Physical Review A

Improved measurement of the He4 i 3D1−3D3 separation: Confirmation of predicted mass-polarization isotopic shift

William C. Martin, Craig J. Sansonetti

Published Jul 1, 1983• 4 citations

Abstract

From new measurements of the $^{4}\mathrm{He}$ $1s2p\ensuremath{-}1s3d$ lines, we have determined the $3^{1}D_{2}\ensuremath{-}3^{3}D_{2}$ separation to be 102 459(15) MHz. The corresponding nonrelativistic $1s3d$ singlet-triplet separation is 102 196(15) MHz, as compared with the value 102 116(5) MHz previously determined for the equivalent $^{3}\mathrm{He}$ separation. The difference of 80(16) MHz agrees with the predicted isotopic difference of these separations, the main contribution being a mass-polarization difference of 79 MHz as recently calculated by Drake. The experimental difference for $1s3d$ is consistent with the rough trend of such isotopic differences of $1snd$ singlet-triplet separations determined in previous experiments. We infer that mass-polarization shifts probably contribute significantly to the previously observed differences, at least up to $n\ensuremath{\simeq}8$.

DOI: 10.1103/physreva.28.502

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Physical Review A

Improved measurement of the He4 i 3D1−3D3 separation: Confirmation of predicted mass-polarization isotopic shift

William C. Martin, Craig J. Sansonetti

Published Jul 1, 1983• 4 citations

Publisher

Abstract

From new measurements of the

^{4}\mathrm{He}

1s2p\ensuremath{-}1s3d

lines, we have determined the

3^{1}D_{2}\ensuremath{-}3^{3}D_{2}

separation to be 102 459(15) MHz. The corresponding nonrelativistic

1s3d

singlet-triplet separation is 102 196(15) MHz, as compared with the value 102 116(5) MHz previously determined for the equivalent

^{3}\mathrm{He}

separation. The difference of 80(16) MHz agrees with the predicted isotopic difference of these separations, the main contribution being a mass-polarization difference of 79 MHz as recently calculated by Drake. The experimental difference for

1s3d

is consistent with the rough trend of such isotopic differences of

1snd

singlet-triplet separations determined in previous experiments. We infer that mass-polarization shifts probably contribute significantly to the previously observed differences, at least up to

n\ensuremath{\simeq}8

DOI: 10.1103/physreva.28.502

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Anticrossing spectroscopy of the n=6,7,8 D1,3 states in He3

R. L. Panock, Richard R. Freeman, Bernard R. Zegarski +1 more

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Alexei M. Frolov

The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$ He $(2^3S)]$ and $e^{+}[^4$ He $(2^3S)]$ . In particular, we have fond that for the $e^{+}[{}^3$ He $(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$ , 76466.5308 $MHz$ and 5824.4019 $MHz$ . In the $e^{+}[{}^4$ He $(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$. In particular, we have fond that for the $e^{+}[{}^3$He$(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$, 76466.5308 $MHz$ and 5824.4019 $MHz$. In the $e^{+}[{}^4$He$(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.

Aug 20, 20120 citations

Observation of mixed singlet-triplet Rb2 Rydberg molecules

Fabian Böttcher, Anita Gaj, K. M. Westphal +6 more

We present high-resolution spectroscopy of ${\mathrm{Rb}}_{\text{2}}$ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet $s$ -wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the $p$ -wave contribution and all orders in the relative momentum $k$ , and compare the obtained molecular binding energies to the experimental data.We present high-resolution spectroscopy of ${\mathrm{Rb}}_{\text{2}}$ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet $s$-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the $p$-wave contribution and all orders in the relative momentum $k$, and compare the obtained molecular binding energies to the experimental data.

arXiv:1510.01097Physical Review AMar 21, 201659 citations

From new measurements of the

^{4}\mathrm{He}

1s2p\ensuremath{-}1s3d

lines, we have determined the

3^{1}D_{2}\ensuremath{-}3^{3}D_{2}

separation to be 102 459(15) MHz. The corresponding nonrelativistic

1s3d

singlet-triplet separation is 102 196(15) MHz, as compared with the value 102 116(5) MHz previously determined for the equivalent

^{3}\mathrm{He}

1s3d

is consistent with the rough trend of such isotopic differences of

1snd

singlet-triplet separations determined in previous experiments. We infer that mass-polarization shifts probably contribute significantly to the previously observed differences, at least up to

n\ensuremath{\simeq}8

The anticrossing spectra of the $n=6,7,8 ^{1}D\ensuremath{-}^{3}D$ states of

^{3}\mathrm{He}

have been observed. From these measurements precise values of the electrostatic singlet-triplet separation of these states have been obtained and are found to differ systematically from the accepted values of the

^{4}\mathrm{He}

singlet-triplet separation by approximately 34 MHz. We have investigated mass-dependent contributions to both the energy-level structure and the magnetic-tuning characteristics of the states of interest. We have found no mechanism that can explain such a large difference in the electrostatic-energy separation of the singlet and triplet

D

states between the two helium isotopes.

The method of singlet-triplet level anticrossing has been extended to the

n=6^{1,3}D

levels of He. Measurement of this anticrossing gives a highly accurate determination of the zero-field singlet-triplet separation and a less accurate determination of the antisymmetric part of the spin-orbit coupling perturbation between the

n=6^{1,3}D

states. The zero-field separation for

n=6

, although considerably more accurate, is in essential agreement with previous optical results, confirming the accuracy of the intercombination line measurements. The singlettriplet intervals calculated by many-body perturbation theory are also found to be in very good agreement with the experimental results.

Two independent anticrossings have been observed between singlet and triplet levels in the He atom, one between the

7^{1}D

and

7^{3}D

states, the other between the

8^{1}D

and

8^{3}D

states. The states are excited by electron bombardment. Compensatory changes in the luminosity of the singlet and triplet states are detected as the levels are tuned through the anticrossing points by a magnetic field. The positions of the anticrossings have been analyzed to provide new values for these singlet-triplet separations accurate to \ensuremath{\sim}0.03 GHz. These results show the previous best optical determinations for the separations to be in error by over a GHz. The widths of the anticrossings are analyzed to provide the most direct measures of the spin-orbit coupling constant between a singlet and a triplet state yet obtained for any system. The measured values of these coupling constants are found to be several times larger than their corresponding diagonal value in the

7^{3}D

and

8^{3}D

states.

Isotope shifts have been measured in the velocity-dependent total cross sections of the

{m}_{1}

=1 magnetic substate of He(3

^{3}

P) formed in low keV

{\mathrm{He}}^{+}

{\mathrm{H}}_{2}

{\mathrm{D}}_{2}

collisions. Similar isotope shifts have been predicted on theoretical grounds and observed in ion-atom collision experiments, where united-atom rotational coupling is the primary excitation mechanism. By extending the basic theoretical ideas to ion-molecule collisions, we can interpret our measured shifts as resulting from rotational coupling within the triatomic

{\mathrm{HeH}}_{2}^{+}

complex.

Hyperfine structure splitting of the positron-helium ions

e^{+}[

(2^3S)]

The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion

e^{+}[^3

(2^3S)]

and

e^{+}[^4

(2^3S)]

. In particular, we have fond that for the

e^{+}[{}^3

(2^3S)]

ion one can observe the three following hyperfine structure splittinings: 5824.3986

MHz

, 76466.5308

MHz

and 5824.4019

MHz

. In the

e^{+}[{}^4

(2^3S)]

ion only one hyperfine structure splitting 82963.0427

MHz

can be observed. All these values can be measured in modern experiments.

We present high-resolution spectroscopy of

{\mathrm{Rb}}_{\text{2}}

ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet

s

-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the

p

-wave contribution and all orders in the relative momentum

k

, and compare the obtained molecular binding energies to the experimental data.