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Physical Review A

Rydberg states of atoms in parallel electric and magnetic fields

José Paulo Santos, Francisca Mota-Furtado, M.F. Laranjeira, F. Parente

Published Feb 1, 1999• 8 citations
Publisher

Abstract

We present theoretical results for the photoabsorption spectrum of an atom in parallel electric and magnetic fields, using the R-matrix method combined with quantum-defect theory. We introduce a radial basis set which is complete and orthonormal over a semi-infinite interval $[{r}_{0},\ensuremath{\infty}),$ to allow calculations to be performed for high Rydberg states in nonhydrogenic atoms without encountering problems due to linear dependence of the basis set. The nonhydrogenic character of the spectra is analyzed for Li and Rb, and a comparison is made with previous high-precision experiments which shows that the theoretical results agree very well with experiment.

DOI
10.1103/physreva.59.1703

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We present theoretical results for the photoabsorption spectrum of an atom in parallel electric and magnetic fields, using the R-matrix method combined with quantum-defect theory. We introduce a radial basis set which is complete and orthonormal over a semi-infinite interval [r0,\ensuremath∞),[{r}_{0},\ensuremath{\infty}),[r0​,\ensuremath∞), to allow calculations to be performed for high Rydberg states in nonhydrogenic atoms without encountering problems due to linear dependence of the basis set. The nonhydrogenic character of the spectra is analyzed for Li and Rb, and a comparison is made with previous high-precision experiments which shows that the theoretical results agree very well with experiment.
By combining the B-spline basis set with model potential (B-spline + MP), we present oscillator strength spectra of Rydberg Li atoms in external fields. The photoabsorption spectra are analyzed. Over the narrow energy ranges considered in this paper, the structure of the spectra can be independent of the initial state chosen for a given atom. Our results are in good agreement with previous high-precision experimental data and theoretical calculations, where the R-matrix approach together with multichannel quantum defect theory (R-matrix+MQDT) was used. It is suggested that the present methods can be applied to deal with the oscillator strength spectra of Rydberg atoms in crossed electric and magnetic fields.
A robust time-dependent approach to the high-resolution photoabsorption spectrum of Rydberg atoms in magnetic fields is presented. Traditionally we have to numerically diagonalize a huge matrix to solve the eigen-problem and then to obtain the spectral information. This matrix operation requires high-speed computers with large memories. Alternatively we present a unitary but very easily parallelized time-evolution method in an inexpensive way, which is very accurate and stable even in long-time scale evolution. With this method, we perform the spectral calculation of hydrogen atom in magnetic field, which agrees well with the experimental observation. It can be extended to study the dynamics of Rydberg atoms in more complicated cases such as in combined electric and magnetic fields.
The radial electric dipole moments of bound-bound, bound-free, and free-free transitions of high-lying (n>15)(n>15)(n>15) Rydberg states and low-lying continuum states $(\ensuremath{\epsilon}<400$ ${\mathrm{cm}}^{\ensuremath{-}1})$ are calculated for hydrogen and the alkali-metal atoms. All dipole matrix elements for the transitions between low-lll (s(s(s, ppp, ddd, and f)f)f) states of H, Li, and Rb are presented. Results of similar calculations for the other alkali-metal atoms (Na, K, and Cs) are summarized. These numerical results, using quantum defect theory, are compared with semiclassical approximations. The dipole matrix elements cross zero at certain combinations of initial and final states. The matrix elements at these so-called Cooper minima in Li, K, Rb, and Cs are presented in detail.
I have calculated the energy spectrum of a highly excited atom which lies in parallel, static electric and magnetic fields. In parallel fields the Coulomb quantum numbers n and m are still "good" quantum numbers but 1 is not: the calculation is for n = 30, m = 1 atoms.;The eigenvalues were obtained by semi-classical quantisation of first-order classical perturbation theory and have been calculated for a large range of electric and magnetic field strengths. The results are in good agreement with those found from first-order degenerate quantum perturbation theory.;The semi-classical analysis provides a correlation diagram connecting the Stark effect states to those of the diamagnetic effect.
We present oscillator strength spectra of Rydberg lithium atoms in parallel electric and magnetic fields obtained via the B-spline basis set method combined with model potential. Both the radial and angular wavefunctions are expanded in terms of B-spline functions. The results are in good agreement with previous high-precision experiments. By analyzing the components of partial-wave, we give an explanation to the oscillator strength of part of the spectrum. The method of this paper is simple and effective. It is suggested that the present method can be applied to deal with the problem of Rydberg atom in crossed magnetic and electric field.