<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>States of the Helium Isoelectronic Sequence up to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn><mml:mn /></mml:math>

Accad, Y.; Pekeris, C. L.; Schiff, B.

doi:10.1103/physreva.4.516

Cited by 530 publications

(173 citation statements)

References 23 publications

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“…We have treated the helium isoelectronic series for Z -2 up to 10 [36,37]. These theoretical results agree throughout with recent experimental data which have come from spectra produced by lasers and in plasmas, as well as from other refined experimental techniques.…”

Section: Introductionsupporting

confidence: 75%

Adventures in applied mathematics

Pekeris¹

1972

Quart. Appl. Math.

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Abstract.A review is given of the work carried out at the Weizmann Institute during the past 25 years in the fields of terrestrial spectroscopy, the dynamo theory of the earth's magnetic field, the tides in the world oceans, theoretical seismograma, hydrodynamic stability, atomic spectroscopy, and the Boltzmann integral equation. Some open problems in the solution of the Schrodinger wave equation are formulated.

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Section: Introductionsupporting

confidence: 75%

Adventures in applied mathematics

Pekeris¹

1972

Quart. Appl. Math.

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“…The general quality of these functions is indicated more specifically in Table 1, where we list such criteria of accuracy as the energy error, ihe overlap, and the degree of satisfaction of the virial theorem and cusp conditions. The expectation values of the operators 6(r,), r, -,, 6(r12), and r1,-, are also listed in Table 1, together with the percentage errors wherever accurate values are available (11)(12)(13)(14)(15). Energetically, these functions are of course still somewhat inferior to the well-known 71n the case of r, -Z and r12-', these formulas (5) strengthen and generalize eqs.…”

Section: Wauefunctionsmentioning

confidence: 91%

“…functions of Pekeris and co-workers (11)(12)(13)(14)(15)(16), but suggests (19) that such properties as (6(r1)) and their portability and compactness give them (6(r12)) might also be represented to a superior certain distinct advantages for our present pur-accuracy by our functions. poses.…”

Section: Wauefunctionsmentioning

confidence: 92%

Lower Bounds to Expectation Values: Two-Electron Atoms

Chong¹,

Hold²

1973

Can. J. Chem.

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Weinhold's lower bound formulas are used on rather accurate wavefunctions for the 1's ground states of H-, He, and Li+, and the 2IS and Z3S excited states of He. The results are found to be of very high quality, as judged by comparison with the best available variational calculations, and can be used to rule out many of the values calculated by Scherr and Knight from high-order perturbation theory. 260 (1973) Introduction The concept of attaching rigorous error limits to theoretical estimates of quantummechanical properties is attractive to many chemists and physicists. Such upper and lower bounds not only provide internal and a pviori measures of reliability, but also enable one to make more meaningful comparisons with experimental results. One of the recent developments in this direction is the application of Gramian determinantal ineq~alities.~ For the lower bounds to expectation values of positive operators, Weinhold (2-5) derived a wide variety of relatively simple formulas and illustrated their use with the familiar Is2 and lsls' trial functions for the 1'S ground state of the helium atom, with promising results. The purpose of this work is to test some of these procedures on better wavefunctions. On the basis of certain preliminary results, we were encouraged to employ some rather accurate wavefunctions which could be expected to yield bounds of a definitive quality for the simple 2-electron atomic systems.

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“…The use of wave functions analogous to [4] to describe the D states of 2pnp requires only a straiglitforward extension (10); however, the calculations would be considerably lengthier because more terms are required in the matrix elements, and we did not explore them for reasons of cost. We did, however, explore the uncorrelated analogue of [4] Can.…”

Section: Lsnrimentioning

confidence: 99%

“…Straightforward niodification of the wave function [4] to give the combinations of y-electron functions appropriate to an S state leads to x [cos 0, cos02 + sinOl sinO2 cos(@, -@,)I where tlie (+) sign corresponds to '5' and the ( -) sign to 'S. Use of this wave fi~nction leads immediately to calculated energies below the observed values for both 2p2 'S and 21,311 3S (for example, with a function x(0;12,1), N = 26. values of -0.723 and -0.579 au, compared with the observed values (3) of -0.620 and -0.558 au respectively).…”

Section: S States 2sns and 2pnpmentioning

confidence: 99%

Variational energies for highly excited states of the helium atom

Ma¹,

Kuriyan²,

Pritchard³

1978

Can. J. Chem.

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The efficient correlated variational wave functions used previously to study the higher 1 sns states of helium have been extended to other states of the helium atom, 1 snp (n ≤ 23), 2pnp1P (n ≤ 25), and 2pnp3P (n ≤ 25); similar uncorrelated wave functions were used for 1snd (n ≤ 21), 2pnp1D (n ≤ 10), and 2pnp3D (n ≤ 10). Attempts to use the same techniques for the 2pnp1,3S states appear to converge variationally to the energies of the 2s21S and 2s3s3S states respectively. Comparison is made with experimental results where appropriate, and agreement is excellent except in the case of the 1snd states above n = 13.A search was made for excited states of H− in each of these configurations, but no new states were found.

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SandPStates of the Helium Isoelectronic Sequence up toZ=10

Cited by 530 publications

References 23 publications

Adventures in applied mathematics

Adventures in applied mathematics

Lower Bounds to Expectation Values: Two-Electron Atoms

Variational energies for highly excited states of the helium atom

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