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Journal of Atomic and Molecular Physics

The calculation for positions and widths of anticrossing for Rubidium Rydberg states in static electric field

Xiaoyong Li, Cheng Jin, Zhou Xiaoxin

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

With a potential model of alkali-metal atoms and B-spline expansion technique,the structure of the energy levels for Rydberg states of Rubidium is investigated.We calculated the positions and widths of anticrossing between(n+3)s and (n,k) Stark states with principal quantum number n between 16 and 25.Our results are in agreement with the experimental data.And we obtained two empirical formulas which can be used to estimate the positions of anticrossing for high Rydberg states of Rubidium in static electric field.

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With a potential model of alkali-metal atoms and B-spline expansion technique,the structure of the energy levels for Rydberg states of Rubidium is investigated.We calculated the positions and widths of anticrossing between(n+3)s and (n,k) Stark states with principal quantum number n between 16 and 25.Our results are in agreement with the experimental data.And we obtained two empirical formulas which can be used to estimate the positions of anticrossing for high Rydberg states of Rubidium in static electric field.
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.
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.
The B-spline expansion technique and the method of model potential of atom have been applied to study the properties of Stark states of lithium. Our results for Stark maps, oscillator strength distributions, avoided crossing positions and widths for Li are in good agreement with other reported theoretical calculations and experimental measurement. It shows that the method we used can be applied to investigate the properties of alkali-metal atoms in external static electric field. Finally, for the first time, we obtained the evolution of the oscillator strength spectrum of Li with varying static electric field.
We have presented a novel method to calculate the widths of the avoided crossings of Rydberg states in a static electric field. The widths of avoided crossings can be decided not directly connected by scanning the static field, but indirectly connected through the Stark electric dipole moments. The method is restricted to the case in which both the two relevant states have linear Stark shifts or only one of the two involved states has linear Stark shifts, but another has no Stark shift. As test examples, we calculated the widths of avoided crossings of Li, Na and K. The Stark electric dipole moments are determined by using the Stark state wavefunctions which are obtained from the diagonalization method at a fixed static electric field amplitude. The results are in excellent agreement with experimental and other theoretical data.
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.