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Chinese Physics B

Exact quantum defect theory approach for lithium in magnetic fields

Jiakun Xu, Haiqing Chen, Hongping Liu

Published Jan 1, 2013• 3 citations
Publisher

Abstract

We calculate the diamagnetic spectrum of lithium at highly excited states up to the positive energy range using the exact quantum defect theory approach. The concerned excitation is one-photon transition from the ground state 2s to the highly excited states n p with π and σ polarizations respectively. Lithium has a small quantum defect value 0.05 for the n p states, and its diamagnetic spectrum is very similar to that of hydrogen in the energy range approaching the ionization limit. However, a careful calculation shows that the spectrum has a significant discrepancy with that of hydrogen when the energy is lower than −70 cm −1 . The effect of the quantum defect is also discussed for the Stark spectrum. It is found that the σ transition to the n p states in an electric field has a similar behavior to that of hydrogen due to zero interaction with channel n s.

DOI
10.1088/1674-1056/22/1/013204

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We calculate the diamagnetic spectrum of lithium at highly excited states up to the positive energy range using the exact quantum defect theory approach. The concerned excitation is one-photon transition from the ground state 2s to the highly excited states n p with π and σ polarizations respectively. Lithium has a small quantum defect value 0.05 for the n p states, and its diamagnetic spectrum is very similar to that of hydrogen in the energy range approaching the ionization limit. However, a careful calculation shows that the spectrum has a significant discrepancy with that of hydrogen when the energy is lower than −70 cm −1 . The effect of the quantum defect is also discussed for the Stark spectrum. It is found that the σ transition to the n p states in an electric field has a similar behavior to that of hydrogen due to zero interaction with channel n s.
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.
Rydberg states in lithium have been excited from the ground state by absorption of \ensuremath{\pi}-polarized photons in the presence of parallel electric F and magnetic B fields. The magnetic field strength (B=3.11 T) is high enough to reach the inter-n-mixing regime, and a small electric field strength (F\ensuremath{\simeq}25 V/cm) is sufficient for the lowest state of the n=30 manifold to penetrate into the high-energy part of the n=29 manifold. The first anticrossing is thoroughly studied. Away from the anticrossing the spectrum exhibits two lines, but at the anticrossing a third component appears in the structure in the same energy range. This provides an experimental confirmation for the existence of pairs of almost-degenerate states with opposite parities in the high-energy part of the diamagnetic manifold of lithium. The two components of this doublet behave differently at the anticrossing. The experimental data have been interpreted in a global treatment in which core effects and intermanifold couplings are simultaneously taken into account. The different behavior of low- and high-lying states of the multiplet with respect to these two interactions is analyzed in detail.
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 have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and π /2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel n p, play an important role in the spectral profile.