with hydrogen and a level anticrossing between different nnn manifolds, characterized by the quantum defect of the concerned angular momentum states. With a complex rotation coordinate technique and a BBB-spline expansion method, we develop a matrix-form Hamiltonian based on an effective potential incorporating the angular-dependent quantum defect into the angular rotation term. The nonhydrogen core effects are investigated by sweeping the quantum defects of different channels in the calculation. Results show that quantum defects of ppp and fff states have a undeniable effect on the intensities and positions of the spectral lines, although barium is closely hydrogenlike in the energy range examined. The anticrossing spectral lines are also identified with the aid of theoretical calculations. The calculations are in good agreement with the experimental observations.
We observe strong energy-dependent quantum defects in the scaled-energy Stark spectra for | M | = 1 Rydberg states of barium atoms at three scaled energies: ε = –2.000, ε = –2.500 and ε = –3.000. In an attempt to explain the observations, theoretical calculations of closed orbit theory based on a model potential including core effect are performed for non-hydrogenic atoms. While such a potential has been uniformly successful for alkali atoms with a single valence electron, it fails to match experimental results for barium atoms in the 6snp Rydberg states with two valence electrons. Our study points out that this discrepancy is due to the strong perturbation from the 5d8p state, which voids the simple approximation for constant quantum defects of principle quantum number n.
The diamagnetic and Stark shifts of strongly perturbed Rydberg spectra such as those of the alkaline earths are expressed in terms of multichannel---quantum-defect parameters. The theory is applicable when the shifts produced by the external fields are smaller than the neighboring Rydberg separations. It is applied to evaluate the diamagnetic shifts in Ba, an atom in which Rydberg and doubly excited channels are strongly mixed. In such complex spectra, the diamagnetic effect can serve a useful purpose as a tool to disentangle the interacting series. The radial sizes and, therefore, the diamagnetic shifts are quite different for singly and doubly excited states even when they are at the same energy. In fact, for the field strengths considered ($\ensuremath{\simeq}40$ kG), the diamagnetic contribution of the doubly excited configuration is quite negligible. As a result, the observed shift is a direct measure of the amount of singly excited configuration in the state of interest. Exactly similar conclusions apply to Stark shifts. The last part of this paper considers states of very high excitation further up in the spectrum which are no longer in a perturbative regime. Spectra of atoms in a magnetic field have shown equally spaced resonances near the ionization threshold with characteristic spacings. By the consideration of the effects of electric fields which are also often simultaneously present, a criterion is established for the nature of these spacings depending on the relative strengths of the crossed electric and magnetic fields. The spacing seen in any particular experiment is shown to depend on the mass and quantum defect of the atom, the strengths of the external fields, and experimental conditions such as the temperature of the atomic vapor whose absorption spectrum is being studied.
We observe strong energy-dependent quantum defects in the scaled-energy Stark spectra for vertical bar M vertical bar = 1 Rydberg states of barium atoms at three scaled energies: epsilon = -2.000, epsilon = -2.500 and epsilon = -3.000. In an attempt to explain the observations, theoretical calculations of closed orbit theory based on a model potential including core effect are performed for non-hydrogenic atoms. While such a potential has been uniformly successful for alkali atoms with a single valence electron, it fails to match experimental results for barium atoms in the 6snp Rydberg states with two valence electrons. Our study points out that this discrepancy is due to the strong perturbation from the 5d8p state, which voids the simple approximation for constant quantum defects of principle quantum number n.