Nonrelativistic energies for the lowest 4P° states of the Li isoelectronic series

Barrois, René; Bekavac, Sabina; Kleindienst, Heinz

doi:10.1016/s0009-2614(97)00209-1

Cited by 12 publications

(7 citation statements)

References 17 publications

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“…The calculated

Δ E

(1s2s3s 4 S – 1s2s2p 4 P ) is in close agreement with the accurate result of Barrois et al who report the value 34,071.36(44) cm −1 in comparison with the present calculation of 34,072.0(17) cm −1 . The error reported by Barrois et al makes no reference to assessment of the relativistic error and the QED contribution is not considered. Both these theoretical values are in close agreement to the experimental value of Levitt and Feldman who report the value 34,071.91(05) cm −1 .…”

Section: Discussionsupporting

confidence: 92%

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High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying ⁴ S levels of the lithium atom

King

2013

Int. J. Quantum Chem.

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High-precision Hylleraas-type calculations of the hyperfine constants for the four lowest excited 1s2sns 4 S e (n 5 3-6) levels of the lithium atom are reported. The transition energies from the lowest 4 P o term to the 1s2sns 4 S e (n 5 3-6) levels for the stable isotopes 6 Li and 7 Li are evaluated. A number of addition expectation values for the four levels studied are also reported, including some moments of the electron-nuclear separation, the electron-electron separation, and the specific mass-shift operator.

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“…The calculated

Δ E

Section: Discussionsupporting

confidence: 92%

“…The excited quartet levels of the lithium atom have attracted considerable experimental and theoretical attention, though these levels have been studied significantly less extensively than both the ground state and some of the low‐lying excited levels of various symmetries for this atomic system …”

Section: Introductionmentioning

confidence: 99%

High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying ⁴ S levels of the lithium atom

King

2013

Int. J. Quantum Chem.

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“…Needless to say that the low‐lying excited states of Li atom and a few members of its isoelectronic sequence, were studied through the years using different approaches, mostly variational and Monte‐Carlo ones. In particular, the accurate variational calculations of spin‐quartet states of Li‐like isoelectronic sequence of the type

((), 1 s 2 s italicns)

n = 3, 4, \dots

and

((), 1 s 2 s italicnp)

n = 2, 3, \dots

were performed in [10–12]. More recent calculations for the Lithium states

((), 1 s 2 s italicns)

for

n = 3 - 8

and

((), 1 s 2 s italicnp)

for

n = 2 - 7

, for the cases of infinite and finite nuclear mass of 7 Li, were done extensively in [13] by using the so‐called double‐basis set in Hylleraas coordinates of size

\sim ((), 5000, 5000)

, where the benchmark energy value for the Li state

((), 1 s 2 s 3 s)

1^{4} S

was found to be

E_{1^{4} S}^{\infty} = - 5.212748247225

a.u.…”

Section: Introductionmentioning

confidence: 99%

Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus: III. Spin‐quartet state (1s2s3s) of the lithium sequence

Nader

Valle

Vieyra

et al. 2022

Int J of Quantum Chemistry

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As a continuation of Part I, dedicated to the ground state of He‐like and Li‐like isoelectronic sequences for nuclear charges Z≤20, and Part II, dedicated to two excited states of He‐like sequence, two ultra‐compact wave functions in the form of generalized Guevara–Harris–Turbiner functions are constructed for Li‐like sequence. They describe accurately the domain of applicability of the non‐relativistic Quantum Mechanics of Coulomb Charges (QMCC) for energies (2–3 significant digits [s.d.]) of the spin‐quartet state 140+ of Li‐like ions (in static approximation with point‐like, infinitely heavy nuclei). Variational parameters are fitted in Z by 2nd degree polynomials. The most accurate ultra‐compact function leads to the absolute accuracy ∼10−3 a.u. for energy, and ∼10−4 for the normalized electron‐nuclear cusp parameter for Z≤20. Critical charge Z=ZB, where the ultra‐compact trial function for the 140+ state loses its square‐integrability, is estimated, ZB()140.1em0+∼1.26−1.30. As a complement to Part I, square integrability for the compact functions constructed for the ground, spin‐doublet state 120.1em0+ of the Li‐like sequence is discussed. The critical charge, for which these functions stop to be normalizable, is estimated as ZB()120.1em0+=1.62−1.65. It implies that at Z=2—the negative helium ion He−—both states, 120.1em0+ and 140.1em0+, exist as states embedded in the continuum.

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“…. were performed in [11][12][13]. More recent calculations for the Lithium states (1s 2s ns) for n = 3 − 8 and (1s 2s np) for n = 2 − 7, for the cases of infinite and finite nuclear mass of 7 Li, were done extensively in [18] by using the so-called double-basis set in Hylleraas coordinates of size ∼ (5000, 5000), where the benchmark energy value for the Li state (1s2s3s) or 1 4 S was found to be E ∞ 1 4 S = −5.212748247225 a.u.…”

Section: Introductionmentioning

confidence: 99%

Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. III. Spin-quartet state of the Lithium sequence

Nader,

del Valle,

Vieyra

et al. 2022

Preprint

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As a continuation of Part I, dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges Z ≤ 20, and Part II, dedicated to two excited states of He-like sequence, two ultra-compact wave functions in the form of generalized Guevara-Harris-Turbiner functions are constructed for Li-like sequence. They describe accurately the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC) for energies (2-3 significant digits (s.d.)) of the spin-quartet state 1 4 0 + of Li-like ions (in static approximation with point-like, infinitely heavy nuclei). Variational parameters are fitted in Z by 2nd degree polynomials. The most accurate ultra-compact function leads to the absolute accuracy ∼ 10 −3 a.u. for energy, and ∼ 10 −4 for the normalized electron-nuclear cusp parameter for Z ≤ 20. Critical charge Z = Z B , where the ultra-compact trial function for the 1 4 0 + state looses its square-integrability, is estimated, Z B (1 4 0 + ) ∼ 1.26 − 1.30. As a complement to Part I, square integrability for the compact functions constructed for the ground, spin-doublet state 1 2 0 + of the Li-like sequence is discussed. The critical charge, for which these functions stop to be normalizable, is estimated as Z B (1 2 0 + ) = 1.62 − 1.65.It implies that at Z = 2 -the negative helium ion He − -both states 1 2 0 + and 1 4 0 + exist as states embedded to continuum.

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Nonrelativistic energies for the lowest 4P° states of the Li isoelectronic series

Cited by 12 publications

References 17 publications

High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying ⁴ S levels of the lithium atom

High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying ⁴ S levels of the lithium atom

Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus: III. Spin‐quartet state (1s2s3s) of the lithium sequence

Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. III. Spin-quartet state of the Lithium sequence

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Nonrelativistic energies for the lowest 4P° states of the Li isoelectronic series

Cited by 12 publications

References 17 publications

High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying 4 S levels of the lithium atom

High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying 4 S levels of the lithium atom

Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus: III. Spin‐quartet state (1s2s3s) of the lithium sequence

Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. III. Spin-quartet state of the Lithium sequence

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Product

Resources

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High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying ⁴ S levels of the lithium atom

High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying ⁴ S levels of the lithium atom