Introduction

Schmid, Erich W.; Spitz, Gerhard; Lösch, Wolfgang

doi:10.1007/978-3-642-97088-7_1

Cited by 3 publications

(6 citation statements)

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“…(B.4) Aside from units (most treatments use the so-called chemistry units), these all agree with results in the literature [3,13]. Use of the optimally determined parameters, c 1 ≈ 0.0803 and c 2 ≈ 0.0099, and k ≈ 0.908 determines the energy via equation (B.1).…”

Section: A4 Matrix Equation For I Max =supporting

confidence: 79%

“…In reality, minimization of the energy with Hy yields E Hy ≈ −78.979 eV, with variational parameters c 1 ≈ 0.0803 and c 2 ≈ 0.0099 and k ≈ 0.908. Evaluating the necessary integrals and obtaining these results is well documented [3,13], and so these are simply summarized in appendix B. The attained energy is within 0.05% of the exact result (−79.014 eV); we consider this sufficiently close to justify our adoption for the present purposes of 1 √ N | Hy as the 'exact' normalized helium wavefunction, with N given below.…”

Section: Hylleraas Wavefunction: Bound Statesmentioning

confidence: 59%

“…For equation ( 13) to be useful we need to know exact ; as mentioned in the introduction, this is known numerically to many digits precision [5], using a Hylleraas-type basis [3,13]:…”

Section: Hylleraas Wavefunction: Bound Statesmentioning

confidence: 99%

“…With a very accurate wavefunction in hand, we can simply utilize equation (13) to determine the probability of each basis state in the ground state wavefunction. The general hydrogenic bound state can be written as many of these integrals are straightforward to calculate analytically-an example will be shown below.…”

Section: B2 Overlap Integrals: Bound Statesmentioning

confidence: 99%

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The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

Hutchinson¹,

Baker²,

Marsiglio³

2012

Eur. J. Phys.

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The two electron configuration in the Helium atom is known to very high precision. Yet, we tend to refer to this configuration as a 1s ↑ 1s ↓ singlet, where the designations refer to Hydrogen orbitals. The high precision calculations utilize basis sets that are suited for high accuracy and ease of calculation, but do not really aid in our understanding of the electron configuration in terms of product states of Hydrogen orbitals. Since undergraduate students are generally taught to think of Helium, and indeed, the rest of the periodic table, in terms of Hydrogenic orbitals, we present in this paper a detailed spectral decomposition of the two electron ground state for Helium in terms of these basis states. The 1s ↑ 1s ↓ singlet contributes less than 93% to the ground state configuration, with other contributions coming from both bound and continuum Hydrogenic states.

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Section: A4 Matrix Equation For I Max =supporting

confidence: 79%

Section: Hylleraas Wavefunction: Bound Statesmentioning

confidence: 59%

“…For equation ( 13) to be useful we need to know exact ; as mentioned in the introduction, this is known numerically to many digits precision [5], using a Hylleraas-type basis [3,13]:…”

Section: Hylleraas Wavefunction: Bound Statesmentioning

confidence: 99%

Section: B2 Overlap Integrals: Bound Statesmentioning

confidence: 99%

See 2 more Smart Citations

The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

Hutchinson¹,

Baker²,

Marsiglio³

2012

Eur. J. Phys.

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“…The nomenclature ν 1 , ν 2 , ν 3 , ν 4 has been consistent since Herzberg (1945), Shimanouchi (1972) and up to the present time (Jäger et al 1986); some authors prefer to call ν 2 'umbrella mode'. In scattering from central potentials the dominant partial cross sections σ shift towards higher with an increase in the effective radius of the potential (Landau and Lifshitz 1965, section 123), and the number of minima in the elastic cross sections as a function of scattering angle increases (Schmid et al 1988, Koonin 1986. It is thus tempting to attribute the 'bumpy' shape of NF 3 (i.e.…”

Section: Elastic Differential Cross Sections and Their Integralsmentioning

confidence: 99%

Vibrationally inelastic and elastic cross sections for collisions

Boesten

Tachibana

Nakano

et al. 1996

J. Phys. B: At. Mol. Opt. Phys.

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Absolute elastic cross sections for electron impact on nitrogen trifluoride have been recorded for impact energies from 1.5 to 100 eV and scattering angles from to . Because of the small dipole moment, estimates of the integrated and momentum-transfer cross sections were obtained by extrapolation of the angular range with the help of a modified phase-shift program and subsequent numerical integration under the fits. Vibrational excitation function measurements show a 2 eV wide resonance at 3 eV impact energy. Vibrational loss spectra were measured near this resonance and resolved into their vibrational components and . From the angular behaviour of these fundamental modes, the resonance can be assigned to a temporary trapping of the impinging electron in the antibonding orbital of irreducible species `e', the LUMO orbit.

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Calculation of the ground-state energy, the first ionization energy and the radial correlation expectation value for He-like atoms

et al. 2006

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Combining perturbation theory with the Ritz variation method, an analytical approach to the ground-state energy, the first ionization energy J(1S0) and the radial correlation expectation value ⟨r12−1 ⟩ (1S0) for He-like atoms is given in this paper. The possibility to extend our present analytical model to the doubly excited states (nl)2 is illustrated in this work by the calculation of the total energies and the radial correlation expectation value for the 2p2 1D, 3p2 1D, 4p2 1D and 5p2 1D singlet doubly excites states of He-like atoms with Z⩽12. The results presented in this paper indicate that the present analytical approach can usefully be performed to show quantitatively the importance of electron correlations in the ground-state and in the doubly excited states mainly for high-Z helium isoelectronic series.

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Introduction

Cited by 3 publications

References 0 publications

The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

Vibrationally inelastic and elastic cross sections for collisions

Calculation of the ground-state energy, the first ionization energy and the radial correlation expectation value for He-like atoms

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