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Journal of Physics B Atomic Molecular and Optical Physics

Calculation of anticrossing signals based on the full fine-structure system

G.G. Tepehan

Published May 14, 1990• 0 citations
Publisher

Abstract

The anticrossing signal shape was calculated on the basis of the full fine-structure system. The shapes, widths, crossing centres and Stark constants derived from this calculation are compared with the experimental results of n=4 of He+. The result shows good agreement with the experiment on the general behaviour of the signals but not on the crossing centres. The current results for the crossing centres and the Stark constants are in good agreement with previous calculations which were based on two-level systems.

DOI
10.1088/0953-4075/23/9/010

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The anticrossing signal shape was calculated on the basis of the full fine-structure system. The shapes, widths, crossing centres and Stark constants derived from this calculation are compared with the experimental results of n=4 of He+. The result shows good agreement with the experiment on the general behaviour of the signals but not on the crossing centres. The current results for the crossing centres and the Stark constants are in good agreement with previous calculations which were based on two-level systems.
With wavefunctions from a kind of atomic potential model including the fine-structure (FS) interaction as a basis, we calculate the positions and widths of anticrossings due to the FS interaction for the case of K Rydberg states in a static electrical field by using the diagonalization method. The results are in good agreement with experimental data; and we confirm that the influence of the FS interaction is very small on anticrossing brought about by core interaction. The accuracy of the potential model wavefunction including the FS interaction is sensitively and numerically tested in the situation of external fields.
Numerical calculations of the positions and widths for anticrossings in Rydberg Stark states are scarce, largely due to the results' sensitive dependence on the wavefunctions chosen. With wavefunctions derived from a kind of potential model as a basis, we calculate the positions and sizes for the anticrossings of potassium Rydberg states in a static electric field by means of diagonalization, and show that the results are in good agreement with available experimental data. The results show that this potential model can be used to deal with the problem of anticrossings, and the accuracy of the potential model is sensitively and numerically tested in the situation of external fields for the first time.
In the spectral range between 480 nm and 630 nm the Stark effect of the transitions n 1Q-2 1S, n 1Q-2 1P and n 3Q-2 3P (n=3÷10, Q=S, P,...) was studied using electric field up to 1500 kV/cm. For such a high field the Stark splitting becomes greater than the simple structure of the atom. Hence anticrossings of the Stark components of the same magnetic quantum number occur. The experimental results have been compared with the theoretically determined shifts. The results of calculations show good agreement with observation.
Atoms moving through a magnetic field suffer a Stark effect whose magnitude is dependent upon the atom's velocity. This velocity-dependent perturbation has recently been exploited as a Doppler narrowing technique, and in this paper we consider atomic anticrossings induced by it. Experimentally such anticrossings are observed between $n^{3}D\ensuremath{-}n^{1,3}F$ states of He for $n=4\ensuremath{-}9$, with n=8n=8n=8 being considered in detail. Theoretical expressions are derived for motional-Stark-effect-induced anticrossing line shapes. Good agreement with the observed line shapes is obtained and the theoretical analysis allows a value of the $n=^{3}D\ensuremath{-}^{1,3}F$ interval to be obtained which is in good agreement with previous predictions.
Anticrossing signals have been detected between n 1 D and n 3 D states of neutral He (n=5 to 7) using external electric field and internal singlet-triplet perturbations to couple the crossing states. Improved results for the n 1 D-n 3 D intervals are obtained: 34066.3(7.2), 20918.0(9.2) and 13632.8(5.3) MHz for n=5, 6, 7 respectively. This type of anticrossing also allows the study of the differential Stark effect, the anisotropic susceptibility chi A and the relativistic fine structure of the n 3 D states.
The authors describe practical methods for calculating the Stark structure of Rydberg states of the alkali metals based on diagnolization of the energy matrix. A survey of Stark structures is presented for all of the alkali metals in the vicinity of n=15n=15n=15. Topics discussed include general methods for evaluating radial matrix elements, the treatment of fine structure, oscillator-strength distribution, scaling laws, the structure of a level anticrossing, and sources of error. Experimental Stark maps are compared with calculated results for lithium and cesium. Experimental studies of the oscillator-strength distribution within a Stark manifold and the structure of a level anticrossing are also presented.