Lifetime calculations for the 5s5p P-3(2) metastable level of Sr-88 I

Liu, Yong, Andersson, Martin, Tomas Brage, Zou, Yaming, R. Hutton

Published Jan 1, 2007• 0 citations

Abstract

We report on a large scale calculation concerning the 5s(2) S-1 and 5s5p P-1,P-3 levels in Sr-88 I, using multiconfiguration Dirac-Fock methods. Our focus is on the P-3(2) meta-stable level, which has been shown to be extremely useful in atom cooling and trapping experiments. The lifetime for this level from our work (1071 s) agrees very well with a previous theoretical value, but not with the available experimental value (520(-140)(+310)s). The results for all the transitions between the 5s2 1S and 5s5p P-1,P-3 levels and within the 5s5p P-1,P-3 terms are also given.

DOI: 10.1103/physreva.75.014502

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Lifetime calculations for the 5s5p P-3(2) metastable level of Sr-88 I

Liu, Yong, Andersson, Martin, Tomas Brage, Zou, Yaming, R. Hutton

Published Jan 1, 2007• 0 citations

Publisher

Abstract

DOI: 10.1103/physreva.75.014502

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Lifetime calculations for the 5s5pP23 metastable level of Sr88I

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We report on a large scale calculation concerning the $5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S$ and $5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P$ levels in $^{88}\mathrm{Sr}\phantom{\rule{0.2em}{0ex}}I$ , using multiconfiguration Dirac-Fock methods. Our focus is on the $^{3}P_{2}$ meta-stable level, which has been shown to be extremely useful in atom cooling and trapping experiments. The lifetime for this level from our work $(1071\phantom{\rule{0.3em}{0ex}}s)$ agrees very well with a previous theoretical value, but not with the available experimental value $({520}_{\ensuremath{-}140}^{+310}\phantom{\rule{0.3em}{0ex}}s)$. The results for all the transitions between the $5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S$ and $5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P$ levels and within the $5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P$ terms are also given.We report on a large scale calculation concerning the $5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S$ and $5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P$ levels in $^{88}\mathrm{Sr}\phantom{\rule{0.2em}{0ex}}I$, using multiconfiguration Dirac-Fock methods. Our focus is on the $^{3}P_{2}$ meta-stable level, which has been shown to be extremely useful in atom cooling and trapping experiments. The lifetime for this level from our work $(1071\phantom{\rule{0.3em}{0ex}}s)$ agrees very well with a previous theoretical value, but not with the available experimental value $({520}_{\ensuremath{-}140}^{+310}\phantom{\rule{0.3em}{0ex}}s)$. The results for all the transitions between the $5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S$ and $5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P$ levels and within the $5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P$ terms are also given.

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The natural lifetime of the metastable $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state in $^{88}\mathrm{Sr}^{+}$ has been measured using a single laser-cooled, trapped ion. The ion was prepared in the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state by laser excitation of the $5s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ quadrupole transition at 674 nm. The decay time was measured by using Dehmelt's electron shelving method to monitor the ion's electronic state. Two separate investigations were conducted under slightly different experimental conditions. 160 000 decay times from the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state were observed in total, and two different methods for determining the statistical value of the measured lifetime have been compared. Systematic effects have also been estimated, and including these effects yields a value of $\ensuremath{\tau}=390.8(1.6)\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ ($1\ensuremath{\sigma}$ uncertainty) for the natural lifetime.The natural lifetime of the metastable $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state in $^{88}\mathrm{Sr}^{+}$ has been measured using a single laser-cooled, trapped ion. The ion was prepared in the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state by laser excitation of the $5s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ quadrupole transition at 674 nm. The decay time was measured by using Dehmelt's electron shelving method to monitor the ion's electronic state. Two separate investigations were conducted under slightly different experimental conditions. 160 000 decay times from the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state were observed in total, and two different methods for determining the statistical value of the measured lifetime have been compared. Systematic effects have also been estimated, and including these effects yields a value of $\ensuremath{\tau}=390.8(1.6)\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ ($1\ensuremath{\sigma}$ uncertainty) for the natural lifetime.

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MF -dependent hyperfine-induced 5s5pP0o3–5s2S01 clock transition rates in an external magnetic field for Sr87

Xiaotong Lu, Feng Guo, Yebing Wang +4 more

In this paper, we theoretically calculate the natural lifetime of the $5s5p\phantom{\rule{4pt}{0ex}}^{3}\mathrm{P}_{0}^{o}$ state of the $^{87}\mathrm{Sr}$ atom and evaluate the effect of an external magnetic field on the lifetimes of Zeeman sublevels. Using the multiconfiguration Dirac-Hartree-Fock method, the hyperfine-induced $5s5p^{3}\mathrm{P}_{0}^{o}--5{s}^{2}\phantom{\rule{0.28em}{0ex}}^{1}\mathrm{S}_{0}$ clock transition rate of $^{87}\mathrm{Sr}$ is estimated as $6.39(37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to a lifetime of 156(9) s. Our result closely agrees with previous measurements after correcting the decay rate due to the black-body radiation effect. Additionally, the transition rates of Zeeman sublevels are calculated as a function of the magnetic-field strength. Our theoretical results reveal that transition rates between different excited Zeeman states are discrepant, and the lifetime of magnetic sublevel $+{M}_{F}^{e}\phantom{\rule{4pt}{0ex}}(\ensuremath{-}{M}_{F}^{e}$; the superscript $e$ refers to the excited state, i.e., the $5s5p\phantom{\rule{0.28em}{0ex}}^{3}\mathrm{P}_{0}^{o}$ state) will increase (decrease) with the magnetic-field strength. Moreover, we measure the coupling strength between the clock laser and the $^{87}\mathrm{Sr}$ atoms, and our findings align well with theoretical estimations regarding changes in normalized coupling strength with external magnetic-field strength.In this paper, we theoretically calculate the natural lifetime of the $5s5p\phantom{\rule{4pt}{0ex}}^{3}\mathrm{P}_{0}^{o}$ state of the $^{87}\mathrm{Sr}$ atom and evaluate the effect of an external magnetic field on the lifetimes of Zeeman sublevels. Using the multiconfiguration Dirac-Hartree-Fock method, the hyperfine-induced $5s5p^{3}\mathrm{P}_{0}^{o}--5{s}^{2}\phantom{\rule{0.28em}{0ex}}^{1}\mathrm{S}_{0}$ clock transition rate of $^{87}\mathrm{Sr}$ is estimated as $6.39(37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to a lifetime of 156(9) s. Our result closely agrees with previous measurements after correcting the decay rate due to the black-body radiation effect. Additionally, the transition rates of Zeeman sublevels are calculated as a function of the magnetic-field strength. Our theoretical results reveal that transition rates between different excited Zeeman states are discrepant, and the lifetime of magnetic sublevel $+{M}_{F}^{e}\phantom{\rule{4pt}{0ex}}(\ensuremath{-}{M}_{F}^{e}$; the superscript $e$ refers to the excited state, i.e., the $5s5p\phantom{\rule{0.28em}{0ex}}^{3}\mathrm{P}_{0}^{o}$ state) will increase (decrease) with the magnetic-field strength. Moreover, we measure the coupling strength between the clock laser and the $^{87}\mathrm{Sr}$ atoms, and our findings align well with theoretical estimations regarding changes in normalized coupling strength with external magnetic-field strength.

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We report on a large scale calculation concerning the

5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S

and

5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P

levels in

^{88}\mathrm{Sr}\phantom{\rule{0.2em}{0ex}}I

, using multiconfiguration Dirac-Fock methods. Our focus is on the

^{3}P_{2}

meta-stable level, which has been shown to be extremely useful in atom cooling and trapping experiments. The lifetime for this level from our work

(1071\phantom{\rule{0.3em}{0ex}}s)

agrees very well with a previous theoretical value, but not with the available experimental value $({520}_{\ensuremath{-}140}^{+310}\phantom{\rule{0.3em}{0ex}}s)$. The results for all the transitions between the

5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S

and

5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P

levels and within the

5s5p\phantom{\rule{0.2em}{0ex}}^{1,3}P

terms are also given.

The lifetime of the metastable autodetaching 1s2s2p

^{4}

{\mathit{P}}_{5/2}

level of the $^{4}\mathrm{He}^{\mathrm{\ensuremath{-}}}$ ion has been measured by a time-of-flight technique to be 350\ifmmode\pm\else\textpm\fi{}15 \ensuremath{\mu}s using a heavy-ion storage ring. Blackbody-induced photodetachment of this weakly bound level is shown to influence the decay rate by nearly 20%, an effect not discussed previously. The magnetic-field-induced mixing effects provide additional information about the lifetime of the close-lying

^{4}

{\mathit{P}}_{3/2}

level, yielding \ensuremath{\tau}

{(}^{4}

{\mathit{P}}_{3/2}

)=12\ifmmode\pm\else\textpm\fi{}2 \ensuremath{\mu}s. The observed lifetimes are consistent with previous experimental values, but the accuracy of the

^{4}

{\mathit{P}}_{5/2}

lifetime is improved by a factor of 6, allowing a detailed test of theoretical predictions to be performed. The

^{4}

{\mathit{P}}_{5/2}

lifetime is significantly shorter than most recent advanced theoretical results, but in agreement with a multiconfiguration Hartree-Fock approach accurately describing the initial bound

^{4}

{\mathit{P}}_{5/2}

and the final continuum

^{2}

{\mathit{F}}_{5/2}

states.

The natural lifetime of the metastable

4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state in

^{88}\mathrm{Sr}^{+}

has been measured using a single laser-cooled, trapped ion. The ion was prepared in the

4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state by laser excitation of the $5s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ quadrupole transition at 674 nm. The decay time was measured by using Dehmelt's electron shelving method to monitor the ion's electronic state. Two separate investigations were conducted under slightly different experimental conditions. 160 000 decay times from the

4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state were observed in total, and two different methods for determining the statistical value of the measured lifetime have been compared. Systematic effects have also been estimated, and including these effects yields a value of $\ensuremath{\tau}=390.8(1.6)\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ ($1\ensuremath{\sigma}$ uncertainty) for the natural lifetime.

In this paper, we theoretically calculate the natural lifetime of the

5s5p\phantom{\rule{4pt}{0ex}}^{3}\mathrm{P}_{0}^{o}

state of the

^{87}\mathrm{Sr}

atom and evaluate the effect of an external magnetic field on the lifetimes of Zeeman sublevels. Using the multiconfiguration Dirac-Hartree-Fock method, the hyperfine-induced

5s5p^{3}\mathrm{P}_{0}^{o}--5{s}^{2}\phantom{\rule{0.28em}{0ex}}^{1}\mathrm{S}_{0}

clock transition rate of

^{87}\mathrm{Sr}

is estimated as $6.39(37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to a lifetime of 156(9) s. Our result closely agrees with previous measurements after correcting the decay rate due to the black-body radiation effect. Additionally, the transition rates of Zeeman sublevels are calculated as a function of the magnetic-field strength. Our theoretical results reveal that transition rates between different excited Zeeman states are discrepant, and the lifetime of magnetic sublevel $+{M}_{F}^{e}\phantom{\rule{4pt}{0ex}}(\ensuremath{-}{M}_{F}^{e}$; the superscript

e

refers to the excited state, i.e., the

5s5p\phantom{\rule{0.28em}{0ex}}^{3}\mathrm{P}_{0}^{o}

state) will increase (decrease) with the magnetic-field strength. Moreover, we measure the coupling strength between the clock laser and the

^{87}\mathrm{Sr}

atoms, and our findings align well with theoretical estimations regarding changes in normalized coupling strength with external magnetic-field strength.