# Collective motion of two-electron atom in hyperspherical adiabatic approximation

## Abstract

This work is devoted to calculate bound states in the two-electron atoms. The separation of variables has carried out in hyper spherical coordinate system (R, θ, α). Assuming collective motion of the electrons, where the hper angle (α∼π/4) and (θ∼π). The separation of the rotational variables leads to system of differential equations with more simple form as compared with non restricted motion. Energy of doubly excited P{sup e} and D{sup 0} states are calculated semi classically by using quantization condition of Bohr -Somerfield. The results compared with previously published data.

- Authors:

- King Saud University, Riyadh, 11491 (Saudi Arabia)
- (Egypt)
- St. Petersburg State University of economics, St. Petersburg, 191023 (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22391321

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1653; Journal Issue: 1; Conference: APMAS 2014: 4. International Congress in Advances in Applied Physics and Materials Science, Fethiye (Turkey), 24-27 Apr 2014; Other Information: (c) 2015 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; ADIABATIC APPROXIMATION; ATOMS; BOHR THEORY; BOUND STATE; COMPARATIVE EVALUATIONS; COORDINATES; D STATES; DIFFERENTIAL EQUATIONS; ELECTRONS; EXCITED STATES; P STATES; QUANTIZATION; SPHERICAL CONFIGURATION

### Citation Formats

```
Mohamed, A. S., E-mail: asalah@ksu.edu.sa, Al-Azhar University, Cairo, Nasr City, and Nikitin, S. I., E-mail: dept.kpme@unecon.ru.
```*Collective motion of two-electron atom in hyperspherical adiabatic approximation*. United States: N. p., 2015.
Web. doi:10.1063/1.4914263.

```
Mohamed, A. S., E-mail: asalah@ksu.edu.sa, Al-Azhar University, Cairo, Nasr City, & Nikitin, S. I., E-mail: dept.kpme@unecon.ru.
```*Collective motion of two-electron atom in hyperspherical adiabatic approximation*. United States. doi:10.1063/1.4914263.

```
Mohamed, A. S., E-mail: asalah@ksu.edu.sa, Al-Azhar University, Cairo, Nasr City, and Nikitin, S. I., E-mail: dept.kpme@unecon.ru. Mon .
"Collective motion of two-electron atom in hyperspherical adiabatic approximation". United States.
doi:10.1063/1.4914263.
```

```
@article{osti_22391321,
```

title = {Collective motion of two-electron atom in hyperspherical adiabatic approximation},

author = {Mohamed, A. S., E-mail: asalah@ksu.edu.sa and Al-Azhar University, Cairo, Nasr City and Nikitin, S. I., E-mail: dept.kpme@unecon.ru},

abstractNote = {This work is devoted to calculate bound states in the two-electron atoms. The separation of variables has carried out in hyper spherical coordinate system (R, θ, α). Assuming collective motion of the electrons, where the hper angle (α∼π/4) and (θ∼π). The separation of the rotational variables leads to system of differential equations with more simple form as compared with non restricted motion. Energy of doubly excited P{sup e} and D{sup 0} states are calculated semi classically by using quantization condition of Bohr -Somerfield. The results compared with previously published data.},

doi = {10.1063/1.4914263},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1653,

place = {United States},

year = {Mon Mar 30 00:00:00 EDT 2015},

month = {Mon Mar 30 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4914263

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