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Physical Review A

Wavelength, oscillator strength, and fine structure for the →44 S° transition of Mg−

Donald R. Beck

Published Sep 1, 1989• 15 citations
Publisher

Abstract

We have calculated the electron affinities, including many-body and relativistic effects, of ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{P}$ and ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{\ifmmode^\circ\else\textdegree\fi{}}$ to be 321 and 536 meV, respectively. The electric dipole f value for the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition is 0.3087 (length) and 0.3000 (velocity), occurring at a theoretically predicted wavelength of 2921 A\r{}. The J=1/2\ensuremath{\rightarrow}3/2 fine-structure splitting for ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{P}$ is predicted to be 11.8 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and the J=3/2\ensuremath{\rightarrow}5/2 splitting 19.4 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. These results should help in the attempt being made by Andersen (private communiation) to observe the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition in the laboratory.

DOI
10.1103/physreva.40.2887

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Determination of magic wavelengths for the 7s S1/22−7p P3/2,1/22 transitions in Fr

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Spectroscopy of laser-cooling transitions in MgF

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We calculate, including many-body effects, that the three lowest bound states of ${\mathrm{Mg}}^{\ensuremath{-}}$, $2{p}^{6}3s3{p}^{2}^{4}P$, $2{p}^{6}3{p}^{3}^{4}S^{0}$ and $2{p}^{5}3s3{p}^{3}^{6}P$, have electron affinities 0.360, 0.514, and 1.321 eV, respectively. The transition $3s3{p}^{2}^{4}P\ensuremath{\rightarrow}3{p}^{3}^{4}S^{0}$ is found to have an electric dipole oscillator strength of 0.295. The lifetimes of the J=12,32,and52J=\frac{1}{2}, \frac{3}{2}, \mathrm{and} \frac{5}{2}J=21​,23​,and25​, 4P^{4}P4P levels are estimated to be 7.8, 9.8, and 1.6 ns, respectively.
We optically excite the electronic state 3s3p ^{3}P_{0} in ^{24}Mg atoms, laser cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift, and the transition frequency to be 468.46(21) nm, -206.6(2.0) MHz/T^{2}, and 655 058 646 691(101) kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.
We report here oscillator strengths, transition rates, branching ratios, and lifetimes due to the allowed transitions in the potassium (K) atom. We evaluate electric dipole (E1E1E1) amplitudes using an all-order relativistic many-body perturbation method. The obtained results are compared with previously available experimental and theoretical studies. Using the E1E1E1 matrix elements mentioned above and estimated from the lifetimes of the 4p2P1/2,3/24p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}4p2P1/2,3/2​ states, we determine precise values of static and dynamic polarizabilities for the first five low-lying states in the considered atom. The static polarizabilities of the ground and 4p2P1/2,3/24p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}4p2P1/2,3/2​ states in the present work are more precise than the available measurements in these states. Only the present work employs relativistic theory to evaluate the polarizabilities in the 3d2D3/2,5/23d{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{3/2,5/2}3d2D3/2,5/2​ states for which no experimental results are known with which to compare. We also reexamine ``magic wavelengths'' for the $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ and $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ transitions due to the linearly polarized light, which are useful to perform the state-insensitive trapping of K atoms.
Magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the $7{S}_{1/2}\ensuremath{-}7{P}_{1/2,3/2}$ transitions (D lines) in Fr were reported by Dammalapati et al. [U. Dammalapati, K. Harada, and Y. Sakemi, Phys. Rev. A 93, 043407 (2016)]. These ${\ensuremath{\lambda}}_{\mathrm{magic}}$ were determined by plotting dynamic polarizabilities ($\ensuremath{\alpha}$) of the involved states with the above transitions against a desired range of wavelengths. Electric dipole (E1) matrix elements listed in [J. E. Sansonetti, J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the 7P1/2,3/27{P}_{1/2,3/2}7P1/2,3/2​ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the 7P7P7P states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the 7P7P7P states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.
After introducing relations linking intensities of spectral lines and oscillator strengths of electric dipole transitions the difficulties of f-value measurements in the near infrared are considered. A new technique is described based on the measurement of the polarisation of infrared radiation generated by stimulated electronic Raman scattering in atomic vapours. Results obtained in caesium are compared with theoretical values for radial matrix element ratios. It is concluded that the anomalous intensity ratios observed in the principal series doublets of caesium can be predicted accurately only by theoretical calculations which include the effects of core polarisation and the correct relativistic spin-orbit interaction. The experimental result for the ratio of the absorption f-values of the previously inaccessible transitions 7s 2 S 1/2 -7p 2 P 3/2 , 1/2 at 2.931 mu m and 3.095 mu m respectively is 4.12+or-0.66. Extensions of these nonlinear optical techniques to magnetic dipole and electric quadrupole transitions are noted.
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