Physical Review A

Hyperfine structure in the 62D3/2 and 62D5/2 states of Rb87 and Rb85

J. R. Brandenberger, R. E. Lindley

Published Jun 19, 2015• 4 citations

Abstract

Improved measurements of hyperfine splittings in the $6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{3/2}$ and $6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}$ states of $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$ have been performed using Doppler-free, double-resonance, optical pumping laser spectroscopy. The small sizes of the splittings and their associated coupling constants limit the fractional precision of the results, but when these results are combined with past measurements and scaling rules, they provide a reasonably complete and satisfactory characterization of the entire hyperfine structure in the $6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{3/2}$ and $6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}$ manifolds of $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$.

DOI: 10.1103/physreva.91.062505

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Spectroscopy of Sr 87 triplet Rydberg states

Roger Ding, J. D. Whalen, S. K. Kanungo +4 more

arXiv:1808.05987Physical Review AOct 12, 201823 citations

Hyperfine-structure investigation of highly excited D2 levels in Rb87 and Cs133 using a cw tunable dye laser in a two-step excitation scheme

Sune R. Svanberg, Pericles G. Tsekeris

Physical Review AApr 1, 197546 citations

Bouble Resonance Optical Pumping in the Transition 5S1/2-5P3/2-4D3/2, 5/2of Rb Atoms

Han Seb Moon

한국광학회지Aug 1, 20050 citations

HYPERFINE STRUCTURE OF THE ELECTRONIC GROUND STATES OF Rb$sup 85$ AND Rb$sup 8$$sup 7$

Siegfried Penselin, Thomas I. Moran, Victor W. Cohen +1 more

Physical ReviewJul 15, 19620 citations

Energies and hyperfine splittings of the 7D levels of atomic francium

Joshua M. Grossman, R. Fliller, T. E. Mehlstäubler +4 more

Physical Review AOct 12, 200031 citations

Hyperfine Structure in the $^{87}$Rb$_{2}$ $1_{g}$ State Below $5^{2}S+5^{2}P_{1/2}$

T. H. Bergeman, Eite Tiesinga, Paul S. Julienne +2 more

APSJun 1, 20121 citation

Physical Review A

Hyperfine structure in the 62D3/2 and 62D5/2 states of Rb87 and Rb85

J. R. Brandenberger, R. E. Lindley

Published Jun 19, 2015• 4 citations

Publisher

Abstract

Improved measurements of hyperfine splittings in the

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{3/2}

and

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}

states of

^{87}\mathrm{Rb}

and

^{85}\mathrm{Rb}

have been performed using Doppler-free, double-resonance, optical pumping laser spectroscopy. The small sizes of the splittings and their associated coupling constants limit the fractional precision of the results, but when these results are combined with past measurements and scaling rules, they provide a reasonably complete and satisfactory characterization of the entire hyperfine structure in the

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{3/2}

and

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}

manifolds of

^{87}\mathrm{Rb}

and

^{85}\mathrm{Rb}

DOI: 10.1103/physreva.91.062505

Related papers

Spectroscopy of Sr 87 triplet Rydberg states

Roger Ding, J. D. Whalen, S. K. Kanungo +4 more

A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet $S$ and $D$ Rydberg states in $^{87}\mathrm{Sr}$ is presented. $^{87}\mathrm{Sr}$ has a large nuclear spin $I=9/2$ , and at high- $n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high- $n S$ states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the $I=0$ isotope $^{88}\mathrm{Sr}$ , which results in good agreement with the present measurements. For the $D$ states, this procedure is reversed by first extracting from the present $^{87}\mathrm{Sr}$ measurements the energies of the ${}^{3}{D}_{1,2,3}$ states to be expected for isotopes without hyperfine structure ( $^{88}\mathrm{Sr}$ ), which allows the determination of corrected quantum defects in the high- $n$ limit.A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet $S$ and $D$ Rydberg states in $^{87}\mathrm{Sr}$ is presented. $^{87}\mathrm{Sr}$ has a large nuclear spin $I=9/2$, and at high-$n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high-$n S$ states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the $I=0$ isotope $^{88}\mathrm{Sr}$, which results in good agreement with the present measurements. For the $D$ states, this procedure is reversed by first extracting from the present $^{87}\mathrm{Sr}$ measurements the energies of the ${}^{3}{D}_{1,2,3}$ states to be expected for isotopes without hyperfine structure ($^{88}\mathrm{Sr}$), which allows the determination of corrected quantum defects in the high-$n$ limit.

arXiv:1808.05987Physical Review AOct 12, 201823 citations

Hyperfine-structure investigation of highly excited D2 levels in Rb87 and Cs133 using a cw tunable dye laser in a two-step excitation scheme

Sune R. Svanberg, Pericles G. Tsekeris

The hyperfine structure of several highly excited $^{2}D$ states in $^{87}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$ has been measured. The $D$ -state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal ${D}_{1}$ and ${D}_{2}$ lines from an rf lamp was used to excite atoms into the first excited $^{2}P$ levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer $P$ -state atoms into highly excited $D$ states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants $a$ and $b$ : For $^{87}\mathrm{Rb}$ , $|a(6^{2}D_{\frac{3}{2}})|=7.84(5)$ , $|b(6^{2}D_{\frac{3}{2}})|=0.53(6)$ ( $\frac{b}{a}>0$ ), $|a(^{2}D_{\frac{5}{2}})|=3.6(7)$ , $|a(7^{2}D_{\frac{3}{2}})|=4.53(3)$ , $|b(7^{2}D_{\frac{3}{2}})|=0.26(4)$ ( $\frac{b}{a}>0$ ), $|a(7^{2}D_{\frac{5}{2}})|=2.2(5)$ . For $^{133}\mathrm{Cs}$ , $|a(8^{2}D_{\frac{3}{2}})|=3.98(8)$ , $|a(8^{2}D_{\frac{5}{2}})|=0.9(4)$ , $|a(9^{2}D_{\frac{3}{2}})|=2.37(3)$ , $|a(9^{2}D_{\frac{5}{2}})|=0.5(2)$ , $|a(10^{2}D_{\frac{3}{2}})|=1.52(3)$ , $|a(10^{2}D_{\frac{5}{2}})|=0.4(2)$ . The $a$ factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For $^{87}\mathrm{Rb}$ a comparison with a recent calculation including polarization effects is made. The $b$ factors for $^{87}\mathrm{Rb}$ are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non- $P$ -state data.The hyperfine structure of several highly excited $^{2}D$ states in $^{87}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$ has been measured. The $D$-state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal ${D}_{1}$ and ${D}_{2}$ lines from an rf lamp was used to excite atoms into the first excited $^{2}P$ levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer $P$-state atoms into highly excited $D$ states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants $a$ and $b$: For $^{87}\mathrm{Rb}$, $|a(6^{2}D_{\frac{3}{2}})|=7.84(5)$, $|b(6^{2}D_{\frac{3}{2}})|=0.53(6)$ ($\frac{b}{a}>0$), $|a(^{2}D_{\frac{5}{2}})|=3.6(7)$, $|a(7^{2}D_{\frac{3}{2}})|=4.53(3)$, $|b(7^{2}D_{\frac{3}{2}})|=0.26(4)$ ($\frac{b}{a}>0$), $|a(7^{2}D_{\frac{5}{2}})|=2.2(5)$. For $^{133}\mathrm{Cs}$, $|a(8^{2}D_{\frac{3}{2}})|=3.98(8)$, $|a(8^{2}D_{\frac{5}{2}})|=0.9(4)$, $|a(9^{2}D_{\frac{3}{2}})|=2.37(3)$, $|a(9^{2}D_{\frac{5}{2}})|=0.5(2)$, $|a(10^{2}D_{\frac{3}{2}})|=1.52(3)$, $|a(10^{2}D_{\frac{5}{2}})|=0.4(2)$. The $a$ factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For $^{87}\mathrm{Rb}$ a comparison with a recent calculation including polarization effects is made. The $b$ factors for $^{87}\mathrm{Rb}$ are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non-$P$-state data.

Physical Review AApr 1, 197546 citations

Bouble Resonance Optical Pumping in the Transition 5S1/2-5P3/2-4D3/2, 5/2of Rb Atoms

Han Seb Moon

우리는 $^{87}Rb$ 원자의 $5S_{1/2}-5P_{3/2}-4D_{3/2,\;5/2}$ 전이선을 이용하여 레이저의 세기, 편광조합, 그리고 정렬상태에 따른 이중공명광펌핑(double resonance optical pumping; DROP) 스펙트럼을 조사하였다. $5P_{3/2}-4D_{5/2}$ 전이선에서 레이저의 세기에 따른 초미세 구조간의 DROP 신호의 변화가 크게 나타났고, 그 원인은 순환전이선의 낮은 광펌핑 효율 때문이었다. 두 레이저의 편광조합을 달리 했을 때 이중공명의 전이율이 변하고, 이러한 효과가DROP스펙트럼의 변화로 나타났다. 또한 두 레이저가 같은 방향으로 진행하는 경우와 반대 방향으로 진행하는 경우를 비교했을 때, 스펙트럼의 선폭은 각각 12.2 MHz 와 6.9 MHz로 측정되었다. We present the double resonance optical pumping(DROP) spectra according to the laser power, the polarization combination of lasers, and the alignment of lasers in the transition $5P_{3/2}-4D_{5/2}\;and\;5P_{3/2}-4D_{5/2}$ of $^{87}Rb.$ We observed obviously changing DROP spectrum according to the laser power in the transition $5P_{3/2}-4D_{5/2}$ involved the cycling transition. The laser power effects are attributed to the low optical-pumping-effect in the cycling transition. We observed changing DROP spectrum depending on the polarizations of the lasers. The laser polarization effects are attributed to the changing transition probability according to the polarizations of lasers. We compared the co-propagation with the counter-propagation and the spectral linewidths were 12.2 MHz and 6.9 MHz, respectively.우리는 $^{87}Rb$ 원자의 $5S_{1/2}-5P_{3/2}-4D_{3/2,\;5/2}$ 전이선을 이용하여 레이저의 세기, 편광조합, 그리고 정렬상태에 따른 이중공명광펌핑(double resonance optical pumping; DROP) 스펙트럼을 조사하였다. $5P_{3/2}-4D_{5/2}$ 전이선에서 레이저의 세기에 따른 초미세 구조간의 DROP 신호의 변화가 크게 나타났고, 그 원인은 순환전이선의 낮은 광펌핑 효율 때문이었다. 두 레이저의 편광조합을 달리 했을 때 이중공명의 전이율이 변하고, 이러한 효과가DROP스펙트럼의 변화로 나타났다. 또한 두 레이저가 같은 방향으로 진행하는 경우와 반대 방향으로 진행하는 경우를 비교했을 때, 스펙트럼의 선폭은 각각 12.2 MHz 와 6.9 MHz로 측정되었다. We present the double resonance optical pumping(DROP) spectra according to the laser power, the polarization combination of lasers, and the alignment of lasers in the transition $5P_{3/2}-4D_{5/2}\;and\;5P_{3/2}-4D_{5/2}$ of $^{87}Rb.$ We observed obviously changing DROP spectrum according to the laser power in the transition $5P_{3/2}-4D_{5/2}$ involved the cycling transition. The laser power effects are attributed to the low optical-pumping-effect in the cycling transition. We observed changing DROP spectrum depending on the polarizations of the lasers. The laser polarization effects are attributed to the changing transition probability according to the polarizations of lasers. We compared the co-propagation with the counter-propagation and the spectral linewidths were 12.2 MHz and 6.9 MHz, respectively.

한국광학회지Aug 1, 20050 citations

HYPERFINE STRUCTURE OF THE ELECTRONIC GROUND STATES OF Rb $sup 85$ AND Rb $sup 8$ $sup 7$ HYPERFINE STRUCTURE OF THE ELECTRONIC GROUND STATES OF Rb$sup 85$ AND Rb$sup 8$$sup 7$

Siegfried Penselin, Thomas I. Moran, Victor W. Cohen +1 more

Physical ReviewJul 15, 19620 citations

Energies and hyperfine splittings of the 7D levels of atomic francium

Joshua M. Grossman, R. Fliller, T. E. Mehlstäubler +4 more

We report optical double-resonance spectroscopy to locate and study the ${7D}_{3/2}$ and ${7D}_{5/2}$ levels of a sample of ${}^{210}\mathrm{Fr}$ atoms confined and cooled in a magneto-optical trap. The upper state of the ${7P}_{3/2}$ trapping transition serves as the resonant intermediate level to reach the $7D$ states. The energy difference to the ground state is measured for the accessible levels. We measure the hyperfine splittings: $\ensuremath{\Delta}{(7D}_{3/2},F=15/2\ensuremath{\leftrightarrow}13/2)=167\ifmmode\pm\else\textpm\fi{}4 \mathrm{MHz},$ $\ensuremath{\Delta}{(7D}_{5/2},F=17/2\ensuremath{\leftrightarrow}15/2)=\ensuremath{-}117.5\ifmmode\pm\else\textpm\fi{}2.5 \mathrm{MHz},$ and $\ensuremath{\Delta}{(7D}_{5/2},F=15/2\ensuremath{\leftrightarrow}13/2)=\ensuremath{-}121\ifmmode\pm\else\textpm\fi{}4$ MHz. Extrapolating the energies of the inaccessible hyperfine levels from the hyperfine constants and assuming ${B(7D}_{3/2})=0,$ the center-of-gravity energy difference to the ground state is ${E(7D}_{3/2})=24244.831\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}$ and ${E(7D}_{5/2})=24333.298\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}.$We report optical double-resonance spectroscopy to locate and study the ${7D}_{3/2}$ and ${7D}_{5/2}$ levels of a sample of ${}^{210}\mathrm{Fr}$ atoms confined and cooled in a magneto-optical trap. The upper state of the ${7P}_{3/2}$ trapping transition serves as the resonant intermediate level to reach the $7D$ states. The energy difference to the ground state is measured for the accessible levels. We measure the hyperfine splittings: $\ensuremath{\Delta}{(7D}_{3/2},F=15/2\ensuremath{\leftrightarrow}13/2)=167\ifmmode\pm\else\textpm\fi{}4 \mathrm{MHz},$ $\ensuremath{\Delta}{(7D}_{5/2},F=17/2\ensuremath{\leftrightarrow}15/2)=\ensuremath{-}117.5\ifmmode\pm\else\textpm\fi{}2.5 \mathrm{MHz},$ and $\ensuremath{\Delta}{(7D}_{5/2},F=15/2\ensuremath{\leftrightarrow}13/2)=\ensuremath{-}121\ifmmode\pm\else\textpm\fi{}4$ MHz. Extrapolating the energies of the inaccessible hyperfine levels from the hyperfine constants and assuming ${B(7D}_{3/2})=0,$ the center-of-gravity energy difference to the ground state is ${E(7D}_{3/2})=24244.831\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}$ and ${E(7D}_{5/2})=24333.298\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}.$

Physical Review AOct 12, 200031 citations

Hyperfine Structure in the $^{87}$ Rb $_{2}$ $1_{g}$ State Below $5^{2}S+5^{2}P_{1/2}$ Hyperfine Structure in the $^{87}$Rb$_{2}$ $1_{g}$ State Below $5^{2}S+5^{2}P_{1/2}$

T. H. Bergeman, Eite Tiesinga, Paul S. Julienne +2 more

APSJun 1, 20121 citation

Improved measurements of hyperfine splittings in the

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{3/2}

and

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}

states of

^{87}\mathrm{Rb}

and

^{85}\mathrm{Rb}

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{3/2}

and

6\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}

manifolds of

^{87}\mathrm{Rb}

and

^{85}\mathrm{Rb}

A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet

S

and

D

Rydberg states in

^{87}\mathrm{Sr}

is presented.

^{87}\mathrm{Sr}

has a large nuclear spin

I=9/2

, and at high-

n

the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high-

n S

states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the

I=0

isotope

^{88}\mathrm{Sr}

, which results in good agreement with the present measurements. For the

D

states, this procedure is reversed by first extracting from the present

^{87}\mathrm{Sr}

measurements the energies of the

{}^{3}{D}_{1,2,3}

states to be expected for isotopes without hyperfine structure (

^{88}\mathrm{Sr}

), which allows the determination of corrected quantum defects in the high-

n

limit.

The hyperfine structure of several highly excited

^{2}D

states in

^{87}\mathrm{Rb}

and

^{133}\mathrm{Cs}

has been measured. The

D

-state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal

{D}_{1}

and

{D}_{2}

lines from an rf lamp was used to excite atoms into the first excited

^{2}P

levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer

P

-state atoms into highly excited

D

states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants

a

and

b

: For

^{87}\mathrm{Rb}

|a(6^{2}D_{\frac{3}{2}})|=7.84(5)

|b(6^{2}D_{\frac{3}{2}})|=0.53(6)

(

\frac{b}{a}>0

|a(^{2}D_{\frac{5}{2}})|=3.6(7)

|a(7^{2}D_{\frac{3}{2}})|=4.53(3)

|b(7^{2}D_{\frac{3}{2}})|=0.26(4)

(

\frac{b}{a}>0

|a(7^{2}D_{\frac{5}{2}})|=2.2(5)

. For

^{133}\mathrm{Cs}

|a(8^{2}D_{\frac{3}{2}})|=3.98(8)

|a(8^{2}D_{\frac{5}{2}})|=0.9(4)

|a(9^{2}D_{\frac{3}{2}})|=2.37(3)

|a(9^{2}D_{\frac{5}{2}})|=0.5(2)

|a(10^{2}D_{\frac{3}{2}})|=1.52(3)

|a(10^{2}D_{\frac{5}{2}})|=0.4(2)

. The

a

factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For

^{87}\mathrm{Rb}

a comparison with a recent calculation including polarization effects is made. The

b

factors for

^{87}\mathrm{Rb}

are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non-

P

-state data.

우리는

^{87}Rb

원자의

5S_{1/2}-5P_{3/2}-4D_{3/2,\;5/2}

전이선을 이용하여 레이저의 세기, 편광조합, 그리고 정렬상태에 따른 이중공명광펌핑(double resonance optical pumping; DROP) 스펙트럼을 조사하였다.

5P_{3/2}-4D_{5/2}

전이선에서 레이저의 세기에 따른 초미세 구조간의 DROP 신호의 변화가 크게 나타났고, 그 원인은 순환전이선의 낮은 광펌핑 효율 때문이었다. 두 레이저의 편광조합을 달리 했을 때 이중공명의 전이율이 변하고, 이러한 효과가DROP스펙트럼의 변화로 나타났다. 또한 두 레이저가 같은 방향으로 진행하는 경우와 반대 방향으로 진행하는 경우를 비교했을 때, 스펙트럼의 선폭은 각각 12.2 MHz 와 6.9 MHz로 측정되었다. We present the double resonance optical pumping(DROP) spectra according to the laser power, the polarization combination of lasers, and the alignment of lasers in the transition

5P_{3/2}-4D_{5/2}\;and\;5P_{3/2}-4D_{5/2}

^{87}Rb.

We observed obviously changing DROP spectrum according to the laser power in the transition

5P_{3/2}-4D_{5/2}

involved the cycling transition. The laser power effects are attributed to the low optical-pumping-effect in the cycling transition. We observed changing DROP spectrum depending on the polarizations of the lasers. The laser polarization effects are attributed to the changing transition probability according to the polarizations of lasers. We compared the co-propagation with the counter-propagation and the spectral linewidths were 12.2 MHz and 6.9 MHz, respectively.

HYPERFINE STRUCTURE OF THE ELECTRONIC GROUND STATES OF Rb

sup 85

AND Rb

sup 8

sup 7

We report optical double-resonance spectroscopy to locate and study the

{7D}_{3/2}

and

{7D}_{5/2}

levels of a sample of

{}^{210}\mathrm{Fr}

atoms confined and cooled in a magneto-optical trap. The upper state of the

{7P}_{3/2}

trapping transition serves as the resonant intermediate level to reach the

7D

states. The energy difference to the ground state is measured for the accessible levels. We measure the hyperfine splittings: $\ensuremath{\Delta}{(7D}_{3/2},F=15/2\ensuremath{\leftrightarrow}13/2)=167\ifmmode\pm\else\textpm\fi{}4 \mathrm{MHz},$ $\ensuremath{\Delta}{(7D}_{5/2},F=17/2\ensuremath{\leftrightarrow}15/2)=\ensuremath{-}117.5\ifmmode\pm\else\textpm\fi{}2.5 \mathrm{MHz},$ and $\ensuremath{\Delta}{(7D}_{5/2},F=15/2\ensuremath{\leftrightarrow}13/2)=\ensuremath{-}121\ifmmode\pm\else\textpm\fi{}4$ MHz. Extrapolating the energies of the inaccessible hyperfine levels from the hyperfine constants and assuming

{B(7D}_{3/2})=0,

the center-of-gravity energy difference to the ground state is ${E(7D}_{3/2})=24244.831\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}$ and ${E(7D}_{5/2})=24333.298\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}.$

Hyperfine Structure in the

^{87}

_{2}

1_{g}

State Below

5^{2}S+5^{2}P_{1/2}