Physical Review A

Improved calculation of the electron affinity of He 1s2sS3

Annik Vivier Bunge, Carlos F. Bunge

Published Nov 1, 1984• 48 citations

Abstract

Large-scale optimization of nonlinear parameters and tighter error-bound estimates yield an accurate value, ${E}_{\mathrm{nr}}=\ensuremath{-}2.1780776(12)$ a.u. ($^{4}\mathrm{He}$) for the nonrelativistic energy of ${\mathrm{He}}^{\ensuremath{-}}$ $1s2s2p^{4}P^{o}$, in agreement with a previous result of -2.1780740(100). Using Chung's recent calculation of relativistic and mass-polarization effects, an electron affinity $A=77.51\ifmmode\pm\else\textpm\fi{}0.04$ meV is obtained. The calculation and significance of error bars in electronic structure calculations is discussed.

DOI: 10.1103/physreva.30.2179

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Physical Review A

Improved calculation of the electron affinity of He 1s2sS3

Annik Vivier Bunge, Carlos F. Bunge

Published Nov 1, 1984• 48 citations

Publisher

Abstract

Large-scale optimization of nonlinear parameters and tighter error-bound estimates yield an accurate value,

{E}_{\mathrm{nr}}=\ensuremath{-}2.1780776(12)

a.u. (

^{4}\mathrm{He}

) for the nonrelativistic energy of

{\mathrm{He}}^{\ensuremath{-}}

1s2s2p^{4}P^{o}

, in agreement with a previous result of -2.1780740(100). Using Chung's recent calculation of relativistic and mass-polarization effects, an electron affinity

A=77.51\ifmmode\pm\else\textpm\fi{}0.04

meV is obtained. The calculation and significance of error bars in electronic structure calculations is discussed.

DOI: 10.1103/physreva.30.2179

Related papers

Relativistic effects of the 1s2s2pP4 of He−

Kwong T. Chung

With the use of an accurate nonrelativistic wave function, the relativistic effects of the ${\mathrm{He}}^{\ensuremath{-}}$ $1s2s2p^{4}P$ state are computed. These include the mass-correction term, Darwin term, and retardation and mass-polarization effects. The calculated result enables us to significantly reduce the uncertainty of the electron affinity given by Bunge and Bunge. To assist future experimental measurement on the fine structure of this ion, the expectation values of the spin-orbit, spin-other-orbit, and spin-spin operators are also calculated.With the use of an accurate nonrelativistic wave function, the relativistic effects of the ${\mathrm{He}}^{\ensuremath{-}}$ $1s2s2p^{4}P$ state are computed. These include the mass-correction term, Darwin term, and retardation and mass-polarization effects. The calculated result enables us to significantly reduce the uncertainty of the electron affinity given by Bunge and Bunge. To assist future experimental measurement on the fine structure of this ion, the expectation values of the spin-orbit, spin-other-orbit, and spin-spin operators are also calculated.

Physical Review AFeb 1, 198411 citations

Binding energy of the lowest state of negative beryllium

Annik Vivier Bunge

Accurate eigenvalues of Schr\"odinger's nonrelativistic equation for Be (1${s}^{2} $2s2p$ {)}^{3}$P and ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$ (1${s}^{2} $2s2$ {p}^{2}$ ${)}^{4}$ P have been calculated yielding a corresponding electron affinity A of 276.1\ifmmode\pm\else\textpm\fi{}6.5 meV. The absolute term value of ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$ (relative to the Be ground state) obtained as the difference between the experimental term value of Be $^{3}\mathrm{P}$ and A is 2.4492\ifmmode\pm\else\textpm\fi{}0.0065 eV, in agreement with a recent measurement of 2.53\ifmmode\pm\else\textpm\fi{}0.11 eV.Accurate eigenvalues of Schr\"odinger's nonrelativistic equation for Be (1${s}^{2}$2s2p${)}^{3}$P and ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$ (1${s}^{2}$2s2${p}^{2}$${)}^{4}$P have been calculated yielding a corresponding electron affinity A of 276.1\ifmmode\pm\else\textpm\fi{}6.5 meV. The absolute term value of ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$ (relative to the Be ground state) obtained as the difference between the experimental term value of Be $^{3}\mathrm{P}$ and A is 2.4492\ifmmode\pm\else\textpm\fi{}0.0065 eV, in agreement with a recent measurement of 2.53\ifmmode\pm\else\textpm\fi{}0.11 eV.

Physical Review AJan 1, 198629 citations

Wavelength, oscillator strength, and fine structure for the →44 S° transition of Mg−

Donald R. Beck

We have calculated the electron affinities, including many-body and relativistic effects, of ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{P}$ and ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{\ifmmode^\circ\else\textdegree\fi{}}$ to be 321 and 536 meV, respectively. The electric dipole f value for the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition is 0.3087 (length) and 0.3000 (velocity), occurring at a theoretically predicted wavelength of 2921 A\r{}. The J=1/2\ensuremath{\rightarrow}3/2 fine-structure splitting for ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{P}$ is predicted to be 11.8 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and the J=3/2\ensuremath{\rightarrow}5/2 splitting 19.4 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. These results should help in the attempt being made by Andersen (private communiation) to observe the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition in the laboratory.We have calculated the electron affinities, including many-body and relativistic effects, of ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{P}$ and ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{\ifmmode^\circ\else\textdegree\fi{}}$ to be 321 and 536 meV, respectively. The electric dipole f value for the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition is 0.3087 (length) and 0.3000 (velocity), occurring at a theoretically predicted wavelength of 2921 A\r{}. The J=1/2\ensuremath{\rightarrow}3/2 fine-structure splitting for ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{P}$ is predicted to be 11.8 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and the J=3/2\ensuremath{\rightarrow}5/2 splitting 19.4 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. These results should help in the attempt being made by Andersen (private communiation) to observe the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition in the laboratory.

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Electron Affinity of Strontium

D. Berkovits, Elisabetta Boaretto, S. Ghelberg +2 more

We have observed a threshold in the electron photodetachment cross section of ${^{88}S\mathrm{r}}^{\ensuremath{-}}$ ions at a photon energy $h\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.820\mathrm{eV}$ and assign it to a $p$ -wave transition from the ${5s}^{2}5p^{2}P$ ground state in ${\mathrm{Sr}}^{\ensuremath{-}}$ to the $5s5p^{3}P$ state in neutral Sr. The measurement was made with a new technique combining the tunable laser photodetachment threshold method with accelerator mass spectrometry. We determine for the first time the electron affinity of Sr to be $48\ifmmode\pm\else\textpm\fi{}6\mathrm{meV}$, much smaller than predicted in recent calculations. The $^{2}P_{1/2}$ - $^{2}P_{3/2}$ fine splitting of the ${\mathrm{Sr}}^{\ensuremath{-}}$ ground state is estimated to be $26\ifmmode\pm\else\textpm\fi{}8\mathrm{meV}$.We have observed a threshold in the electron photodetachment cross section of ${^{88}S\mathrm{r}}^{\ensuremath{-}}$ ions at a photon energy $h\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.820\mathrm{eV}$ and assign it to a $p$-wave transition from the ${5s}^{2}5p^{2}P$ ground state in ${\mathrm{Sr}}^{\ensuremath{-}}$ to the $5s5p^{3}P$ state in neutral Sr. The measurement was made with a new technique combining the tunable laser photodetachment threshold method with accelerator mass spectrometry. We determine for the first time the electron affinity of Sr to be $48\ifmmode\pm\else\textpm\fi{}6\mathrm{meV}$, much smaller than predicted in recent calculations. The $^{2}P_{1/2}$- $^{2}P_{3/2}$ fine splitting of the ${\mathrm{Sr}}^{\ensuremath{-}}$ ground state is estimated to be $26\ifmmode\pm\else\textpm\fi{}8\mathrm{meV}$.

Physical Review LettersJul 17, 199525 citations

Measurement of the electron affinity of thulium

V. T. Davis, J. S. Thompson

The electron affinity of thulium has been measured using laser photodetachment electron spectroscopy. The electron affinity of $\mathrm{Tm}{(}^{2}{F}_{7/2})$ was determined to be $1.029\ifmmode\pm\else\textpm\fi{}0.022\mathrm{eV}.$ The data also show that ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}$ has at least one bound excited state with a binding energy of $0.979\ifmmode\pm\else\textpm\fi{}0.017\mathrm{eV}$ relative to the ground state of the thulium atom. The present experimental measurements are compared to a recent calculation of the electronic structure of ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}$ and a recent experimental investigation of ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}.$The electron affinity of thulium has been measured using laser photodetachment electron spectroscopy. The electron affinity of $\mathrm{Tm}{(}^{2}{F}_{7/2})$ was determined to be $1.029\ifmmode\pm\else\textpm\fi{}0.022\mathrm{eV}.$ The data also show that ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}$ has at least one bound excited state with a binding energy of $0.979\ifmmode\pm\else\textpm\fi{}0.017\mathrm{eV}$ relative to the ground state of the thulium atom. The present experimental measurements are compared to a recent calculation of the electronic structure of ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}$ and a recent experimental investigation of ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}.$

Physical Review ADec 12, 200120 citations

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

William C. Martin, Craig J. Sansonetti

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 $n\ensuremath{\simeq}8$.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 $n\ensuremath{\simeq}8$.

Physical Review AJul 1, 19834 citations

Large-scale optimization of nonlinear parameters and tighter error-bound estimates yield an accurate value,

{E}_{\mathrm{nr}}=\ensuremath{-}2.1780776(12)

a.u. (

^{4}\mathrm{He}

) for the nonrelativistic energy of

{\mathrm{He}}^{\ensuremath{-}}

1s2s2p^{4}P^{o}

, in agreement with a previous result of -2.1780740(100). Using Chung's recent calculation of relativistic and mass-polarization effects, an electron affinity

A=77.51\ifmmode\pm\else\textpm\fi{}0.04

meV is obtained. The calculation and significance of error bars in electronic structure calculations is discussed.

With the use of an accurate nonrelativistic wave function, the relativistic effects of the ${\mathrm{He}}^{\ensuremath{-}}$

1s2s2p^{4}P

state are computed. These include the mass-correction term, Darwin term, and retardation and mass-polarization effects. The calculated result enables us to significantly reduce the uncertainty of the electron affinity given by Bunge and Bunge. To assist future experimental measurement on the fine structure of this ion, the expectation values of the spin-orbit, spin-other-orbit, and spin-spin operators are also calculated.

Accurate eigenvalues of Schr\"odinger's nonrelativistic equation for Be (1${s}^{2}

2s2p

{)}^{3}$P and ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$ (1${s}^{2}

2s2

{p}^{2}$

{)}^{4}

P have been calculated yielding a corresponding electron affinity A of 276.1\ifmmode\pm\else\textpm\fi{}6.5 meV. The absolute term value of ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$ (relative to the Be ground state) obtained as the difference between the experimental term value of Be

^{3}\mathrm{P}

and A is 2.4492\ifmmode\pm\else\textpm\fi{}0.0065 eV, in agreement with a recent measurement of 2.53\ifmmode\pm\else\textpm\fi{}0.11 eV.

We have calculated the electron affinities, including many-body and relativistic effects, of ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$

^{4}\mathrm{P}

and ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$ $^{4}\mathrm{\ifmmode^\circ\else\textdegree\fi{}}$ to be 321 and 536 meV, respectively. The electric dipole f value for the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition is 0.3087 (length) and 0.3000 (velocity), occurring at a theoretically predicted wavelength of 2921 A\r{}. The J=1/2\ensuremath{\rightarrow}3/2 fine-structure splitting for ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$

^{4}\mathrm{P}

is predicted to be 11.8 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and the J=3/2\ensuremath{\rightarrow}5/2 splitting 19.4 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. These results should help in the attempt being made by Andersen (private communiation) to observe the $^{4}\ensuremath{\rightarrow}^{4}$S\ifmmode^\circ\else\textdegree\fi{} transition in the laboratory.

p

-wave transition from the

{5s}^{2}5p^{2}P

ground state in ${\mathrm{Sr}}^{\ensuremath{-}}$ to the

5s5p^{3}P

state in neutral Sr. The measurement was made with a new technique combining the tunable laser photodetachment threshold method with accelerator mass spectrometry. We determine for the first time the electron affinity of Sr to be $48\ifmmode\pm\else\textpm\fi{}6\mathrm{meV}$, much smaller than predicted in recent calculations. The

^{2}P_{1/2}

^{2}P_{3/2}

fine splitting of the ${\mathrm{Sr}}^{\ensuremath{-}}$ ground state is estimated to be $26\ifmmode\pm\else\textpm\fi{}8\mathrm{meV}$.

The electron affinity of thulium has been measured using laser photodetachment electron spectroscopy. The electron affinity of

\mathrm{Tm}{(}^{2}{F}_{7/2})

was determined to be $1.029\ifmmode\pm\else\textpm\fi{}0.022\mathrm{eV}.$ The data also show that ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}$ has at least one bound excited state with a binding energy of $0.979\ifmmode\pm\else\textpm\fi{}0.017\mathrm{eV}$ relative to the ground state of the thulium atom. The present experimental measurements are compared to a recent calculation of the electronic structure of ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}$ and a recent experimental investigation of ${\mathrm{Tm}}^{\mathrm{\ensuremath{-}}}.$

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 $n\ensuremath{\simeq}8$.