Physical Review A

Binding energy of the lowest state of negative beryllium

Annik Vivier Bunge

Published Jan 1, 1986• 29 citations

Abstract

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.

DOI: 10.1103/physreva.33.82

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Physical Review A

Binding energy of the lowest state of negative beryllium

Annik Vivier Bunge

Published Jan 1, 1986• 29 citations

Publisher

Abstract

Accurate eigenvalues of Schr"odinger's nonrelativistic equation for Be (1

{s}^{2}

2s2p

{)}^{3}

P and

{\mathrm{Be}}^{\mathrm{\ensuremath{-}}}

{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.

DOI: 10.1103/physreva.33.82

Related papers

Improved calculation of the electron affinity of He 1s2sS3

Annik Vivier Bunge, Carlos F. Bunge

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.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.

Physical Review ANov 1, 198448 citations

La− binding energies by analysis of its photodetachment spectra

Lin Pan, Donald R. Beck

This study reinterprets an earlier experimental photoelectron kinetic energy spectrum of the negative ion of lanthanum [A. M. Covington, D. Calabrese, J. S. Thompson, and T. J. Kvale, J. Phys. B 31, L855 (1998)] by carrying out relativistic configuration interaction (RCI) photodetachment calculations. The results confirm the earlier RCI calculation for the electron affinity of lanthanum (0.545 eV) [S. M. O'Malley and D. R. Beck, Phys. Rev. A 79, 012511 (2009)] and revise it to a slightly larger value of 0.550 eV, thus modifying the experimental interpretation of $0.47\ifmmode\pm\else\textpm\fi{}0.02$ eV. The calculation also yields the binding energies of the other thirteen bound states of ${\mathrm{La}}^{\ensuremath{-}}$. Good agreement has been found when these energies are compared to the results of a recent experimental study on ${\mathrm{La}}^{\ensuremath{-}}$ [C. W. Walter, N. D. Gibson, D. J. Matyas, C. T. Crocker, K. A. Dungan, B. R. Matola, and J. Rohl\'en, Phys. Rev. Lett. 113, 063001 (2014)]. Finally, our analysis confirms the transition energy for the potential laser cooling transition of ${}^{3}{F}_{2}^{e}\ensuremath{\rightarrow}{}^{3}{D}_{1}^{o}$ in ${\mathrm{La}}^{\ensuremath{-}}$.This study reinterprets an earlier experimental photoelectron kinetic energy spectrum of the negative ion of lanthanum [A. M. Covington, D. Calabrese, J. S. Thompson, and T. J. Kvale, J. Phys. B 31, L855 (1998)] by carrying out relativistic configuration interaction (RCI) photodetachment calculations. The results confirm the earlier RCI calculation for the electron affinity of lanthanum (0.545 eV) [S. M. O'Malley and D. R. Beck, Phys. Rev. A 79, 012511 (2009)] and revise it to a slightly larger value of 0.550 eV, thus modifying the experimental interpretation of $0.47\ifmmode\pm\else\textpm\fi{}0.02$ eV. The calculation also yields the binding energies of the other thirteen bound states of ${\mathrm{La}}^{\ensuremath{-}}$. Good agreement has been found when these energies are compared to the results of a recent experimental study on ${\mathrm{La}}^{\ensuremath{-}}$ [C. W. Walter, N. D. Gibson, D. J. Matyas, C. T. Crocker, K. A. Dungan, B. R. Matola, and J. Rohl\'en, Phys. Rev. Lett. 113, 063001 (2014)]. Finally, our analysis confirms the transition energy for the potential laser cooling transition of ${}^{3}{F}_{2}^{e}\ensuremath{\rightarrow}{}^{3}{D}_{1}^{o}$ in ${\mathrm{La}}^{\ensuremath{-}}$.

Physical Review AJun 1, 201610 citations

Bound-state properties of the positronium negative ion Ps−

Alexei M. Frolov

Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{\ensuremath{-}}$ or ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=\ensuremath{-}0.2620050702329757\mathrm{a}.\mathrm{u}.$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $\ensuremath{-}0.326674721317821\mathrm{eV}).$ The computation of the second-order relativistic corrections $(\ensuremath{\simeq}{\ensuremath{\alpha}}^{2})$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{\ensuremath{-}}$ ion is presented.Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{\ensuremath{-}}$ or ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=\ensuremath{-}0.2620050702329757\mathrm{a}.\mathrm{u}.$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $\ensuremath{-}0.326674721317821\mathrm{eV}).$ The computation of the second-order relativistic corrections $(\ensuremath{\simeq}{\ensuremath{\alpha}}^{2})$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{\ensuremath{-}}$ ion is presented.

Physical Review AOct 1, 199972 citations

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

Relativistic corrections to the ground-state energy of the positronium molecule

Sergiy Bubin, Monika Stanke, Dariusz Kędziera +1 more

The leading-order relativistic corrections to the ground-state energy of the positronium molecule $({\mathrm{Ps}}_{2})$ have been computed within the framework of perturbation theory. As the zero-order wave function we used a highly accurate nonrelativistic variational expansion in terms of 6000 explicitly correlated Gaussians that yielded the lowest variational upper bound for this system to date. We also report some expectation values representing the properties of ${\mathrm{Ps}}_{2}$ .The leading-order relativistic corrections to the ground-state energy of the positronium molecule $({\mathrm{Ps}}_{2})$ have been computed within the framework of perturbation theory. As the zero-order wave function we used a highly accurate nonrelativistic variational expansion in terms of 6000 explicitly correlated Gaussians that yielded the lowest variational upper bound for this system to date. We also report some expectation values representing the properties of ${\mathrm{Ps}}_{2}$.

Physical Review AJun 11, 200728 citations

Structural properties of the negative strontium ion: Binding energy and fine-structure splitting

H. H. Andersen, V. V. Petrunin, P. Kristensen +1 more

The binding energy and fine-structure splitting of the ground state of the ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$n(${5\mathrm{s}}^{2} $5p$ {\mathrm{}}^{2}$P) ion have been measured by means of the laser photodetachment threshold technique combined with state-selective detection of neutral atoms using resonant ionization spectroscopy. We find binding energies of 32.17\ifmmode\pm\else\textpm\fi{}0.03 meV (J=3/2) and 52.06\ifmmode\pm\else\textpm\fi{}0.06 meV (J=1/2), yielding a fine-structure splitting of 19.89\ifmmode\pm\else\textpm\fi{}0.07 meV. This represents an improvement of two orders of magnitude compared to the recent data based on a combination of laser photodetachment and accelerator mass spectroscopy [D. Berkovits et al., Phys. Rev. Lett. 75, 414 (1995)].The binding energy and fine-structure splitting of the ground state of the ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$n(${5\mathrm{s}}^{2}$5p${\mathrm{}}^{2}$P) ion have been measured by means of the laser photodetachment threshold technique combined with state-selective detection of neutral atoms using resonant ionization spectroscopy. We find binding energies of 32.17\ifmmode\pm\else\textpm\fi{}0.03 meV (J=3/2) and 52.06\ifmmode\pm\else\textpm\fi{}0.06 meV (J=1/2), yielding a fine-structure splitting of 19.89\ifmmode\pm\else\textpm\fi{}0.07 meV. This represents an improvement of two orders of magnitude compared to the recent data based on a combination of laser photodetachment and accelerator mass spectroscopy [D. Berkovits et al., Phys. Rev. Lett. 75, 414 (1995)].

Physical Review AApr 1, 199726 citations

Accurate eigenvalues of Schr"odinger's nonrelativistic equation for Be (1

{s}^{2}

2s2p

{)}^{3}

P and

{\mathrm{Be}}^{\mathrm{\ensuremath{-}}}

{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.

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.

The leading-order relativistic corrections to the ground-state energy of the positronium molecule

({\mathrm{Ps}}_{2})

have been computed within the framework of perturbation theory. As the zero-order wave function we used a highly accurate nonrelativistic variational expansion in terms of 6000 explicitly correlated Gaussians that yielded the lowest variational upper bound for this system to date. We also report some expectation values representing the properties of

{\mathrm{Ps}}_{2}

The binding energy and fine-structure splitting of the ground state of the ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$n(${5\mathrm{s}}^{2}

5p

{\mathrm{}}^{2}$P) ion have been measured by means of the laser photodetachment threshold technique combined with state-selective detection of neutral atoms using resonant ionization spectroscopy. We find binding energies of 32.17\ifmmode\pm\else\textpm\fi{}0.03 meV (J=3/2) and 52.06\ifmmode\pm\else\textpm\fi{}0.06 meV (J=1/2), yielding a fine-structure splitting of 19.89\ifmmode\pm\else\textpm\fi{}0.07 meV. This represents an improvement of two orders of magnitude compared to the recent data based on a combination of laser photodetachment and accelerator mass spectroscopy [D. Berkovits et al., Phys. Rev. Lett. 75, 414 (1995)].