# Analytic matrix elements for the two-electron atomic basis with logarithmic terms

## Abstract

The two-electron problem for the helium-like atoms in S-state is considered. The basis containing the integer powers of ln r, where r is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions for the matrix elements of the corresponding Hamiltonian are presented. These expressions include only elementary and special functions, what enables very fast and accurate computation of the matrix elements. The decisive contribution of the correct logarithmic terms to the behavior of the two-electron wave function in the vicinity of the triple-coalescence point is reaffirmed.

- Authors:

- Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)

- Publication Date:

- OSTI Identifier:
- 22306081

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; ELECTRONS; HAMILTONIANS; MATRIX ELEMENTS; S STATES; WAVE FUNCTIONS

### Citation Formats

```
Liverts, Evgeny Z., and Barnea, Nir.
```*Analytic matrix elements for the two-electron atomic basis with logarithmic terms*. United States: N. p., 2014.
Web. doi:10.1063/1.4890562.

```
Liverts, Evgeny Z., & Barnea, Nir.
```*Analytic matrix elements for the two-electron atomic basis with logarithmic terms*. United States. doi:10.1063/1.4890562.

```
Liverts, Evgeny Z., and Barnea, Nir. Fri .
"Analytic matrix elements for the two-electron atomic basis with logarithmic terms". United States.
doi:10.1063/1.4890562.
```

```
@article{osti_22306081,
```

title = {Analytic matrix elements for the two-electron atomic basis with logarithmic terms},

author = {Liverts, Evgeny Z. and Barnea, Nir},

abstractNote = {The two-electron problem for the helium-like atoms in S-state is considered. The basis containing the integer powers of ln r, where r is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions for the matrix elements of the corresponding Hamiltonian are presented. These expressions include only elementary and special functions, what enables very fast and accurate computation of the matrix elements. The decisive contribution of the correct logarithmic terms to the behavior of the two-electron wave function in the vicinity of the triple-coalescence point is reaffirmed.},

doi = {10.1063/1.4890562},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 55,

place = {United States},

year = {Fri Aug 01 00:00:00 EDT 2014},

month = {Fri Aug 01 00:00:00 EDT 2014}

}

DOI: 10.1063/1.4890562

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