Physical Review A

Hyperfine structure and three-channel quantum-defect theory of 6sndD21 Rydberg states of Ba

Herbert H. Rinneberg, Jörg Neukammer

Published Apr 1, 1983• 37 citations

Abstract

The hyperfine structure of $6snd^{1}D_{2}$ Rydberg states of $^{135,137}\mathrm{Ba}$ is reported for principal quantum numbers ranging between $n=10$ and $n=50$. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of $6snd^{1}D_{2} \mathrm{and} ^{3}D_{2}$ Rydberg states in the vicinity of the $5d7d^{1}D_{2}$ perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.

DOI: 10.1103/physreva.27.1779

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Physical Review A

Hyperfine structure and three-channel quantum-defect theory of 6sndD21 Rydberg states of Ba

Herbert H. Rinneberg, Jörg Neukammer

Published Apr 1, 1983• 37 citations

Publisher

Abstract

The hyperfine structure of

6snd^{1}D_{2}

Rydberg states of

^{135,137}\mathrm{Ba}

is reported for principal quantum numbers ranging between

n=10

and

n=50

. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of

6snd^{1}D_{2} \mathrm{and} ^{3}D_{2}

Rydberg states in the vicinity of the

5d7d^{1}D_{2}

perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.

DOI: 10.1103/physreva.27.1779

Related papers

Resonance in Singlet-Triplet Mixing in Two-Electron Systems Caused by Perturbing Configurations

Herbert H. Rinneberg, Jörg Neukammer

The hyperfine structure of the $6snd^{1}D_{2}$ ( $10<~n<~50$ ) Rydberg states of barium has been measured and analyzed in terms of singlet-triplet mixing. A dispersionlike resonant behavior of the mixing coefficient $\ensuremath{\Omega}$ was observed for barium and strontium in the vicinity of doubly excited configurations. In barium strong disagreement with multichannel-quantum-defect-theory wave functions was found. The present results are compared with the spin polarization and anisotropy of photoelectrons.The hyperfine structure of the $6snd^{1}D_{2}$ ($10<~n<~50$) Rydberg states of barium has been measured and analyzed in terms of singlet-triplet mixing. A dispersionlike resonant behavior of the mixing coefficient $\ensuremath{\Omega}$ was observed for barium and strontium in the vicinity of doubly excited configurations. In barium strong disagreement with multichannel-quantum-defect-theory wave functions was found. The present results are compared with the spin polarization and anisotropy of photoelectrons.

Physical Review LettersJul 12, 198234 citations

Configuration interaction and singlet-triplet mixing probed by hyperfine structure of 6s14d1D2and3D1,2,3barium Rydberg states

Jörg Neukammer, Herbert H. Rinneberg

Journal of Physics B Atomic and Molecular PhysicsNov 14, 198213 citations

Singlet-triplet mixing in 4snd Rydberg states of Ca

R. Beigang, K. Lücke, Andre Timmermann

Singlet-triplet mixing of $4snd ^{1}D_{2}$ and $^{3}D_{2}$ states of Ca was determined between principal quantum numbers $7<~n<~42$ with the use of Doppler-free two-photon spectroscopy. The hyperfine structure of the $4snd ^{1}D_{2}$ states was used to probe admixtures of triplet character into the singlet wave functions. It turned out that, in the region of series crossings, an enlarged singlet-triplet mixing was observed.Singlet-triplet mixing of $4snd ^{1}D_{2}$ and $^{3}D_{2}$ states of Ca was determined between principal quantum numbers $7<~n<~42$ with the use of Doppler-free two-photon spectroscopy. The hyperfine structure of the $4snd ^{1}D_{2}$ states was used to probe admixtures of triplet character into the singlet wave functions. It turned out that, in the region of series crossings, an enlarged singlet-triplet mixing was observed.

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Influence of Singlet-Triplet Mixing on the Hyperfine Structure of 5snd Rydberg States in Sr87

R. Beigang, Eckart Matthias, Andre Timmermann

A systematic study of the hyperfine structure of $5snd$ $^{1}D_{2}$ and $^{3}D_{2}$ states of $^{87}\mathrm{Sr}$ was carried out by Doppler-free two-photon excitation. In the region of strong singlet-triplet mixing around $n=16$ , the hyperfine structure exhibits a marked $n$ dependence which is related to the amount of singlet-triplet mixing.A systematic study of the hyperfine structure of $5snd$ $^{1}D_{2}$ and $^{3}D_{2}$ states of $^{87}\mathrm{Sr}$ was carried out by Doppler-free two-photon excitation. In the region of strong singlet-triplet mixing around $n=16$, the hyperfine structure exhibits a marked $n$ dependence which is related to the amount of singlet-triplet mixing.

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Hyperfine structure of extremely high Rydberg msns1S0and msns3S1series in odd alkaline-earth isotopes

Jun-Qiang Sun, K. T. Lu

In extremely high Rydberg states of odd alkaline-earth isotopes, the Fermi constant a ms is comparable to the energy separation between levels belonging to different principal quantum numbers n and hyperfine interactions dominate the structure of the levels. The multichannel quantum defect theory of fine structure has been developed and applied to hyperfine structure and thus the HFS can be analysed directly by MQDT. A two-channel quantum defect model for extremely high Rydberg msns 1 S 0 and msns 3 S 1 series in odd alkaline-earth isotopes for F=I is described. The U i(F)i matrix is given analytically and the relationship between the eigenquantum defects of HFS and the quantum defects of fine structure is derived. The HFS of two extremely high Rydberg 5sns 1 S 0 and 3 S 1 series in 87 Sr has been calculated by the model and an excellent agreement between the theoretical and experimental results has been achieved. The HFS of extremely high Rydberg msns 1 S 0 and 3 S 1 series in 43 Ca, 135 Ba and 137 Ba are also analysed by the model.In extremely high Rydberg states of odd alkaline-earth isotopes, the Fermi constant a ms is comparable to the energy separation between levels belonging to different principal quantum numbers n and hyperfine interactions dominate the structure of the levels. The multichannel quantum defect theory of fine structure has been developed and applied to hyperfine structure and thus the HFS can be analysed directly by MQDT. A two-channel quantum defect model for extremely high Rydberg msns 1 S 0 and msns 3 S 1 series in odd alkaline-earth isotopes for F=I is described. The U i(F)i matrix is given analytically and the relationship between the eigenquantum defects of HFS and the quantum defects of fine structure is derived. The HFS of two extremely high Rydberg 5sns 1 S 0 and 3 S 1 series in 87 Sr has been calculated by the model and an excellent agreement between the theoretical and experimental results has been achieved. The HFS of extremely high Rydberg msns 1 S 0 and 3 S 1 series in 43 Ca, 135 Ba and 137 Ba are also analysed by the model.

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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

The hyperfine structure of

6snd^{1}D_{2}

Rydberg states of

^{135,137}\mathrm{Ba}

is reported for principal quantum numbers ranging between

n=10

and

n=50

. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of

6snd^{1}D_{2} \mathrm{and} ^{3}D_{2}

Rydberg states in the vicinity of the

5d7d^{1}D_{2}

The hyperfine structure of the

6snd^{1}D_{2}

(

10<~n<~50

) Rydberg states of barium has been measured and analyzed in terms of singlet-triplet mixing. A dispersionlike resonant behavior of the mixing coefficient $\ensuremath{\Omega}$ was observed for barium and strontium in the vicinity of doubly excited configurations. In barium strong disagreement with multichannel-quantum-defect-theory wave functions was found. The present results are compared with the spin polarization and anisotropy of photoelectrons.

Singlet-triplet mixing of

4snd ^{1}D_{2}

and

^{3}D_{2}

states of Ca was determined between principal quantum numbers

7<~n<~42

with the use of Doppler-free two-photon spectroscopy. The hyperfine structure of the

4snd ^{1}D_{2}

states was used to probe admixtures of triplet character into the singlet wave functions. It turned out that, in the region of series crossings, an enlarged singlet-triplet mixing was observed.

A systematic study of the hyperfine structure of

5snd

^{1}D_{2}

and

^{3}D_{2}

states of

^{87}\mathrm{Sr}

was carried out by Doppler-free two-photon excitation. In the region of strong singlet-triplet mixing around

n=16

, the hyperfine structure exhibits a marked

n

dependence which is related to the amount of singlet-triplet mixing.

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.