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arXiv:0707.3576 · Physical Review A

Relativistic multireference Fock-space coupled-cluster calculation of the forbidden 6s2S01→6s5dD13 magnetic-dipole transition in ytterbium

Chiranjib Sur, Rajat K. Chaudhuri

Published Jul 20, 2007• 9 citations
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Abstract

We report the forbidden $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}6s5d\phantom{\rule{0.2em}{0ex}}^{3}D_{1}$ magnetic-dipole transition amplitude computed using multireference Fock-space coupled-cluster theory. Our computed transition matrix element $(1.34\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}){\ensuremath{\mu}}_{B}$ is in excellent agreement with the experimental value $(1.33\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}){\ensuremath{\mu}}_{B}$. This value in combination with other known quantities will be helpful in determining the parity-nonconserving amplitude for the $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}6s5d\phantom{\rule{0.2em}{0ex}}^{3}D_{1}$ transition in atomic Yb. To our knowledge, this calculation is the most accurate to date, and can be very important in the search for physics beyond the standard model. We further report the $6s6p\phantom{\rule{0.2em}{0ex}}^{3}P_{0}\ensuremath{\rightarrow}6s6p\phantom{\rule{0.2em}{0ex}}^{1}P_{1}$ and $6s5d\phantom{\rule{0.2em}{0ex}}^{3}D_{1}\ensuremath{\rightarrow}6s6p\phantom{\rule{0.2em}{0ex}}^{3}P_{0}$ transition matrix elements, which are also in good agreement with the earlier theoretical estimates.

DOI
10.1103/physreva.76.012509

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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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We report the forbidden 6s21S0\ensuremath→6s5d3D16{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}6s5d\phantom{\rule{0.2em}{0ex}}^{3}D_{1}6s21S0​\ensuremath→6s5d3D1​ magnetic-dipole transition amplitude computed using multireference Fock-space coupled-cluster theory. Our computed transition matrix element (1.34\ifmmode×\else\texttimes\fi10\ensuremath−4)\ensuremathμB(1.34\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}){\ensuremath{\mu}}_{B}(1.34\ifmmode×\else\texttimes\fi10\ensuremath−4)\ensuremathμB​ is in excellent agreement with the experimental value (1.33\ifmmode×\else\texttimes\fi10\ensuremath−4)\ensuremathμB(1.33\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}){\ensuremath{\mu}}_{B}(1.33\ifmmode×\else\texttimes\fi10\ensuremath−4)\ensuremathμB​. This value in combination with other known quantities will be helpful in determining the parity-nonconserving amplitude for the 6s21S0\ensuremath→6s5d3D16{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}6s5d\phantom{\rule{0.2em}{0ex}}^{3}D_{1}6s21S0​\ensuremath→6s5d3D1​ transition in atomic Yb. To our knowledge, this calculation is the most accurate to date, and can be very important in the search for physics beyond the standard model. We further report the 6s6p3P0\ensuremath→6s6p1P16s6p\phantom{\rule{0.2em}{0ex}}^{3}P_{0}\ensuremath{\rightarrow}6s6p\phantom{\rule{0.2em}{0ex}}^{1}P_{1}6s6p3P0​\ensuremath→6s6p1P1​ and 6s5d3D1\ensuremath→6s6p3P06s5d\phantom{\rule{0.2em}{0ex}}^{3}D_{1}\ensuremath{\rightarrow}6s6p\phantom{\rule{0.2em}{0ex}}^{3}P_{0}6s5d3D1​\ensuremath→6s6p3P0​ transition matrix elements, which are also in good agreement with the earlier theoretical estimates.
A high-precision experiment to measure parity-nonconservation in atomic Yb has been proposed recently [D. De Mille, Phys. Rev. Lett. 74, 4165 (1995)]. We use a relativistic configuration-interaction approach to highlight the importance of correlation effects in the ${6s}^{2}{(}^{1}{S}_{0})\ensuremath{\rightarrow}{6s5d(}^{3}{D}_{1})$ parity-nonconserving electric transition amplitude for Yb. Our result shows that this transition amplitude is dramatically altered by the strong mixing between some of the configurations that make up the odd-parity 6s6p(1P1){6s6p(}^{1}{P}_{1})6s6p(1P1​) atomic state.
We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the 6s21S06{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}6s21S0​, 6s6p3P0o6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}6s6p3P0o​, and 6s6p3P1o6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}6s6p3P1o​ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the C6{C}_{6}C6​ coefficients for the Yb-Yb 1S0+3P0,1o{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}1S0​+3P0,1o​ and 3P0o+3P0o{}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}3P0o​+3P0o​ dimers and C8{C}_{8}C8​ coefficients for the 1S0+1S0{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}1S0​+1S0​ and 1S0+3P1o{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}1S0​+3P1o​ dimers.
We have developed an all-particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine structure constants, and electric dipole matrix elements of Sr, Ba, and Yb. Furthermore, we calculate the electric quadrupole hyperfine structure constants and the electric dipole matrix elements of Sr+{\mathrm{Sr}}^{+}Sr+, Ba+{\mathrm{Ba}}^{+}Ba+, and Yb+{\mathrm{Yb}}^{+}Yb+. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine structure constants of Yb+{\mathrm{Yb}}^{+}Yb+.
We report a measurement of the ratio of electric dipole transition matrix elements of cesium for the $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ transitions. We determine this ratio of matrix elements through comparisons of two-color, two-photon excitation rates of the 7s2S1/27s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}7s2S1/2​ state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of $R\ensuremath{\equiv}\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}/\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=1.5272(17)$ is in excellent agreement with a theoretical prediction of R=1.5270(27)R=1.5270(27)R=1.5270(27). Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of RRR. Combined with our recent determination of the lifetime of the 7s2S1/27s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}7s2S1/2​ state, we determine reduced matrix elements for these two transitions, $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}=\ensuremath{-}6.489(5)\phantom{\rule{4pt}{0ex}}{a}_{0}$ and $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=\ensuremath{-}4.249(4)\phantom{\rule{4pt}{0ex}}{a}_{0}$. These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.
The electric-dipole and quadrupole polarizabilities of the 5s5p3P1o5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}5s5p3P1o​ state and the C6{C}_{6}C6​ and C8{C}_{8}C8​ coefficients for the 1S0+1S0{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}1S0​+1S0​ and 1S0+3P1o{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}1S0​+3P1o​ dimers of strontium are calculated using a high-precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the 0u{0}_{u}0u​ and 1u{1}_{u}1u​ energy levels are C6(0u)=3771(32){C}_{6}({0}_{u})=3771(32)C6​(0u​)=3771(32) a.u. and C6(1u)=4001(33){C}_{6}({1}_{u})=4001(33)C6​(1u​)=4001(33) a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate C8{C}_{8}C8​ coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the ${}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{1}^{o}$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.
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.