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Chinese Physics B

Calculations of the dynamic dipole polarizabilities for the Li + ion

Yong-Hui Zhang, Li-Yan Tang, Xianzhou Zhang, Ting-Yun Shi

Published Sep 23, 2016• 6 citations
Publisher

Abstract

The B-spline configuration-interaction method is applied to the investigations of dynamic dipole polarizabilities for the four lowest triplet states (2 3 S, 3 3 S, 2 3 P, and 3 3 P) of the Li + ion. The accurate energies for the triplet states of n 3 S, n 3 P, and n 3 D, the dipole oscillator strengths for 2 3 S(3 3 S) → n 3 P, 2 3 P(3 3 P) → n 3 S, and 2 3 P(3 3 P) → n 3 D transitions, with the main quantum number n up to 10 are tabulated for references. The dynamic dipole polarizabilities for the four triplet states under a wide range of photon energy are also listed, which provide input data for analyzing the Stark shift of the Li + ion. Furthermore, the tune-out wavelengths in the range from 100 nm to 1.2 μm for the four triplet states, and the magic wavelengths in the range from 100 nm to 600 nm for the 2 3 S → 3 3 S, 2 3 S → 2 3 P, and 2 3 S → 3 3 P transitions are determined accurately for the experimental design of the Li + ion.

DOI
10.1088/1674-1056/25/10/103101

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The B-spline configuration-interaction method is applied to the investigations of dynamic dipole polarizabilities for the four lowest triplet states (2 3 S, 3 3 S, 2 3 P, and 3 3 P) of the Li + ion. The accurate energies for the triplet states of n 3 S, n 3 P, and n 3 D, the dipole oscillator strengths for 2 3 S(3 3 S) → n 3 P, 2 3 P(3 3 P) → n 3 S, and 2 3 P(3 3 P) → n 3 D transitions, with the main quantum number n up to 10 are tabulated for references. The dynamic dipole polarizabilities for the four triplet states under a wide range of photon energy are also listed, which provide input data for analyzing the Stark shift of the Li + ion. Furthermore, the tune-out wavelengths in the range from 100 nm to 1.2 μm for the four triplet states, and the magic wavelengths in the range from 100 nm to 600 nm for the 2 3 S → 3 3 S, 2 3 S → 2 3 P, and 2 3 S → 3 3 P transitions are determined accurately for the experimental design of the Li + ion.
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The dynamic dipole polarizabilities for the four lowest triplet states (23S,33S,23P2{\phantom{\rule{0.16em}{0ex}}}^{3}S, 3{\phantom{\rule{0.16em}{0ex}}}^{3}S, 2{\phantom{\rule{0.16em}{0ex}}}^{3}P23S,33S,23P, and 33P3{\phantom{\rule{0.16em}{0ex}}}^{3}P33P) of helium are calculated using the BBB-spline configuration interaction method. Present values of the static dipole polarizabilities in the length, velocity, and acceleration gauges are in good agreement with the best Hylleraas results. Also the tune-out wavelengths in the range 400 nm--4.2 $\ensuremath{\mu}\mathrm{m}$ for the four lowest triplet states are identified, and the magic wavelengths in the range 460 nm--3.5 $\ensuremath{\mu}\mathrm{m}$ for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}S, 2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{3}P$, and $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transitions are determined. We show that the tune-out wavelength of 23S2{\phantom{\rule{0.16em}{0ex}}}^{3}S23S state is 413.03828(3)413.038\phantom{\rule{0.16em}{0ex}}28(3)413.03828(3) nm, which corroborates the value of Mitroy and Tang [Phys. Rev. A 88, 052515 (2013)], and the magic wavelength around 1066 nm for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transition can be expected for precision measurement to determine the ratio of transition matrix elements $(2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{3}P)/(3{\phantom{\rule{0.16em}{0ex}}}^{3}P\ensuremath{\rightarrow}6{\phantom{\rule{0.16em}{0ex}}}^{3}S)$.
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The electric dipole polarizabilities and the tune-out wavelengths for the n3S1 (n = 2, 3) states of Be2+ are determined through the application of the relativistic full-configuration-interaction approach. Our calculations directly integrate the mass shift operator into the Dirac-Coulomb-Breit Hamiltonian and further assess the quantum electrodynamics (QED) correction to the dynamic dipole polarizabilities using perturbation theory. The results reveal that the static electric dipole polarizability of the 23S1 and 33S1 states, as well as the 93 nm tune-out wavelength of the 23S1 state and the 238 nm tune-out wavelength of the 33S1 state, exhibits a high sensitivity to QED correction, which exceeds 80 ppm, providing a sensitive test for atomic structure theory.