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Physical Review A

Lifetimes and branching ratios of excited states in La− , Os− , Lu− , Lr− , and Pr−

Steven M. O’Malley, Donald R. Beck

Published Mar 5, 2010• 28 citations
Publisher

Abstract

Relativistic configuration-interaction calculations have been performed for all possible $E1$, $M1$, and $E2$ transitions between bound anion states of ${\mathrm{La}}^{\ensuremath{-}}$ and ${\mathrm{Os}}^{\ensuremath{-}}$. We pay particular attention to $E1$ transitions in each case that may be of use in laser cooling of these anions. Although the ${\mathrm{La}}^{\ensuremath{-}}$ transition energy is approximately one-third of the ${\mathrm{Os}}^{\ensuremath{-}}$ transition, our results indicate that the Einstein $A$ coefficient is nearly two orders of magnitude larger, which would lead to more efficient laser cooling. We have also explored long-lived opposite-parity excited states in ${\mathrm{Lu}}^{\ensuremath{-}}$ and ${\mathrm{Lr}}^{\ensuremath{-}}$ which are restricted to $M2$ decay by selection rules. Finally, in ${\mathrm{Pr}}^{\ensuremath{-}}$, we find sufficient mixing between a weakly bound excited $4{f}^{2}5{d}^{2}6{s}^{2}$ state with a nearby $4{f}^{3}6{s}^{2}6p$ resonance to result in a lifetime similar to that of the other excited anion states, despite the fact that the dominant configurations of these $M1$ and $E2$ transitions differ by two electrons.

DOI
10.1103/physreva.81.032503

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High-resolution photoelectron energy spectra of osmium anions are obtained using the slow-electron velocity-map imaging method. The energy levels of excited states 4 F 7/2, 4 F 5/2 and 4 F 3/2 of Os− are determined to be 148.730(13), 155.69(15), and 176.76(13) THz [or 4961.09(41), 5193.4(49), and 5896.1(42) cm−1], respectively. The lifetime of the opposite-parity excited state 6 D 9 / 2 o is determined to be 201(10) μs using a cold ion trap, about 15 times shorter than the previous result 3(1) ms. Our high-level multi-configuration Dirac–Hartree–Fock calculations yield a theoretical lifetime 527 μs. Our work shows that the laser cooling rate of Os− is as fast as that of Th−. The advantages of Os− are its near-IR range cooling transition and simple electronic structure, which make Os− a promising candidate for laser cooling of negative ions. We propose a general approach to produce cold atoms and molecules based on the sympathetic cooling of negative ions in combination with a threshold photodetachment.

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•Jan 1, 2009•1 citation
Relativistic configuration-interaction calculations have been performed for all possible E1E1E1, M1M1M1, and E2E2E2 transitions between bound anion states of La\ensuremath−{\mathrm{La}}^{\ensuremath{-}}La\ensuremath− and Os\ensuremath−{\mathrm{Os}}^{\ensuremath{-}}Os\ensuremath−. We pay particular attention to E1E1E1 transitions in each case that may be of use in laser cooling of these anions. Although the La\ensuremath−{\mathrm{La}}^{\ensuremath{-}}La\ensuremath− transition energy is approximately one-third of the Os\ensuremath−{\mathrm{Os}}^{\ensuremath{-}}Os\ensuremath− transition, our results indicate that the Einstein AAA coefficient is nearly two orders of magnitude larger, which would lead to more efficient laser cooling. We have also explored long-lived opposite-parity excited states in Lu\ensuremath−{\mathrm{Lu}}^{\ensuremath{-}}Lu\ensuremath− and Lr\ensuremath−{\mathrm{Lr}}^{\ensuremath{-}}Lr\ensuremath− which are restricted to M2M2M2 decay by selection rules. Finally, in Pr\ensuremath−{\mathrm{Pr}}^{\ensuremath{-}}Pr\ensuremath−, we find sufficient mixing between a weakly bound excited 4f25d26s24{f}^{2}5{d}^{2}6{s}^{2}4f25d26s2 state with a nearby 4f36s26p4{f}^{3}6{s}^{2}6p4f36s26p resonance to result in a lifetime similar to that of the other excited anion states, despite the fact that the dominant configurations of these M1M1M1 and E2E2E2 transitions differ by two electrons.
This brief report is a follow-up to the recent proposal to use La${}^{\ensuremath{-}}$ as another candidate, in addition to Os${}^{\ensuremath{-}}$, in laser cooling of anions, which can then be used to cool antiprotons sympathetically. Using the relativistic configuration interaction formalism, we calculate the photodetachment cross sections of the upper laser cooling state La${}^{\ensuremath{-}}$ 5d5d5d6s26{s}^{2}6s26p3D16p {}^{3}{D}_{1}6p3D1​ and Os${}^{\ensuremath{-}}$ 5d65{d}^{6}5d66s26{s}^{2}6s26p6D9/26p {}^{6}{D}_{9/2}6p6D9/2​. Our results show that La${}^{\ensuremath{-}}$ has a very similar two-photon detachment loss as Os${}^{\ensuremath{-}}$, retaining it as another promising candidate for cooling antiprotons sympathetically.
High-resolution photoelectron energy spectra of osmium anions are obtained using the slow-electron velocity-map imaging method. The energy levels of excited states 4 F 7/2, 4 F 5/2 and 4 F 3/2 of Os− are determined to be 148.730(13), 155.69(15), and 176.76(13) THz [or 4961.09(41), 5193.4(49), and 5896.1(42) cm−1], respectively. The lifetime of the opposite-parity excited state 6 D 9 / 2 o is determined to be 201(10) μs using a cold ion trap, about 15 times shorter than the previous result 3(1) ms. Our high-level multi-configuration Dirac–Hartree–Fock calculations yield a theoretical lifetime 527 μs. Our work shows that the laser cooling rate of Os− is as fast as that of Th−. The advantages of Os− are its near-IR range cooling transition and simple electronic structure, which make Os− a promising candidate for laser cooling of negative ions. We propose a general approach to produce cold atoms and molecules based on the sympathetic cooling of negative ions in combination with a threshold photodetachment.
The energy levels and transition rates of promising laser-cooling candidate thorium anion ($\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$) are experimentally measured in the current work. Three excited states between the lower and upper states for the bound-bound electric dipole (E1) transition ${\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}^{o}\ensuremath{\leftrightarrow}{\phantom{\rule{4pt}{0ex}}}^{4}{F}_{3/2}^{e}$ of $\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$ are observed: 4G5/2o,4F9/2e{\phantom{\rule{4pt}{0ex}}}^{4}{G}_{5/2}^{o}, {\phantom{\rule{4pt}{0ex}}}^{4}{F}_{9/2}^{e}4G5/2o​,4F9/2e​, and 4F7/2o{\phantom{\rule{4pt}{0ex}}}^{4}{F}_{7/2}^{o}4F7/2o​, and their energy levels are determined to be 1847(13), 3166.8(59), and 3666(12) $\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, respectively. Meanwhile, the lifetime of the upper state 2S1/2o{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}^{o}2S1/2o​ of the E1 transition is experimentally determined to be 30(2) \textmu{}s, substantially shorter than the previously calculated result, which makes $\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$ the most promising candidate for laser cooling of negative ions. Furthermore, the lifetimes of two other short-lived odd-parity excited states of $\mathrm{T}{\mathrm{h}}^{\ensuremath{-}}$ are also measured to be 62(5) and 53(3) \textmu{}s, respectively.
Despite the fact that the laser-cooling method is a well-established technique to obtain ultracold neutral atoms and atomic cations, it has rarely if ever been applied to atomic anions due to the lack of suitable electric-dipole transitions. Efforts of more than a decade have until recently only resulted in ${\mathrm{La}}^{\ensuremath{-}}$ as a promising anion candidate for laser cooling, but our previous work [Tang et al., Phys. Rev. Lett. 123, 203002 (2019)] showed that ${\mathrm{Th}}^{\ensuremath{-}}$ is also a potential candidate. Here we report on a combination of experimental and theoretical studies to determine the frequencies and rates, as well as branching ratios, for the relevant transitions in ${\mathrm{Th}}^{\ensuremath{-}}$. The resonant frequency of the laser-cooling transition is determined to be $\ensuremath{\nu}=123.455(30)$ THz $[\ensuremath{\lambda}=2428.4(6)\phantom{\rule{0.16em}{0ex}}\mathrm{nm}]$. The transition rate is calculated as $A=1.17\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Since the branching fraction to dark states is negligible, $1.47\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, this represents an ideal closed cycle in ${\mathrm{Th}}^{\ensuremath{-}}$ for laser cooling. Furthermore, the zero nuclear spin of 232Th^{232}\mathrm{Th}232Th makes the cooling process possible in a Penning trap, which can be used to confine both antiprotons and ${\mathrm{Th}}^{\ensuremath{-}}$ ions. The presented ion dynamics simulations show that the laser-cooled ${\mathrm{Th}}^{\ensuremath{-}}$ anions can effectively cool antiprotons to a temperature around 10 mK.
The negative osmium ion ${\text{Os}}^{\ensuremath{-}}$ is one of very few atomic anions potentially suitable for laser cooling. We have made a measurement of the Zeeman splitting of a bound-bound transition in 192{}^{192}192${\text{Os}}^{\ensuremath{-}}$ by studying the laser excitation from the 5${d}^{7}666{s}^{2}$ 4{}^{4}4FFF9/2e{}_{9/2}^{e}9/2e​ ground to the 5${d}^{6}666{s}^{2}666p$ 6{}^{6}6DDD9/2o{}_{9/2}^{o}9/2o​ excited state in a homogeneous external magnetic field. The experimental Land\'e factors gJ=1.31(7){g}_{J}=1.31(7)gJ​=1.31(7) and gJ=1.50(8){g}_{J}=1.50(8)gJ​=1.50(8), respectively, agree well with calculated values. Both levels are found to split into 10 Zeeman sublevels, resulting in 28 allowed transitions of different relative intensities, in agreement with calculations based on pure and composite LSLSLS states. In view of the experimental results, the prospects for laser cooling of ${\text{Os}}^{\ensuremath{-}}$ are discussed.
Laser cooling of neutral atoms or positive ions is today routinely employed in numerous experiments. Negative ions, in contrast, have distinct characteristics which hamper the application of lasers for cooling. But in 1999, the discovery of the unique bound–bound electric dipole transition in the negative osmium ion provided the motivation for a first cooling attempt. This thesis presents the first milestones toward the ultimate goal of laser cooling negative osmium, including high-resolution laser spectroscopy of the relevant bound–bound E1 transition. Its frequency – between the ground 4F9/2 and the 6DJe1 (bound) excited states – was determined to be 257.831190(35) THz in 192Os-, in agreement\nwith a previous measurement, but two orders of magnitude more precise. The determination of the resonant cross-section implicitly provided the corresponding Einstein A coefficient, which was found to be A ~ 330 s-1. Furthermore, the isotope shift of the E1 transition and the hyperfine structure constants of the ground and excited state were obtained, for the first time, from the analysis of the spectra of all naturally abundant isotopes. The hyperfine structure revealed the heretofore unknown total angular momentum of the excited state to be Je1 = 9/2. Finally, laser spectroscopy in an external magnetic field confirmed the expected line splitting for Os- due to the Zeeman effect. Based on all these experimental results the prospect of laser cooling negative osmium is reviewed.